added video link
This commit is contained in:
Morten Hjorth-Jensen
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -318,7 +359,7 @@ MathJax.Hub.Config({
|
||||
</center>
|
||||
<br>
|
||||
<center>
|
||||
<h4>Nov 3, 2022</h4>
|
||||
<h4>Nov 4, 2022</h4>
|
||||
</center> <!-- date -->
|
||||
<br>
|
||||
|
||||
@@ -343,7 +384,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs008.html">9</a></li>
|
||||
<li><a href="._week44-bs009.html">10</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -346,7 +387,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs009.html">10</a></li>
|
||||
<li><a href="._week44-bs010.html">11</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs002.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -328,7 +369,7 @@ accelerate scientific discovery.
|
||||
<li><a href="._week44-bs010.html">11</a></li>
|
||||
<li><a href="._week44-bs011.html">12</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs003.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -345,7 +386,7 @@ where we then finally end up in so called <b>leaf nodes</b>.
|
||||
<li><a href="._week44-bs011.html">12</a></li>
|
||||
<li><a href="._week44-bs012.html">13</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs004.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -333,7 +374,7 @@ given some assumptions, make predictions about the target feature value
|
||||
<li><a href="._week44-bs012.html">13</a></li>
|
||||
<li><a href="._week44-bs013.html">14</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs005.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -326,7 +367,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs013.html">14</a></li>
|
||||
<li><a href="._week44-bs014.html">15</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs006.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -326,7 +367,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs014.html">15</a></li>
|
||||
<li><a href="._week44-bs015.html">16</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs007.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -332,7 +373,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs015.html">16</a></li>
|
||||
<li><a href="._week44-bs016.html">17</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs008.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -337,7 +378,7 @@ node.
|
||||
<li><a href="._week44-bs016.html">17</a></li>
|
||||
<li><a href="._week44-bs017.html">18</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs009.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -338,7 +379,7 @@ predicting the target features of query instances is as follows:
|
||||
<li><a href="._week44-bs017.html">18</a></li>
|
||||
<li><a href="._week44-bs018.html">19</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs010.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -437,7 +478,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week44-bs018.html">19</a></li>
|
||||
<li><a href="._week44-bs019.html">20</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs011.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -348,7 +389,7 @@ within box \( j \).
|
||||
<li><a href="._week44-bs019.html">20</a></li>
|
||||
<li><a href="._week44-bs020.html">21</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs012.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -341,7 +382,7 @@ better tree in some future step.
|
||||
<li><a href="._week44-bs020.html">21</a></li>
|
||||
<li><a href="._week44-bs021.html">22</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs013.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -373,7 +414,7 @@ region contains more than five observations.
|
||||
<li><a href="._week44-bs021.html">22</a></li>
|
||||
<li><a href="._week44-bs022.html">23</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs014.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -343,7 +384,7 @@ parameter \( \alpha \).
|
||||
<li><a href="._week44-bs022.html">23</a></li>
|
||||
<li><a href="._week44-bs023.html">24</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs015.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -355,7 +396,7 @@ subtree corresponding to \( \alpha \).
|
||||
<li><a href="._week44-bs023.html">24</a></li>
|
||||
<li><a href="._week44-bs024.html">25</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs016.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -346,7 +387,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs024.html">25</a></li>
|
||||
<li><a href="._week44-bs025.html">26</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs017.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -341,7 +382,7 @@ fall into that region.
|
||||
<li><a href="._week44-bs025.html">26</a></li>
|
||||
<li><a href="._week44-bs026.html">27</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs018.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -346,7 +387,7 @@ than is the classification error rate.
|
||||
<li><a href="._week44-bs026.html">27</a></li>
|
||||
<li><a href="._week44-bs027.html">28</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs019.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -368,7 +409,7 @@ $$
|
||||
<li><a href="._week44-bs027.html">28</a></li>
|
||||
<li><a href="._week44-bs028.html">29</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs020.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -382,7 +423,7 @@ os<span style="color: #666666">.</span>system(cmd)
|
||||
<li><a href="._week44-bs028.html">29</a></li>
|
||||
<li><a href="._week44-bs029.html">30</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs021.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -373,7 +414,7 @@ os<span style="color: #666666">.</span>system(cmd)
|
||||
<li><a href="._week44-bs029.html">30</a></li>
|
||||
<li><a href="._week44-bs030.html">31</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs022.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -359,7 +400,7 @@ tree<span style="color: #666666">.</span>plot_tree(tree_clf)
|
||||
<li><a href="._week44-bs030.html">31</a></li>
|
||||
<li><a href="._week44-bs031.html">32</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs023.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -362,7 +403,7 @@ r <span style="color: #666666">=</span> export_text(decision_tree, feature_names
|
||||
<li><a href="._week44-bs031.html">32</a></li>
|
||||
<li><a href="._week44-bs032.html">33</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs024.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -338,7 +379,7 @@ in two branches.
|
||||
<li><a href="._week44-bs032.html">33</a></li>
|
||||
<li><a href="._week44-bs033.html">34</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs025.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -350,7 +391,7 @@ hyperparameters control additional stopping conditions such as the \( min\_sampl
|
||||
<li><a href="._week44-bs033.html">34</a></li>
|
||||
<li><a href="._week44-bs034.html">35</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs026.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -350,7 +391,7 @@ just like for classification tasks, is prone to overfitting.
|
||||
<li><a href="._week44-bs034.html">35</a></li>
|
||||
<li><a href="._week44-bs035.html">36</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs027.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -333,7 +374,7 @@ achieved by a series of binary split and this is normally preferred.
|
||||
<li><a href="._week44-bs035.html">36</a></li>
|
||||
<li><a href="._week44-bs036.html">37</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs028.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -342,7 +383,7 @@ recently has gotten grades below average or above.
|
||||
<li><a href="._week44-bs036.html">37</a></li>
|
||||
<li><a href="._week44-bs037.html">38</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs029.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -349,7 +390,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs037.html">38</a></li>
|
||||
<li><a href="._week44-bs038.html">39</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs030.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -339,7 +380,7 @@ these binary classes, they can easily be split into ones and zeros.
|
||||
<li><a href="._week44-bs038.html">39</a></li>
|
||||
<li><a href="._week44-bs039.html">40</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs031.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -335,7 +376,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs039.html">40</a></li>
|
||||
<li><a href="._week44-bs040.html">41</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs032.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -337,7 +378,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs040.html">41</a></li>
|
||||
<li><a href="._week44-bs041.html">42</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs033.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -410,7 +451,7 @@ os<span style="color: #666666">.</span>system(cmd)
|
||||
<li><a href="._week44-bs041.html">42</a></li>
|
||||
<li><a href="._week44-bs042.html">43</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs034.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -366,7 +407,7 @@ humidity and weak and strong for wind.
|
||||
<li><a href="._week44-bs042.html">43</a></li>
|
||||
<li><a href="._week44-bs043.html">44</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs035.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -417,7 +458,7 @@ os<span style="color: #666666">.</span>system(cmd)
|
||||
<li><a href="._week44-bs043.html">44</a></li>
|
||||
<li><a href="._week44-bs044.html">45</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs036.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -418,7 +459,7 @@ split <span style="color: #666666">=</span> get_split(dataset)
|
||||
<li><a href="._week44-bs044.html">45</a></li>
|
||||
<li><a href="._week44-bs045.html">46</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs037.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -413,7 +454,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week44-bs045.html">46</a></li>
|
||||
<li><a href="._week44-bs046.html">47</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs038.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -369,7 +410,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week44-bs046.html">47</a></li>
|
||||
<li><a href="._week44-bs047.html">48</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs039.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -378,7 +419,7 @@ tree_reg<span style="color: #666666">.</span>fit(X, y)
|
||||
<li><a href="._week44-bs047.html">48</a></li>
|
||||
<li><a href="._week44-bs048.html">49</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs040.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -434,7 +475,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week44-bs048.html">49</a></li>
|
||||
<li><a href="._week44-bs049.html">50</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs041.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -336,7 +377,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs049.html">50</a></li>
|
||||
<li><a href="._week44-bs050.html">51</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs042.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -341,7 +382,7 @@ trees can be substantially improved.
|
||||
<li><a href="._week44-bs050.html">51</a></li>
|
||||
<li><a href="._week44-bs051.html">52</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs043.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -348,7 +389,7 @@ try to explain here. These are
|
||||
<li><a href="._week44-bs051.html">52</a></li>
|
||||
<li><a href="._week44-bs052.html">53</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs044.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -333,7 +374,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs052.html">53</a></li>
|
||||
<li><a href="._week44-bs053.html">54</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs045.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -344,7 +385,7 @@ each iteration.
|
||||
<li><a href="._week44-bs053.html">54</a></li>
|
||||
<li><a href="._week44-bs054.html">55</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs046.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -352,7 +393,7 @@ numbers kicking in.
|
||||
<li><a href="._week44-bs054.html">55</a></li>
|
||||
<li><a href="._week44-bs055.html">56</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs047.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -387,7 +428,7 @@ DATA_ID <span style="color: #666666">=</span> <span style="color: #BA2121">"
|
||||
<li><a href="._week44-bs055.html">56</a></li>
|
||||
<li><a href="._week44-bs056.html">57</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs048.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -370,6 +411,8 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week44-bs055.html">56</a></li>
|
||||
<li><a href="._week44-bs056.html">57</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs049.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -391,6 +432,9 @@ voting_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<li><a href="._week44-bs055.html">56</a></li>
|
||||
<li><a href="._week44-bs056.html">57</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs058.html">59</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs050.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -442,6 +483,10 @@ voting_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<li><a href="._week44-bs055.html">56</a></li>
|
||||
<li><a href="._week44-bs056.html">57</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs058.html">59</a></li>
|
||||
<li><a href="._week44-bs059.html">60</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs051.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -337,6 +378,11 @@ learning method.
|
||||
<li><a href="._week44-bs055.html">56</a></li>
|
||||
<li><a href="._week44-bs056.html">57</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs058.html">59</a></li>
|
||||
<li><a href="._week44-bs059.html">60</a></li>
|
||||
<li><a href="._week44-bs060.html">61</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs052.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -346,6 +387,12 @@ predictor, averaged over all \( B \) trees.
|
||||
<li><a href="._week44-bs055.html">56</a></li>
|
||||
<li><a href="._week44-bs056.html">57</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs058.html">59</a></li>
|
||||
<li><a href="._week44-bs059.html">60</a></li>
|
||||
<li><a href="._week44-bs060.html">61</a></li>
|
||||
<li><a href="._week44-bs061.html">62</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs053.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -404,6 +445,13 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week44-bs055.html">56</a></li>
|
||||
<li><a href="._week44-bs056.html">57</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs058.html">59</a></li>
|
||||
<li><a href="._week44-bs059.html">60</a></li>
|
||||
<li><a href="._week44-bs060.html">61</a></li>
|
||||
<li><a href="._week44-bs061.html">62</a></li>
|
||||
<li><a href="._week44-bs062.html">63</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs054.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -359,6 +400,14 @@ this setting.
|
||||
<li><a href="._week44-bs055.html">56</a></li>
|
||||
<li><a href="._week44-bs056.html">57</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs058.html">59</a></li>
|
||||
<li><a href="._week44-bs059.html">60</a></li>
|
||||
<li><a href="._week44-bs060.html">61</a></li>
|
||||
<li><a href="._week44-bs061.html">62</a></li>
|
||||
<li><a href="._week44-bs062.html">63</a></li>
|
||||
<li><a href="._week44-bs063.html">64</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs055.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -334,6 +375,15 @@ MathJax.Hub.Config({
|
||||
<li class="active"><a href="._week44-bs055.html">56</a></li>
|
||||
<li><a href="._week44-bs056.html">57</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs058.html">59</a></li>
|
||||
<li><a href="._week44-bs059.html">60</a></li>
|
||||
<li><a href="._week44-bs060.html">61</a></li>
|
||||
<li><a href="._week44-bs061.html">62</a></li>
|
||||
<li><a href="._week44-bs062.html">63</a></li>
|
||||
<li><a href="._week44-bs063.html">64</a></li>
|
||||
<li><a href="._week44-bs064.html">65</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs056.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -410,6 +451,16 @@ discrimination threshold is varied. It plots the true positive rate against the
|
||||
<li><a href="._week44-bs055.html">56</a></li>
|
||||
<li class="active"><a href="._week44-bs056.html">57</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs058.html">59</a></li>
|
||||
<li><a href="._week44-bs059.html">60</a></li>
|
||||
<li><a href="._week44-bs060.html">61</a></li>
|
||||
<li><a href="._week44-bs061.html">62</a></li>
|
||||
<li><a href="._week44-bs062.html">63</a></li>
|
||||
<li><a href="._week44-bs063.html">64</a></li>
|
||||
<li><a href="._week44-bs064.html">65</a></li>
|
||||
<li><a href="._week44-bs065.html">66</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs057.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -368,6 +409,18 @@ np<span style="color: #666666">.</span>sum(y_pred <span style="color: #666666">=
|
||||
<li><a href="._week44-bs055.html">56</a></li>
|
||||
<li><a href="._week44-bs056.html">57</a></li>
|
||||
<li class="active"><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs058.html">59</a></li>
|
||||
<li><a href="._week44-bs059.html">60</a></li>
|
||||
<li><a href="._week44-bs060.html">61</a></li>
|
||||
<li><a href="._week44-bs061.html">62</a></li>
|
||||
<li><a href="._week44-bs062.html">63</a></li>
|
||||
<li><a href="._week44-bs063.html">64</a></li>
|
||||
<li><a href="._week44-bs064.html">65</a></li>
|
||||
<li><a href="._week44-bs065.html">66</a></li>
|
||||
<li><a href="._week44-bs066.html">67</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs058.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
</div> <!-- end container -->
|
||||
|
||||
@@ -38,10 +38,6 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
{'highest level': 2,
|
||||
'sections': [('Overview of week 44', 2, None, 'overview-of-week-44'),
|
||||
('Digression First', 2, None, 'digression-first'),
|
||||
('A short Discussion of Project 2',
|
||||
2,
|
||||
None,
|
||||
'a-short-discussion-of-project-2'),
|
||||
('Decision trees, overarching aims',
|
||||
2,
|
||||
None,
|
||||
@@ -201,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -238,62 +265,71 @@ MathJax.Hub.Config({
|
||||
<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs001.html#overview-of-week-44" style="font-size: 80%;">Overview of week 44</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs002.html#digression-first" style="font-size: 80%;">Digression First</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#a-short-discussion-of-project-2" style="font-size: 80%;">A short Discussion of Project 2</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#another-example-the-moons" style="font-size: 80%;">Another example, the moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs049.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#another-example-the-moons" style="font-size: 80%;">Another example, the moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs049.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -305,58 +341,19 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0058"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="compare-bagging-on-trees-with-random-forests" class="anchor">Compare Bagging on Trees with Random Forests </h2>
|
||||
<h2 id="boosting-a-bird-s-eye-view" class="anchor">Boosting, a Bird's Eye View </h2>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;">bag_clf <span style="color: #666666">=</span> BaggingClassifier(
|
||||
DecisionTreeClassifier(splitter<span style="color: #666666">=</span><span style="color: #BA2121">"random"</span>, max_leaf_nodes<span style="color: #666666">=16</span>, random_state<span style="color: #666666">=42</span>),
|
||||
n_estimators<span style="color: #666666">=500</span>, max_samples<span style="color: #666666">=1.0</span>, bootstrap<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>, n_jobs<span style="color: #666666">=-1</span>, random_state<span style="color: #666666">=42</span>)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;">bag_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
y_pred <span style="color: #666666">=</span> bag_clf<span style="color: #666666">.</span>predict(X_test)
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> RandomForestClassifier
|
||||
rnd_clf <span style="color: #666666">=</span> RandomForestClassifier(n_estimators<span style="color: #666666">=500</span>, max_leaf_nodes<span style="color: #666666">=16</span>, n_jobs<span style="color: #666666">=-1</span>, random_state<span style="color: #666666">=42</span>)
|
||||
rnd_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
y_pred_rf <span style="color: #666666">=</span> rnd_clf<span style="color: #666666">.</span>predict(X_test)
|
||||
np<span style="color: #666666">.</span>sum(y_pred <span style="color: #666666">==</span> y_pred_rf) <span style="color: #666666">/</span> <span style="color: #008000">len</span>(y_pred)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>The basic idea is to combine weak classifiers in order to create a good
|
||||
classifier. With a weak classifier we often intend a classifier which
|
||||
produces results which are only slightly better than we would get by
|
||||
random guesses.
|
||||
</p>
|
||||
|
||||
<p>This is done by applying in an iterative way a weak (or a standard
|
||||
classifier like decision trees) to modify the data. In each iteration
|
||||
we emphasize those observations which are misclassified by weighting
|
||||
them with a factor.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -373,6 +370,16 @@ np<span style="color: #666666">.</span>sum(y_pred <span style="color: #666666">=
|
||||
<li><a href="._week44-bs056.html">57</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li class="active"><a href="._week44-bs058.html">59</a></li>
|
||||
<li><a href="._week44-bs059.html">60</a></li>
|
||||
<li><a href="._week44-bs060.html">61</a></li>
|
||||
<li><a href="._week44-bs061.html">62</a></li>
|
||||
<li><a href="._week44-bs062.html">63</a></li>
|
||||
<li><a href="._week44-bs063.html">64</a></li>
|
||||
<li><a href="._week44-bs064.html">65</a></li>
|
||||
<li><a href="._week44-bs065.html">66</a></li>
|
||||
<li><a href="._week44-bs066.html">67</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs059.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
</div> <!-- end container -->
|
||||
|
||||
@@ -38,10 +38,6 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
{'highest level': 2,
|
||||
'sections': [('Overview of week 44', 2, None, 'overview-of-week-44'),
|
||||
('Digression First', 2, None, 'digression-first'),
|
||||
('A short Discussion of Project 2',
|
||||
2,
|
||||
None,
|
||||
'a-short-discussion-of-project-2'),
|
||||
('Decision trees, overarching aims',
|
||||
2,
|
||||
None,
|
||||
@@ -149,10 +145,10 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'computing-the-gini-factor'),
|
||||
('Another example, the moons again',
|
||||
('Another example, the moons',
|
||||
2,
|
||||
None,
|
||||
'another-example-the-moons-again'),
|
||||
'another-example-the-moons'),
|
||||
('Playing around with regions',
|
||||
2,
|
||||
None,
|
||||
@@ -173,26 +169,6 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'an-overview-of-ensemble-methods'),
|
||||
('Bagging', 2, None, 'bagging'),
|
||||
('More bagging', 2, None, 'more-bagging'),
|
||||
('Simple Voting Example, head or tail',
|
||||
2,
|
||||
None,
|
||||
'simple-voting-example-head-or-tail'),
|
||||
('Using the Voting Classifier',
|
||||
2,
|
||||
None,
|
||||
'using-the-voting-classifier'),
|
||||
('Please, not the moons again! Voting and Bagging',
|
||||
2,
|
||||
None,
|
||||
'please-not-the-moons-again-voting-and-bagging'),
|
||||
('Bagging Examples', 2, None, 'bagging-examples'),
|
||||
('Making your own Bootstrap: Changing the Level of the Decision '
|
||||
'Tree',
|
||||
2,
|
||||
None,
|
||||
'making-your-own-bootstrap-changing-the-level-of-the-decision-tree'),
|
||||
('Why Voting?', 2, None, 'why-voting'),
|
||||
('Tossing coins', 2, None, 'tossing-coins'),
|
||||
('Standard imports first', 2, None, 'standard-imports-first'),
|
||||
@@ -205,6 +181,13 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
None,
|
||||
'using-the-voting-classifier'),
|
||||
('Voting and Bagging', 2, None, 'voting-and-bagging'),
|
||||
('Bagging', 2, None, 'bagging'),
|
||||
('More bagging', 2, None, 'more-bagging'),
|
||||
('Making your own Bootstrap: Changing the Level of the Decision '
|
||||
'Tree',
|
||||
2,
|
||||
None,
|
||||
'making-your-own-bootstrap-changing-the-level-of-the-decision-tree'),
|
||||
('Random forests', 2, None, 'random-forests'),
|
||||
('Random Forest Algorithm', 2, None, 'random-forest-algorithm'),
|
||||
('Random Forests Compared with other Methods on the Cancer Data',
|
||||
@@ -214,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -251,66 +265,71 @@ MathJax.Hub.Config({
|
||||
<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs001.html#overview-of-week-44" style="font-size: 80%;">Overview of week 44</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs002.html#digression-first" style="font-size: 80%;">Digression First</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#a-short-discussion-of-project-2" style="font-size: 80%;">A short Discussion of Project 2</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#another-example-the-moons-again" style="font-size: 80%;">Another example, the moons again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#please-not-the-moons-again-voting-and-bagging" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#bagging-examples" style="font-size: 80%;">Bagging Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#another-example-the-moons" style="font-size: 80%;">Another example, the moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs049.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -322,47 +341,53 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0059"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="random-forests" class="anchor">Random forests </h2>
|
||||
<h2 id="what-is-boosting-additive-modelling-iterative-fitting" class="anchor">What is boosting? Additive Modelling/Iterative Fitting </h2>
|
||||
|
||||
<p>Random forests provide an improvement over bagged trees by way of a
|
||||
small tweak that decorrelates the trees.
|
||||
<p>Boosting is a way of fitting an additive expansion in a set of
|
||||
elementary basis functions like for example some simple polynomials.
|
||||
Assume for example that we have a function
|
||||
</p>
|
||||
$$
|
||||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||||
$$
|
||||
|
||||
<p>where \( \beta_m \) are the expansion parameters to be determined in a
|
||||
minimization process and \( b(x;\gamma_m) \) are some simple functions of
|
||||
the multivariable parameter \( x \) which is characterized by the
|
||||
parameters \( \gamma_m \).
|
||||
</p>
|
||||
|
||||
<p>As in bagging, we build a
|
||||
number of decision trees on bootstrapped training samples. But when
|
||||
building these decision trees, each time a split in a tree is
|
||||
considered, a random sample of \( m \) predictors is chosen as split
|
||||
candidates from the full set of \( p \) predictors. The split is allowed to
|
||||
use only one of those \( m \) predictors.
|
||||
</p>
|
||||
|
||||
<p>A fresh sample of \( m \) predictors is
|
||||
taken at each split, and typically we choose
|
||||
<p>As an example, consider the Sigmoid function we used in logistic
|
||||
regression. In that case, we can translate the function
|
||||
\( b(x;\gamma_m) \) into the Sigmoid function
|
||||
</p>
|
||||
|
||||
$$
|
||||
m\approx \sqrt{p}.
|
||||
\sigma(t) = \frac{1}{1+\exp{(-t)}},
|
||||
$$
|
||||
|
||||
<p>In building a random forest, at
|
||||
each split in the tree, the algorithm is not even allowed to consider
|
||||
a majority of the available predictors.
|
||||
<p>where \( t=\gamma_0+\gamma_1 x \) and the parameters \( \gamma_0 \) and
|
||||
\( \gamma_1 \) were determined by the Logistic Regression fitting
|
||||
algorithm.
|
||||
</p>
|
||||
|
||||
<p>The reason for this is rather clever. Suppose that there is one very
|
||||
strong predictor in the data set, along with a number of other
|
||||
moderately strong predictors. Then in the collection of bagged
|
||||
variable importance random forest trees, most or all of the trees will
|
||||
use this strong predictor in the top split. Consequently, all of the
|
||||
bagged trees will look quite similar to each other. Hence the
|
||||
predictions from the bagged trees will be highly correlated.
|
||||
Unfortunately, averaging many highly correlated quantities does not
|
||||
lead to as large of a reduction in variance as averaging many
|
||||
uncorrelated quantities. In particular, this means that bagging will
|
||||
not lead to a substantial reduction in variance over a single tree in
|
||||
this setting.
|
||||
<p>As another example, consider the cost function we defined for linear regression</p>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
|
||||
$$
|
||||
|
||||
<p>In this case the function \( f(x) \) was replaced by the design matrix
|
||||
\( \boldsymbol{X} \) and the unknown linear regression parameters \( \boldsymbol{\beta} \),
|
||||
that is \( \boldsymbol{f}=\boldsymbol{X}\boldsymbol{\beta} \). In linear regression we can
|
||||
simply invert a matrix and obtain the parameters \( \beta \) by
|
||||
</p>
|
||||
|
||||
$$
|
||||
\boldsymbol{\beta}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}.
|
||||
$$
|
||||
|
||||
<p>In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters \( \beta_m \) and \( \gamma_m \).</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -381,6 +406,11 @@ this setting.
|
||||
<li><a href="._week44-bs060.html">61</a></li>
|
||||
<li><a href="._week44-bs061.html">62</a></li>
|
||||
<li><a href="._week44-bs062.html">63</a></li>
|
||||
<li><a href="._week44-bs063.html">64</a></li>
|
||||
<li><a href="._week44-bs064.html">65</a></li>
|
||||
<li><a href="._week44-bs065.html">66</a></li>
|
||||
<li><a href="._week44-bs066.html">67</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs060.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -38,10 +38,6 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
{'highest level': 2,
|
||||
'sections': [('Overview of week 44', 2, None, 'overview-of-week-44'),
|
||||
('Digression First', 2, None, 'digression-first'),
|
||||
('A short Discussion of Project 2',
|
||||
2,
|
||||
None,
|
||||
'a-short-discussion-of-project-2'),
|
||||
('Decision trees, overarching aims',
|
||||
2,
|
||||
None,
|
||||
@@ -149,10 +145,10 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'computing-the-gini-factor'),
|
||||
('Another example, the moons again',
|
||||
('Another example, the moons',
|
||||
2,
|
||||
None,
|
||||
'another-example-the-moons-again'),
|
||||
'another-example-the-moons'),
|
||||
('Playing around with regions',
|
||||
2,
|
||||
None,
|
||||
@@ -173,26 +169,6 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'an-overview-of-ensemble-methods'),
|
||||
('Bagging', 2, None, 'bagging'),
|
||||
('More bagging', 2, None, 'more-bagging'),
|
||||
('Simple Voting Example, head or tail',
|
||||
2,
|
||||
None,
|
||||
'simple-voting-example-head-or-tail'),
|
||||
('Using the Voting Classifier',
|
||||
2,
|
||||
None,
|
||||
'using-the-voting-classifier'),
|
||||
('Please, not the moons again! Voting and Bagging',
|
||||
2,
|
||||
None,
|
||||
'please-not-the-moons-again-voting-and-bagging'),
|
||||
('Bagging Examples', 2, None, 'bagging-examples'),
|
||||
('Making your own Bootstrap: Changing the Level of the Decision '
|
||||
'Tree',
|
||||
2,
|
||||
None,
|
||||
'making-your-own-bootstrap-changing-the-level-of-the-decision-tree'),
|
||||
('Why Voting?', 2, None, 'why-voting'),
|
||||
('Tossing coins', 2, None, 'tossing-coins'),
|
||||
('Standard imports first', 2, None, 'standard-imports-first'),
|
||||
@@ -205,6 +181,13 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
None,
|
||||
'using-the-voting-classifier'),
|
||||
('Voting and Bagging', 2, None, 'voting-and-bagging'),
|
||||
('Bagging', 2, None, 'bagging'),
|
||||
('More bagging', 2, None, 'more-bagging'),
|
||||
('Making your own Bootstrap: Changing the Level of the Decision '
|
||||
'Tree',
|
||||
2,
|
||||
None,
|
||||
'making-your-own-bootstrap-changing-the-level-of-the-decision-tree'),
|
||||
('Random forests', 2, None, 'random-forests'),
|
||||
('Random Forest Algorithm', 2, None, 'random-forest-algorithm'),
|
||||
('Random Forests Compared with other Methods on the Cancer Data',
|
||||
@@ -214,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -251,66 +265,71 @@ MathJax.Hub.Config({
|
||||
<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs001.html#overview-of-week-44" style="font-size: 80%;">Overview of week 44</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs002.html#digression-first" style="font-size: 80%;">Digression First</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#a-short-discussion-of-project-2" style="font-size: 80%;">A short Discussion of Project 2</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#another-example-the-moons-again" style="font-size: 80%;">Another example, the moons again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#please-not-the-moons-again-voting-and-bagging" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#bagging-examples" style="font-size: 80%;">Bagging Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#another-example-the-moons" style="font-size: 80%;">Another example, the moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs049.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -322,23 +341,25 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0060"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="random-forest-algorithm" class="anchor">Random Forest Algorithm </h2>
|
||||
<p>The algorithm described here can be applied to both classification and regression problems.</p>
|
||||
<h2 id="iterative-fitting-regression-and-squared-error-cost-function" class="anchor">Iterative Fitting, Regression and Squared-error Cost Function </h2>
|
||||
|
||||
<p>The way we proceed is as follows (here we specialize to the squared-error cost function)</p>
|
||||
|
||||
<p>We will grow of forest of say \( B \) trees.</p>
|
||||
<ol>
|
||||
<li> For \( b=1:B \)</li>
|
||||
<ul>
|
||||
<li> Draw a bootstrap sample from the training data organized in our \( \boldsymbol{X} \) matrix.</li>
|
||||
<li> We grow then a random forest tree \( T_b \) based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached</li>
|
||||
<ol>
|
||||
<li> we select \( m \le p \) variables at random from the \( p \) predictors/features</li>
|
||||
<li> pick the best split point among the \( m \) features using for example the CART algorithm and create a new node</li>
|
||||
<li> split the node into daughter nodes</li>
|
||||
<li> Establish a cost function, here \( {\cal C}(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f_M(x_i))^2 \) with \( f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m) \).</li>
|
||||
<li> Initialize with a guess \( f_0(x) \). It could be one or even zero or some random numbers.</li>
|
||||
<li> For \( m=1:M \)
|
||||
<ol type="a"></li>
|
||||
<li> minimize \( \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 \) wrt \( \gamma \) and \( \beta \)</li>
|
||||
<li> This gives the optimal values \( \beta_m \) and \( \gamma_m \)</li>
|
||||
<li> Determine then the new values \( f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m) \)</li>
|
||||
</ol>
|
||||
</ul>
|
||||
<li> Output then the ensemble of trees \( \{T_b\}_1^{B} \) and make predictions for either a regression type of problem or a classification type of problem.</li>
|
||||
</ol>
|
||||
<p>We could use any of the algorithms we have discussed till now. If we
|
||||
use trees, \( \gamma \) parameterizes the split variables and split points
|
||||
at the internal nodes, and the predictions at the terminal nodes.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -356,6 +377,11 @@ MathJax.Hub.Config({
|
||||
<li class="active"><a href="._week44-bs060.html">61</a></li>
|
||||
<li><a href="._week44-bs061.html">62</a></li>
|
||||
<li><a href="._week44-bs062.html">63</a></li>
|
||||
<li><a href="._week44-bs063.html">64</a></li>
|
||||
<li><a href="._week44-bs064.html">65</a></li>
|
||||
<li><a href="._week44-bs065.html">66</a></li>
|
||||
<li><a href="._week44-bs066.html">67</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs061.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -38,10 +38,6 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
{'highest level': 2,
|
||||
'sections': [('Overview of week 44', 2, None, 'overview-of-week-44'),
|
||||
('Digression First', 2, None, 'digression-first'),
|
||||
('A short Discussion of Project 2',
|
||||
2,
|
||||
None,
|
||||
'a-short-discussion-of-project-2'),
|
||||
('Decision trees, overarching aims',
|
||||
2,
|
||||
None,
|
||||
@@ -149,10 +145,10 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'computing-the-gini-factor'),
|
||||
('Another example, the moons again',
|
||||
('Another example, the moons',
|
||||
2,
|
||||
None,
|
||||
'another-example-the-moons-again'),
|
||||
'another-example-the-moons'),
|
||||
('Playing around with regions',
|
||||
2,
|
||||
None,
|
||||
@@ -173,26 +169,6 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'an-overview-of-ensemble-methods'),
|
||||
('Bagging', 2, None, 'bagging'),
|
||||
('More bagging', 2, None, 'more-bagging'),
|
||||
('Simple Voting Example, head or tail',
|
||||
2,
|
||||
None,
|
||||
'simple-voting-example-head-or-tail'),
|
||||
('Using the Voting Classifier',
|
||||
2,
|
||||
None,
|
||||
'using-the-voting-classifier'),
|
||||
('Please, not the moons again! Voting and Bagging',
|
||||
2,
|
||||
None,
|
||||
'please-not-the-moons-again-voting-and-bagging'),
|
||||
('Bagging Examples', 2, None, 'bagging-examples'),
|
||||
('Making your own Bootstrap: Changing the Level of the Decision '
|
||||
'Tree',
|
||||
2,
|
||||
None,
|
||||
'making-your-own-bootstrap-changing-the-level-of-the-decision-tree'),
|
||||
('Why Voting?', 2, None, 'why-voting'),
|
||||
('Tossing coins', 2, None, 'tossing-coins'),
|
||||
('Standard imports first', 2, None, 'standard-imports-first'),
|
||||
@@ -205,6 +181,13 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
None,
|
||||
'using-the-voting-classifier'),
|
||||
('Voting and Bagging', 2, None, 'voting-and-bagging'),
|
||||
('Bagging', 2, None, 'bagging'),
|
||||
('More bagging', 2, None, 'more-bagging'),
|
||||
('Making your own Bootstrap: Changing the Level of the Decision '
|
||||
'Tree',
|
||||
2,
|
||||
None,
|
||||
'making-your-own-bootstrap-changing-the-level-of-the-decision-tree'),
|
||||
('Random forests', 2, None, 'random-forests'),
|
||||
('Random Forest Algorithm', 2, None, 'random-forest-algorithm'),
|
||||
('Random Forests Compared with other Methods on the Cancer Data',
|
||||
@@ -214,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -251,66 +265,71 @@ MathJax.Hub.Config({
|
||||
<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs001.html#overview-of-week-44" style="font-size: 80%;">Overview of week 44</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs002.html#digression-first" style="font-size: 80%;">Digression First</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#a-short-discussion-of-project-2" style="font-size: 80%;">A short Discussion of Project 2</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#another-example-the-moons-again" style="font-size: 80%;">Another example, the moons again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#please-not-the-moons-again-voting-and-bagging" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#bagging-examples" style="font-size: 80%;">Bagging Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#another-example-the-moons" style="font-size: 80%;">Another example, the moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs049.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -322,103 +341,46 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0061"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="random-forests-compared-with-other-methods-on-the-cancer-data" class="anchor">Random Forests Compared with other Methods on the Cancer Data </h2>
|
||||
<h2 id="squared-error-example-and-iterative-fitting" class="anchor">Squared-Error Example and Iterative Fitting </h2>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;"><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_breast_cancer
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.svm</span> <span style="color: #008000; font-weight: bold">import</span> SVC
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LogisticRegression
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.tree</span> <span style="color: #008000; font-weight: bold">import</span> DecisionTreeClassifier
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> BaggingClassifier
|
||||
<p>To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.</p>
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Load the data</span>
|
||||
cancer <span style="color: #666666">=</span> load_breast_cancer()
|
||||
<p>For simplicity we assume also that our functions \( b(x;\gamma)=1+\gamma x \). </p>
|
||||
|
||||
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(cancer<span style="color: #666666">.</span>data,cancer<span style="color: #666666">.</span>target,random_state<span style="color: #666666">=0</span>)
|
||||
<span style="color: #008000">print</span>(X_train<span style="color: #666666">.</span>shape)
|
||||
<span style="color: #008000">print</span>(X_test<span style="color: #666666">.</span>shape)
|
||||
<span style="color: #408080; font-style: italic"># Logistic Regression</span>
|
||||
logreg <span style="color: #666666">=</span> LogisticRegression(solver<span style="color: #666666">=</span><span style="color: #BA2121">'lbfgs'</span>)
|
||||
logreg<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"Test set accuracy with Logistic Regression: </span><span style="color: #BB6688; font-weight: bold">{:.2f}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test,y_test)))
|
||||
<span style="color: #408080; font-style: italic"># Support vector machine</span>
|
||||
svm <span style="color: #666666">=</span> SVC(gamma<span style="color: #666666">=</span><span style="color: #BA2121">'auto'</span>, C<span style="color: #666666">=100</span>)
|
||||
svm<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"Test set accuracy with SVM: </span><span style="color: #BB6688; font-weight: bold">{:.2f}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(svm<span style="color: #666666">.</span>score(X_test,y_test)))
|
||||
<span style="color: #408080; font-style: italic"># Decision Trees</span>
|
||||
deep_tree_clf <span style="color: #666666">=</span> DecisionTreeClassifier(max_depth<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">None</span>)
|
||||
deep_tree_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"Test set accuracy with Decision Trees: </span><span style="color: #BB6688; font-weight: bold">{:.2f}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(deep_tree_clf<span style="color: #666666">.</span>score(X_test,y_test)))
|
||||
<span style="color: #408080; font-style: italic">#now scale the data</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> StandardScaler
|
||||
scaler <span style="color: #666666">=</span> StandardScaler()
|
||||
scaler<span style="color: #666666">.</span>fit(X_train)
|
||||
X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_train)
|
||||
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
|
||||
<span style="color: #408080; font-style: italic"># Logistic Regression</span>
|
||||
logreg<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"Test set accuracy Logistic Regression with scaled data: </span><span style="color: #BB6688; font-weight: bold">{:.2f}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test_scaled,y_test)))
|
||||
<span style="color: #408080; font-style: italic"># Support Vector Machine</span>
|
||||
svm<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"Test set accuracy SVM with scaled data: </span><span style="color: #BB6688; font-weight: bold">{:.2f}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test_scaled,y_test)))
|
||||
<span style="color: #408080; font-style: italic"># Decision Trees</span>
|
||||
deep_tree_clf<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"Test set accuracy with Decision Trees and scaled data: </span><span style="color: #BB6688; font-weight: bold">{:.2f}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(deep_tree_clf<span style="color: #666666">.</span>score(X_test_scaled,y_test)))
|
||||
<p>This means that for every iteration \( m \), we need to optimize</p>
|
||||
|
||||
$$
|
||||
(\beta_m,\gamma_m) = \mathrm{argmin}_{\beta,\lambda}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2=\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(1+\gamma x_i))^2.
|
||||
$$
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> RandomForestClassifier
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> LabelEncoder
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> cross_validate
|
||||
<span style="color: #408080; font-style: italic"># Data set not specificied</span>
|
||||
<span style="color: #408080; font-style: italic">#Instantiate the model with 500 trees and entropy as splitting criteria</span>
|
||||
Random_Forest_model <span style="color: #666666">=</span> RandomForestClassifier(n_estimators<span style="color: #666666">=500</span>,criterion<span style="color: #666666">=</span><span style="color: #BA2121">"entropy"</span>)
|
||||
Random_Forest_model<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
<span style="color: #408080; font-style: italic">#Cross validation</span>
|
||||
accuracy <span style="color: #666666">=</span> cross_validate(Random_Forest_model,X_test_scaled,y_test,cv<span style="color: #666666">=10</span>)[<span style="color: #BA2121">'test_score'</span>]
|
||||
<span style="color: #008000">print</span>(accuracy)
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"Test set accuracy with Random Forests and scaled data: </span><span style="color: #BB6688; font-weight: bold">{:.2f}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(Random_Forest_model<span style="color: #666666">.</span>score(X_test_scaled,y_test)))
|
||||
<p>We start our iteration by simply setting \( f_0(x)=0 \).
|
||||
Taking the derivatives with respect to \( \beta \) and \( \gamma \) we obtain
|
||||
</p>
|
||||
$$
|
||||
\frac{\partial {\cal C}}{\partial \beta} = -2\sum_{i}(1+\gamma x_i)(y_i-\beta(1+\gamma x_i))=0,
|
||||
$$
|
||||
|
||||
<p>and</p>
|
||||
$$
|
||||
\frac{\partial {\cal C}}{\partial \gamma} =-2\sum_{i}\beta x_i(y_i-\beta(1+\gamma x_i))=0.
|
||||
$$
|
||||
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scikitplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">skplt</span>
|
||||
y_pred <span style="color: #666666">=</span> Random_Forest_model<span style="color: #666666">.</span>predict(X_test_scaled)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_confusion_matrix(y_test, y_pred, normalize<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
y_probas <span style="color: #666666">=</span> Random_Forest_model<span style="color: #666666">.</span>predict_proba(X_test_scaled)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_roc(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_cumulative_gain(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>We can then rewrite these equations as (defining \( \boldsymbol{w}=\boldsymbol{e}+\gamma \boldsymbol{x}) \) with \( \boldsymbol{e} \) being the unit vector)</p>
|
||||
$$
|
||||
\gamma \boldsymbol{w}^T(\boldsymbol{y}-\beta\gamma \boldsymbol{w})=0,
|
||||
$$
|
||||
|
||||
<p>Recall that the cumulative gains curve shows the percentage of the
|
||||
overall number of cases in a given category <em>gained</em> by targeting a
|
||||
percentage of the total number of cases.
|
||||
<p>which gives us \( \beta = \boldsymbol{w}^T\boldsymbol{y}/(\boldsymbol{w}^T\boldsymbol{w}) \). Similarly we have </p>
|
||||
$$
|
||||
\beta\gamma \boldsymbol{x}^T(\boldsymbol{y}-\beta(1+\gamma \boldsymbol{x}))=0,
|
||||
$$
|
||||
|
||||
<p>which leads to \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\boldsymbol{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
|
||||
for \( \beta \) gives us an equation for \( \gamma \). This is a non-linear equation in the unknown \( \gamma \) and has to be solved numerically.
|
||||
</p>
|
||||
|
||||
<p>Similarly, the receiver operating characteristic curve, or ROC curve,
|
||||
displays the diagnostic ability of a binary classifier system as its
|
||||
discrimination threshold is varied. It plots the true positive rate against the false positive rate.
|
||||
<p>The solution to these two equations gives us in turn \( \beta_1 \) and \( \gamma_1 \) leading to the new expression for \( f_1(x) \) as
|
||||
\( f_1(x) = \beta_1(1+\gamma_1x) \). Doing this \( M \) times results in our final estimate for the function \( f \).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -437,6 +399,11 @@ discrimination threshold is varied. It plots the true positive rate against the
|
||||
<li><a href="._week44-bs060.html">61</a></li>
|
||||
<li class="active"><a href="._week44-bs061.html">62</a></li>
|
||||
<li><a href="._week44-bs062.html">63</a></li>
|
||||
<li><a href="._week44-bs063.html">64</a></li>
|
||||
<li><a href="._week44-bs064.html">65</a></li>
|
||||
<li><a href="._week44-bs065.html">66</a></li>
|
||||
<li><a href="._week44-bs066.html">67</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs062.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -38,10 +38,6 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
{'highest level': 2,
|
||||
'sections': [('Overview of week 44', 2, None, 'overview-of-week-44'),
|
||||
('Digression First', 2, None, 'digression-first'),
|
||||
('A short Discussion of Project 2',
|
||||
2,
|
||||
None,
|
||||
'a-short-discussion-of-project-2'),
|
||||
('Decision trees, overarching aims',
|
||||
2,
|
||||
None,
|
||||
@@ -149,10 +145,10 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'computing-the-gini-factor'),
|
||||
('Another example, the moons again',
|
||||
('Another example, the moons',
|
||||
2,
|
||||
None,
|
||||
'another-example-the-moons-again'),
|
||||
'another-example-the-moons'),
|
||||
('Playing around with regions',
|
||||
2,
|
||||
None,
|
||||
@@ -173,26 +169,6 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'an-overview-of-ensemble-methods'),
|
||||
('Bagging', 2, None, 'bagging'),
|
||||
('More bagging', 2, None, 'more-bagging'),
|
||||
('Simple Voting Example, head or tail',
|
||||
2,
|
||||
None,
|
||||
'simple-voting-example-head-or-tail'),
|
||||
('Using the Voting Classifier',
|
||||
2,
|
||||
None,
|
||||
'using-the-voting-classifier'),
|
||||
('Please, not the moons again! Voting and Bagging',
|
||||
2,
|
||||
None,
|
||||
'please-not-the-moons-again-voting-and-bagging'),
|
||||
('Bagging Examples', 2, None, 'bagging-examples'),
|
||||
('Making your own Bootstrap: Changing the Level of the Decision '
|
||||
'Tree',
|
||||
2,
|
||||
None,
|
||||
'making-your-own-bootstrap-changing-the-level-of-the-decision-tree'),
|
||||
('Why Voting?', 2, None, 'why-voting'),
|
||||
('Tossing coins', 2, None, 'tossing-coins'),
|
||||
('Standard imports first', 2, None, 'standard-imports-first'),
|
||||
@@ -205,6 +181,13 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
None,
|
||||
'using-the-voting-classifier'),
|
||||
('Voting and Bagging', 2, None, 'voting-and-bagging'),
|
||||
('Bagging', 2, None, 'bagging'),
|
||||
('More bagging', 2, None, 'more-bagging'),
|
||||
('Making your own Bootstrap: Changing the Level of the Decision '
|
||||
'Tree',
|
||||
2,
|
||||
None,
|
||||
'making-your-own-bootstrap-changing-the-level-of-the-decision-tree'),
|
||||
('Random forests', 2, None, 'random-forests'),
|
||||
('Random Forest Algorithm', 2, None, 'random-forest-algorithm'),
|
||||
('Random Forests Compared with other Methods on the Cancer Data',
|
||||
@@ -214,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -251,66 +265,71 @@ MathJax.Hub.Config({
|
||||
<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs001.html#overview-of-week-44" style="font-size: 80%;">Overview of week 44</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs002.html#digression-first" style="font-size: 80%;">Digression First</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#a-short-discussion-of-project-2" style="font-size: 80%;">A short Discussion of Project 2</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#another-example-the-moons-again" style="font-size: 80%;">Another example, the moons again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#please-not-the-moons-again-voting-and-bagging" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#bagging-examples" style="font-size: 80%;">Bagging Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#another-example-the-moons" style="font-size: 80%;">Another example, the moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs049.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -322,57 +341,35 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0062"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="compare-bagging-on-trees-with-random-forests" class="anchor">Compare Bagging on Trees with Random Forests </h2>
|
||||
<h2 id="iterative-fitting-classification-and-adaboost" class="anchor">Iterative Fitting, Classification and AdaBoost </h2>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;">bag_clf <span style="color: #666666">=</span> BaggingClassifier(
|
||||
DecisionTreeClassifier(splitter<span style="color: #666666">=</span><span style="color: #BA2121">"random"</span>, max_leaf_nodes<span style="color: #666666">=16</span>, random_state<span style="color: #666666">=42</span>),
|
||||
n_estimators<span style="color: #666666">=500</span>, max_samples<span style="color: #666666">=1.0</span>, bootstrap<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>, n_jobs<span style="color: #666666">=-1</span>, random_state<span style="color: #666666">=42</span>)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;">bag_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
y_pred <span style="color: #666666">=</span> bag_clf<span style="color: #666666">.</span>predict(X_test)
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> RandomForestClassifier
|
||||
rnd_clf <span style="color: #666666">=</span> RandomForestClassifier(n_estimators<span style="color: #666666">=500</span>, max_leaf_nodes<span style="color: #666666">=16</span>, n_jobs<span style="color: #666666">=-1</span>, random_state<span style="color: #666666">=42</span>)
|
||||
rnd_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
y_pred_rf <span style="color: #666666">=</span> rnd_clf<span style="color: #666666">.</span>predict(X_test)
|
||||
np<span style="color: #666666">.</span>sum(y_pred <span style="color: #666666">==</span> y_pred_rf) <span style="color: #666666">/</span> <span style="color: #008000">len</span>(y_pred)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
|
||||
observations. We define a classification function \( G(x) \) which produces a prediction taking one or the other of the two values
|
||||
\( \{-1,1\} \).
|
||||
</p>
|
||||
|
||||
<p>The error rate of the training sample is then</p>
|
||||
|
||||
$$
|
||||
\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i)).
|
||||
$$
|
||||
|
||||
<p>The iterative procedure starts with defining a weak classifier whose
|
||||
error rate is barely better than random guessing. The iterative
|
||||
procedure in boosting is to sequentially apply a weak
|
||||
classification algorithm to repeatedly modified versions of the data
|
||||
producing a sequence of weak classifiers \( G_m(x) \).
|
||||
</p>
|
||||
|
||||
<p>Here we will express our function \( f(x) \) in terms of \( G(x) \). That is</p>
|
||||
$$
|
||||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||||
$$
|
||||
|
||||
<p>will be a function of </p>
|
||||
$$
|
||||
G_M(x) = \mathrm{sign} \sum_{i=1}^M \alpha_m G_m(x).
|
||||
$$
|
||||
|
||||
|
||||
<p>
|
||||
@@ -390,6 +387,12 @@ np<span style="color: #666666">.</span>sum(y_pred <span style="color: #666666">=
|
||||
<li><a href="._week44-bs060.html">61</a></li>
|
||||
<li><a href="._week44-bs061.html">62</a></li>
|
||||
<li class="active"><a href="._week44-bs062.html">63</a></li>
|
||||
<li><a href="._week44-bs063.html">64</a></li>
|
||||
<li><a href="._week44-bs064.html">65</a></li>
|
||||
<li><a href="._week44-bs065.html">66</a></li>
|
||||
<li><a href="._week44-bs066.html">67</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs063.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
</div> <!-- end container -->
|
||||
|
||||
@@ -38,10 +38,6 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
{'highest level': 2,
|
||||
'sections': [('Overview of week 44', 2, None, 'overview-of-week-44'),
|
||||
('Digression First', 2, None, 'digression-first'),
|
||||
('A short Discussion of Project 2',
|
||||
2,
|
||||
None,
|
||||
'a-short-discussion-of-project-2'),
|
||||
('Decision trees, overarching aims',
|
||||
2,
|
||||
None,
|
||||
@@ -149,40 +145,10 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'computing-the-gini-factor'),
|
||||
('Another example, the moons again',
|
||||
('Another example, the moons',
|
||||
2,
|
||||
None,
|
||||
'another-example-the-moons-again'),
|
||||
('Playing around with regions',
|
||||
2,
|
||||
None,
|
||||
'playing-around-with-regions'),
|
||||
('Regression trees', 2, None, 'regression-trees'),
|
||||
('Final regressor code', 2, None, 'final-regressor-code'),
|
||||
('Example: Computing the Gini index',
|
||||
2,
|
||||
None,
|
||||
'example-computing-the-gini-index'),
|
||||
('Simple Python Code to read in Data and perform Classification',
|
||||
2,
|
||||
None,
|
||||
'simple-python-code-to-read-in-data-and-perform-classification'),
|
||||
('Computing the Gini Factor',
|
||||
2,
|
||||
None,
|
||||
'computing-the-gini-factor'),
|
||||
('Entropy and the ID3 algorithm',
|
||||
2,
|
||||
None,
|
||||
'entropy-and-the-id3-algorithm'),
|
||||
('Cancer Data again now with Decision Trees and other Methods',
|
||||
2,
|
||||
None,
|
||||
'cancer-data-again-now-with-decision-trees-and-other-methods'),
|
||||
('Another example, the moons again',
|
||||
2,
|
||||
None,
|
||||
'another-example-the-moons-again'),
|
||||
'another-example-the-moons'),
|
||||
('Playing around with regions',
|
||||
2,
|
||||
None,
|
||||
@@ -203,26 +169,6 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'an-overview-of-ensemble-methods'),
|
||||
('Bagging', 2, None, 'bagging'),
|
||||
('More bagging', 2, None, 'more-bagging'),
|
||||
('Simple Voting Example, head or tail',
|
||||
2,
|
||||
None,
|
||||
'simple-voting-example-head-or-tail'),
|
||||
('Using the Voting Classifier',
|
||||
2,
|
||||
None,
|
||||
'using-the-voting-classifier'),
|
||||
('Please, not the moons again! Voting and Bagging',
|
||||
2,
|
||||
None,
|
||||
'please-not-the-moons-again-voting-and-bagging'),
|
||||
('Bagging Examples', 2, None, 'bagging-examples'),
|
||||
('Making your own Bootstrap: Changing the Level of the Decision '
|
||||
'Tree',
|
||||
2,
|
||||
None,
|
||||
'making-your-own-bootstrap-changing-the-level-of-the-decision-tree'),
|
||||
('Why Voting?', 2, None, 'why-voting'),
|
||||
('Tossing coins', 2, None, 'tossing-coins'),
|
||||
('Standard imports first', 2, None, 'standard-imports-first'),
|
||||
@@ -235,6 +181,13 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
None,
|
||||
'using-the-voting-classifier'),
|
||||
('Voting and Bagging', 2, None, 'voting-and-bagging'),
|
||||
('Bagging', 2, None, 'bagging'),
|
||||
('More bagging', 2, None, 'more-bagging'),
|
||||
('Making your own Bootstrap: Changing the Level of the Decision '
|
||||
'Tree',
|
||||
2,
|
||||
None,
|
||||
'making-your-own-bootstrap-changing-the-level-of-the-decision-tree'),
|
||||
('Random forests', 2, None, 'random-forests'),
|
||||
('Random Forest Algorithm', 2, None, 'random-forest-algorithm'),
|
||||
('Random Forests Compared with other Methods on the Cancer Data',
|
||||
@@ -244,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -281,75 +265,71 @@ MathJax.Hub.Config({
|
||||
<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs001.html#overview-of-week-44" style="font-size: 80%;">Overview of week 44</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs002.html#digression-first" style="font-size: 80%;">Digression First</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#a-short-discussion-of-project-2" style="font-size: 80%;">A short Discussion of Project 2</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#another-example-the-moons-again" style="font-size: 80%;">Another example, the moons again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs049.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#example-computing-the-gini-index" style="font-size: 80%;">Example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#entropy-and-the-id3-algorithm" style="font-size: 80%;">Entropy and the ID3 algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#cancer-data-again-now-with-decision-trees-and-other-methods" style="font-size: 80%;">Cancer Data again now with Decision Trees and other Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#another-example-the-moons-again" style="font-size: 80%;">Another example, the moons again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs049.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#please-not-the-moons-again-voting-and-bagging" style="font-size: 80%;">Please, not the moons again! Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#bagging-examples" style="font-size: 80%;">Bagging Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs068.html#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs069.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs070.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs071.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#decision-trees-overarching-aims" style="font-size: 80%;">Decision trees, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#basics-of-a-tree" style="font-size: 80%;">Basics of a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#a-sketch-of-a-tree-regression-problem" style="font-size: 80%;">A Sketch of a Tree, Regression problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#a-sketch-of-a-tree-classification-problem" style="font-size: 80%;">A Sketch of a Tree, Classification problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#a-typical-decision-tree-with-its-pertinent-jargon-classification-problem" style="font-size: 80%;">A typical Decision Tree with its pertinent Jargon, Classification Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#general-features" style="font-size: 80%;">General Features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs009.html#how-do-we-set-it-up" style="font-size: 80%;">How do we set it up?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs010.html#decision-trees-and-regression" style="font-size: 80%;">Decision trees and Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs011.html#building-a-tree-regression" style="font-size: 80%;">Building a tree, regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#a-top-down-approach-recursive-binary-splitting" style="font-size: 80%;">A top-down approach, recursive binary splitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#making-a-tree" style="font-size: 80%;">Making a tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#pruning-the-tree" style="font-size: 80%;">Pruning the tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#cost-complexity-pruning" style="font-size: 80%;">Cost complexity pruning</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#schematic-regression-procedure" style="font-size: 80%;">Schematic Regression Procedure</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#a-classification-tree" style="font-size: 80%;">A Classification Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#growing-a-classification-tree" style="font-size: 80%;">Growing a classification tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs019.html#classification-tree-how-to-split-nodes" style="font-size: 80%;">Classification tree, how to split nodes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs020.html#visualizing-the-tree-classification" style="font-size: 80%;">Visualizing the Tree, Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#visualizing-the-tree-the-moons" style="font-size: 80%;">Visualizing the Tree, The Moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#other-ways-of-visualizing-the-trees" style="font-size: 80%;">Other ways of visualizing the trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#printing-out-as-text" style="font-size: 80%;">Printing out as text</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#algorithms-for-setting-up-decision-trees" style="font-size: 80%;">Algorithms for Setting up Decision Trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#the-cart-algorithm-for-classification" style="font-size: 80%;">The CART algorithm for Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#the-cart-algorithm-for-regression" style="font-size: 80%;">The CART algorithm for Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#why-binary-splits" style="font-size: 80%;">Why binary splits?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#computing-a-tree-using-the-gini-index" style="font-size: 80%;">Computing a Tree using the Gini Index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#the-table" style="font-size: 80%;">The Table</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#computing-the-various-gini-indices" style="font-size: 80%;">Computing the various Gini Indices</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#computing-the-various-gini-indices-hours-slept" style="font-size: 80%;">Computing the various Gini Indices, Hours slept</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#computing-the-various-gini-indices-hours-studied" style="font-size: 80%;">Computing the various Gini Indices, Hours studied</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#a-possible-code-using-scikit-learn" style="font-size: 80%;">A possible code using Scikit-Learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#further-example-computing-the-gini-index" style="font-size: 80%;">Further example: Computing the Gini index</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#simple-python-code-to-read-in-data-and-perform-classification" style="font-size: 80%;">Simple Python Code to read in Data and perform Classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#computing-the-gini-factor" style="font-size: 80%;">Computing the Gini Factor</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#another-example-the-moons" style="font-size: 80%;">Another example, the moons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#playing-around-with-regions" style="font-size: 80%;">Playing around with regions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#regression-trees" style="font-size: 80%;">Regression trees</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#final-regressor-code" style="font-size: 80%;">Final regressor code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#pros-and-cons-of-trees-pros" style="font-size: 80%;">Pros and cons of trees, pros</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#disadvantages" style="font-size: 80%;">Disadvantages</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" style="font-size: 80%;">Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#an-overview-of-ensemble-methods" style="font-size: 80%;">An Overview of Ensemble Methods</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#why-voting" style="font-size: 80%;">Why Voting?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#tossing-coins" style="font-size: 80%;">Tossing coins</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#standard-imports-first" style="font-size: 80%;">Standard imports first</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#simple-voting-example-head-or-tail" style="font-size: 80%;">Simple Voting Example, head or tail</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs049.html#using-the-voting-classifier" style="font-size: 80%;">Using the Voting Classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#voting-and-bagging" style="font-size: 80%;">Voting and Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#bagging" style="font-size: 80%;">Bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#more-bagging" style="font-size: 80%;">More bagging</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" style="font-size: 80%;">Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs054.html#random-forests" style="font-size: 80%;">Random forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -361,32 +341,29 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0063"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="tossing-coins" class="anchor">Tossing coins </h2>
|
||||
<h2 id="adaptive-boosting-adaboost" class="anchor">Adaptive Boosting, AdaBoost </h2>
|
||||
|
||||
<p>The simplest case is a so-called voting ensemble. To illustrate this,
|
||||
think of yourself tossing coins with a biased outcome of 51 per cent
|
||||
for heads and 49% for tails. With only few tosses,
|
||||
you may not clearly see this distribution for heads and tails. However, after some
|
||||
thousands of tosses, there will be a clear majority of heads. With 2000 tosses
|
||||
you should see approximately 1020 heads and 980 tails.
|
||||
<p>In our iterative procedure we define thus</p>
|
||||
$$
|
||||
f_m(x) = f_{m-1}(x)+\beta_mG_m(x).
|
||||
$$
|
||||
|
||||
<p>The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the
|
||||
exponential cost/loss function defined as
|
||||
</p>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{(-y_i(f_{m-1}(x_i)+\beta G(x_i))}.
|
||||
$$
|
||||
|
||||
<p>We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in the regression case.
|
||||
This is normally done in two steps. Let us however first rewrite the cost function as
|
||||
</p>
|
||||
|
||||
<p>We can then state that the outcome is a clear majority of heads. If
|
||||
you do this ten thousand times, it is easy to see that there is a 97%
|
||||
likelihood of a majority of heads.
|
||||
</p>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{(-y_i\beta G(x_i))},
|
||||
$$
|
||||
|
||||
<p>Another example would be to collect all polls before an
|
||||
election. Different polls may show different likelihoods for a
|
||||
candidate winning with say a majority of the popular vote. The majority vote
|
||||
would then consist in many polls indicating that this candidate will
|
||||
actually win.
|
||||
</p>
|
||||
|
||||
<p>The example here shows how we can implement the coin tossing case,
|
||||
clealry demostrating that after some tosses we see the <a href="https://en.wikipedia.org/wiki/Law_of_large_numbers" target="_self">law of large</a>
|
||||
numbers kicking in.
|
||||
</p>
|
||||
<p>where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \).</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -407,10 +384,6 @@ numbers kicking in.
|
||||
<li><a href="._week44-bs065.html">66</a></li>
|
||||
<li><a href="._week44-bs066.html">67</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs068.html">69</a></li>
|
||||
<li><a href="._week44-bs069.html">70</a></li>
|
||||
<li><a href="._week44-bs070.html">71</a></li>
|
||||
<li><a href="._week44-bs071.html">72</a></li>
|
||||
<li><a href="._week44-bs064.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -197,7 +197,38 @@ doconce format html week44.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -289,6 +320,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs055.html#random-forest-algorithm" style="font-size: 80%;">Random Forest Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs056.html#random-forests-compared-with-other-methods-on-the-cancer-data" style="font-size: 80%;">Random Forests Compared with other Methods on the Cancer Data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs057.html#compare-bagging-on-trees-with-random-forests" style="font-size: 80%;">Compare Bagging on Trees with Random Forests</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs058.html#boosting-a-bird-s-eye-view" style="font-size: 80%;">Boosting, a Bird's Eye View</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs059.html#what-is-boosting-additive-modelling-iterative-fitting" style="font-size: 80%;">What is boosting? Additive Modelling/Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#iterative-fitting-regression-and-squared-error-cost-function" style="font-size: 80%;">Iterative Fitting, Regression and Squared-error Cost Function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs061.html#squared-error-example-and-iterative-fitting" style="font-size: 80%;">Squared-Error Example and Iterative Fitting</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs062.html#iterative-fitting-classification-and-adaboost" style="font-size: 80%;">Iterative Fitting, Classification and AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs063.html#adaptive-boosting-adaboost" style="font-size: 80%;">Adaptive Boosting, AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs064.html#building-up-adaboost" style="font-size: 80%;">Building up AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs065.html#adaptive-boosting-adaboost-basic-algorithm" style="font-size: 80%;">Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs066.html#basic-steps-of-adaboost" style="font-size: 80%;">Basic Steps of AdaBoost</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week44-bs067.html#adaboost-examples" style="font-size: 80%;">AdaBoost Examples</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -318,7 +359,7 @@ MathJax.Hub.Config({
|
||||
</center>
|
||||
<br>
|
||||
<center>
|
||||
<h4>Nov 3, 2022</h4>
|
||||
<h4>Nov 4, 2022</h4>
|
||||
</center> <!-- date -->
|
||||
<br>
|
||||
|
||||
@@ -343,7 +384,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week44-bs008.html">9</a></li>
|
||||
<li><a href="._week44-bs009.html">10</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week44-bs057.html">58</a></li>
|
||||
<li><a href="._week44-bs067.html">68</a></li>
|
||||
<li><a href="._week44-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -184,7 +184,7 @@ MathJax.Hub.Config({
|
||||
</center>
|
||||
<br>
|
||||
<center>
|
||||
<h4>Nov 3, 2022</h4>
|
||||
<h4>Nov 4, 2022</h4>
|
||||
</center> <!-- date -->
|
||||
<br>
|
||||
|
||||
@@ -2467,6 +2467,391 @@ np.sum(y_pred == y_pred_rf) / <span style="color: #658b00">len</span>(y_pred)
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="boosting-a-bird-s-eye-view">Boosting, a Bird's Eye View </h2>
|
||||
|
||||
<p>The basic idea is to combine weak classifiers in order to create a good
|
||||
classifier. With a weak classifier we often intend a classifier which
|
||||
produces results which are only slightly better than we would get by
|
||||
random guesses.
|
||||
</p>
|
||||
|
||||
<p>This is done by applying in an iterative way a weak (or a standard
|
||||
classifier like decision trees) to modify the data. In each iteration
|
||||
we emphasize those observations which are misclassified by weighting
|
||||
them with a factor.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="what-is-boosting-additive-modelling-iterative-fitting">What is boosting? Additive Modelling/Iterative Fitting </h2>
|
||||
|
||||
<p>Boosting is a way of fitting an additive expansion in a set of
|
||||
elementary basis functions like for example some simple polynomials.
|
||||
Assume for example that we have a function
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>where \( \beta_m \) are the expansion parameters to be determined in a
|
||||
minimization process and \( b(x;\gamma_m) \) are some simple functions of
|
||||
the multivariable parameter \( x \) which is characterized by the
|
||||
parameters \( \gamma_m \).
|
||||
</p>
|
||||
|
||||
<p>As an example, consider the Sigmoid function we used in logistic
|
||||
regression. In that case, we can translate the function
|
||||
\( b(x;\gamma_m) \) into the Sigmoid function
|
||||
</p>
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
\sigma(t) = \frac{1}{1+\exp{(-t)}},
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>where \( t=\gamma_0+\gamma_1 x \) and the parameters \( \gamma_0 \) and
|
||||
\( \gamma_1 \) were determined by the Logistic Regression fitting
|
||||
algorithm.
|
||||
</p>
|
||||
|
||||
<p>As another example, consider the cost function we defined for linear regression</p>
|
||||
<p> <br>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>In this case the function \( f(x) \) was replaced by the design matrix
|
||||
\( \boldsymbol{X} \) and the unknown linear regression parameters \( \boldsymbol{\beta} \),
|
||||
that is \( \boldsymbol{f}=\boldsymbol{X}\boldsymbol{\beta} \). In linear regression we can
|
||||
simply invert a matrix and obtain the parameters \( \beta \) by
|
||||
</p>
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
\boldsymbol{\beta}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}.
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters \( \beta_m \) and \( \gamma_m \).</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="iterative-fitting-regression-and-squared-error-cost-function">Iterative Fitting, Regression and Squared-error Cost Function </h2>
|
||||
|
||||
<p>The way we proceed is as follows (here we specialize to the squared-error cost function)</p>
|
||||
|
||||
<ol>
|
||||
<p><li> Establish a cost function, here \( {\cal C}(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f_M(x_i))^2 \) with \( f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m) \).</li>
|
||||
<p><li> Initialize with a guess \( f_0(x) \). It could be one or even zero or some random numbers.</li>
|
||||
<p><li> For \( m=1:M \)
|
||||
<ol type="a"></li>
|
||||
<p><li> minimize \( \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 \) wrt \( \gamma \) and \( \beta \)</li>
|
||||
<p><li> This gives the optimal values \( \beta_m \) and \( \gamma_m \)</li>
|
||||
<p><li> Determine then the new values \( f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m) \)</li>
|
||||
</ol>
|
||||
<p>
|
||||
</ol>
|
||||
<p>
|
||||
<p>We could use any of the algorithms we have discussed till now. If we
|
||||
use trees, \( \gamma \) parameterizes the split variables and split points
|
||||
at the internal nodes, and the predictions at the terminal nodes.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="squared-error-example-and-iterative-fitting">Squared-Error Example and Iterative Fitting </h2>
|
||||
|
||||
<p>To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.</p>
|
||||
|
||||
<p>For simplicity we assume also that our functions \( b(x;\gamma)=1+\gamma x \). </p>
|
||||
|
||||
<p>This means that for every iteration \( m \), we need to optimize</p>
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
(\beta_m,\gamma_m) = \mathrm{argmin}_{\beta,\lambda}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2=\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(1+\gamma x_i))^2.
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>We start our iteration by simply setting \( f_0(x)=0 \).
|
||||
Taking the derivatives with respect to \( \beta \) and \( \gamma \) we obtain
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\frac{\partial {\cal C}}{\partial \beta} = -2\sum_{i}(1+\gamma x_i)(y_i-\beta(1+\gamma x_i))=0,
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>and</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\frac{\partial {\cal C}}{\partial \gamma} =-2\sum_{i}\beta x_i(y_i-\beta(1+\gamma x_i))=0.
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>We can then rewrite these equations as (defining \( \boldsymbol{w}=\boldsymbol{e}+\gamma \boldsymbol{x}) \) with \( \boldsymbol{e} \) being the unit vector)</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\gamma \boldsymbol{w}^T(\boldsymbol{y}-\beta\gamma \boldsymbol{w})=0,
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>which gives us \( \beta = \boldsymbol{w}^T\boldsymbol{y}/(\boldsymbol{w}^T\boldsymbol{w}) \). Similarly we have </p>
|
||||
<p> <br>
|
||||
$$
|
||||
\beta\gamma \boldsymbol{x}^T(\boldsymbol{y}-\beta(1+\gamma \boldsymbol{x}))=0,
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>which leads to \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\boldsymbol{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
|
||||
for \( \beta \) gives us an equation for \( \gamma \). This is a non-linear equation in the unknown \( \gamma \) and has to be solved numerically.
|
||||
</p>
|
||||
|
||||
<p>The solution to these two equations gives us in turn \( \beta_1 \) and \( \gamma_1 \) leading to the new expression for \( f_1(x) \) as
|
||||
\( f_1(x) = \beta_1(1+\gamma_1x) \). Doing this \( M \) times results in our final estimate for the function \( f \).
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="iterative-fitting-classification-and-adaboost">Iterative Fitting, Classification and AdaBoost </h2>
|
||||
|
||||
<p>Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
|
||||
observations. We define a classification function \( G(x) \) which produces a prediction taking one or the other of the two values
|
||||
\( \{-1,1\} \).
|
||||
</p>
|
||||
|
||||
<p>The error rate of the training sample is then</p>
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i)).
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>The iterative procedure starts with defining a weak classifier whose
|
||||
error rate is barely better than random guessing. The iterative
|
||||
procedure in boosting is to sequentially apply a weak
|
||||
classification algorithm to repeatedly modified versions of the data
|
||||
producing a sequence of weak classifiers \( G_m(x) \).
|
||||
</p>
|
||||
|
||||
<p>Here we will express our function \( f(x) \) in terms of \( G(x) \). That is</p>
|
||||
<p> <br>
|
||||
$$
|
||||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>will be a function of </p>
|
||||
<p> <br>
|
||||
$$
|
||||
G_M(x) = \mathrm{sign} \sum_{i=1}^M \alpha_m G_m(x).
|
||||
$$
|
||||
<p> <br>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="adaptive-boosting-adaboost">Adaptive Boosting, AdaBoost </h2>
|
||||
|
||||
<p>In our iterative procedure we define thus</p>
|
||||
<p> <br>
|
||||
$$
|
||||
f_m(x) = f_{m-1}(x)+\beta_mG_m(x).
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the
|
||||
exponential cost/loss function defined as
|
||||
</p>
|
||||
<p> <br>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{(-y_i(f_{m-1}(x_i)+\beta G(x_i))}.
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in the regression case.
|
||||
This is normally done in two steps. Let us however first rewrite the cost function as
|
||||
</p>
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{(-y_i\beta G(x_i))},
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \).</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="building-up-adaboost">Building up AdaBoost </h2>
|
||||
|
||||
<p>First, for any \( \beta > 0 \), we optimize \( G \) by setting</p>
|
||||
<p> <br>
|
||||
$$
|
||||
G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)),
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>which is the classifier that minimizes the weighted error rate in predicting \( y \).</p>
|
||||
|
||||
<p>We can do this by rewriting</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\exp{-(\beta)}\sum_{y_i=G(x_i)}w_i^m+\exp{(\beta)}\sum_{y_i\ne G(x_i)}w_i^m,
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>which can be rewritten as</p>
|
||||
<p> <br>
|
||||
$$
|
||||
(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{(-\beta)}\sum_{i=0}^{n-1}w_i^m=0,
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>which leads to</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\beta_m = \frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}},
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>where we have redefined the error as </p>
|
||||
<p> <br>
|
||||
$$
|
||||
\mathrm{\overline{err}}_m=\frac{1}{n}\frac{\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i)}{\sum_{i=0}^{n-1}w_i^m},
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>which leads to an update of</p>
|
||||
<p> <br>
|
||||
$$
|
||||
f_m(x) = f_{m-1}(x) +\beta_m G_m(x).
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>This leads to the new weights</p>
|
||||
<p> <br>
|
||||
$$
|
||||
w_i^{m+1} = w_i^m \exp{(-y_i\beta_m G_m(x_i))}
|
||||
$$
|
||||
<p> <br>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="adaptive-boosting-adaboost-basic-algorithm">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
|
||||
<p>The algorithm here is rather straightforward. Assume that our weak
|
||||
classifier is a decision tree and we consider a binary set of outputs
|
||||
with \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
|
||||
observations. Our design matrix is given in terms of the
|
||||
feature/predictor vectors
|
||||
\( \boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1}] \). Finally, we define also a
|
||||
classifier determined by our data via a function \( G(x) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \).
|
||||
</p>
|
||||
|
||||
<p>We have already defined the misclassification error \( \mathrm{err} \) as</p>
|
||||
<p> <br>
|
||||
$$
|
||||
\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i)),
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>where the function \( I() \) is one if we misclassify and zero if we classify correctly. </p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="basic-steps-of-adaboost">Basic Steps of AdaBoost </h2>
|
||||
|
||||
<p>With the above definitions we are now ready to set up the algorithm for AdaBoost.
|
||||
The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.
|
||||
</p>
|
||||
<ol>
|
||||
<p><li> We start by initializing all weights to \( w_i = 1/n \), with \( i=0,1,2,\dots n-1 \). It is easy to see that we must have \( \sum_{i=0}^{n-1}w_i = 1 \).</li>
|
||||
<p><li> We rewrite the misclassification error as</li>
|
||||
</ol>
|
||||
<p>
|
||||
<p> <br>
|
||||
$$
|
||||
\mathrm{\overline{err}}_m=\frac{\sum_{i=0}^{n-1}w_i^m I(y_i\ne G(x_i))}{\sum_{i=0}^{n-1}w_i},
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<ol>
|
||||
<p><li> Then we start looping over all attempts at classifying, namely we start an iterative process for \( m=1:M \), where \( M \) is the final number of classifications. Our given classifier could for example be a plain decision tree.
|
||||
<ol type="a"></li>
|
||||
<p><li> Fit then a given classifier to the training set using the weights \( w_i \).</li>
|
||||
<p><li> Compute then \( \mathrm{err} \) and figure out which events are classified properly and which are classified wrongly.</li>
|
||||
<p><li> Define a quantity \( \alpha_{m} = \log{(1-\mathrm{\overline{err}}_m)/\mathrm{\overline{err}}_m} \)</li>
|
||||
<p><li> Set the new weights to \( w_i = w_i\times \exp{(\alpha_m I(y_i\ne G(x_i)} \).</li>
|
||||
</ol>
|
||||
<p>
|
||||
<p><li> Compute the new classifier \( G(x)= \sum_{i=0}^{n-1}\alpha_m I(y_i\ne G(x_i) \).</li>
|
||||
</ol>
|
||||
<p>
|
||||
<p>For the iterations with \( m \le 2 \) the weights are modified
|
||||
individually at each steps. The observations which were misclassified
|
||||
at iteration \( m-1 \) have a weight which is larger than those which were
|
||||
classified properly. As this proceeds, the observations which were
|
||||
difficult to classifiy correctly are given a larger influence. Each
|
||||
new classification step \( m \) is then forced to concentrate on those
|
||||
observations that are missed in the previous iterations.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="adaboost-examples">AdaBoost Examples </h2>
|
||||
|
||||
<p>Using <b>Scikit-Learn</b> it is easy to apply the adaptive boosting algorithm, as done here.</p>
|
||||
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #eeeedd">
|
||||
<pre style="font-size: 80%; line-height: 125%;"><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.ensemble</span> <span style="color: #8B008B; font-weight: bold">import</span> AdaBoostClassifier
|
||||
|
||||
ada_clf = AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth=<span style="color: #B452CD">1</span>), n_estimators=<span style="color: #B452CD">200</span>,
|
||||
algorithm=<span style="color: #CD5555">"SAMME.R"</span>, learning_rate=<span style="color: #B452CD">0.5</span>, random_state=<span style="color: #B452CD">42</span>)
|
||||
ada_clf.fit(X_train, y_train)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.ensemble</span> <span style="color: #8B008B; font-weight: bold">import</span> AdaBoostClassifier
|
||||
|
||||
ada_clf = AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth=<span style="color: #B452CD">1</span>), n_estimators=<span style="color: #B452CD">200</span>,
|
||||
algorithm=<span style="color: #CD5555">"SAMME.R"</span>, learning_rate=<span style="color: #B452CD">0.5</span>, random_state=<span style="color: #B452CD">42</span>)
|
||||
ada_clf.fit(X_train_scaled, y_train)
|
||||
y_pred = ada_clf.predict(X_test_scaled)
|
||||
skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=<span style="color: #8B008B; font-weight: bold">True</span>)
|
||||
plt.show()
|
||||
y_probas = ada_clf.predict_proba(X_test_scaled)
|
||||
skplt.metrics.plot_roc(y_test, y_probas)
|
||||
plt.show()
|
||||
skplt.metrics.plot_cumulative_gain(y_test, y_probas)
|
||||
plt.show()
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
|
||||
|
||||
</div> <!-- class="slides" -->
|
||||
|
||||
@@ -224,7 +224,38 @@ div.toc p,a {
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -262,7 +293,7 @@ MathJax.Hub.Config({
|
||||
</center>
|
||||
<br>
|
||||
<center>
|
||||
<h4>Nov 3, 2022</h4>
|
||||
<h4>Nov 4, 2022</h4>
|
||||
</center> <!-- date -->
|
||||
<br>
|
||||
|
||||
@@ -2449,6 +2480,330 @@ np.sum(y_pred == y_pred_rf) / <span style="color: #658b00">len</span>(y_pred)
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="boosting-a-bird-s-eye-view">Boosting, a Bird's Eye View </h2>
|
||||
|
||||
<p>The basic idea is to combine weak classifiers in order to create a good
|
||||
classifier. With a weak classifier we often intend a classifier which
|
||||
produces results which are only slightly better than we would get by
|
||||
random guesses.
|
||||
</p>
|
||||
|
||||
<p>This is done by applying in an iterative way a weak (or a standard
|
||||
classifier like decision trees) to modify the data. In each iteration
|
||||
we emphasize those observations which are misclassified by weighting
|
||||
them with a factor.
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="what-is-boosting-additive-modelling-iterative-fitting">What is boosting? Additive Modelling/Iterative Fitting </h2>
|
||||
|
||||
<p>Boosting is a way of fitting an additive expansion in a set of
|
||||
elementary basis functions like for example some simple polynomials.
|
||||
Assume for example that we have a function
|
||||
</p>
|
||||
$$
|
||||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||||
$$
|
||||
|
||||
<p>where \( \beta_m \) are the expansion parameters to be determined in a
|
||||
minimization process and \( b(x;\gamma_m) \) are some simple functions of
|
||||
the multivariable parameter \( x \) which is characterized by the
|
||||
parameters \( \gamma_m \).
|
||||
</p>
|
||||
|
||||
<p>As an example, consider the Sigmoid function we used in logistic
|
||||
regression. In that case, we can translate the function
|
||||
\( b(x;\gamma_m) \) into the Sigmoid function
|
||||
</p>
|
||||
|
||||
$$
|
||||
\sigma(t) = \frac{1}{1+\exp{(-t)}},
|
||||
$$
|
||||
|
||||
<p>where \( t=\gamma_0+\gamma_1 x \) and the parameters \( \gamma_0 \) and
|
||||
\( \gamma_1 \) were determined by the Logistic Regression fitting
|
||||
algorithm.
|
||||
</p>
|
||||
|
||||
<p>As another example, consider the cost function we defined for linear regression</p>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
|
||||
$$
|
||||
|
||||
<p>In this case the function \( f(x) \) was replaced by the design matrix
|
||||
\( \boldsymbol{X} \) and the unknown linear regression parameters \( \boldsymbol{\beta} \),
|
||||
that is \( \boldsymbol{f}=\boldsymbol{X}\boldsymbol{\beta} \). In linear regression we can
|
||||
simply invert a matrix and obtain the parameters \( \beta \) by
|
||||
</p>
|
||||
|
||||
$$
|
||||
\boldsymbol{\beta}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}.
|
||||
$$
|
||||
|
||||
<p>In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters \( \beta_m \) and \( \gamma_m \).</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="iterative-fitting-regression-and-squared-error-cost-function">Iterative Fitting, Regression and Squared-error Cost Function </h2>
|
||||
|
||||
<p>The way we proceed is as follows (here we specialize to the squared-error cost function)</p>
|
||||
|
||||
<ol>
|
||||
<li> Establish a cost function, here \( {\cal C}(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f_M(x_i))^2 \) with \( f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m) \).</li>
|
||||
<li> Initialize with a guess \( f_0(x) \). It could be one or even zero or some random numbers.</li>
|
||||
<li> For \( m=1:M \)
|
||||
<ol type="a"></li>
|
||||
<li> minimize \( \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 \) wrt \( \gamma \) and \( \beta \)</li>
|
||||
<li> This gives the optimal values \( \beta_m \) and \( \gamma_m \)</li>
|
||||
<li> Determine then the new values \( f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m) \)</li>
|
||||
</ol>
|
||||
</ol>
|
||||
<p>We could use any of the algorithms we have discussed till now. If we
|
||||
use trees, \( \gamma \) parameterizes the split variables and split points
|
||||
at the internal nodes, and the predictions at the terminal nodes.
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="squared-error-example-and-iterative-fitting">Squared-Error Example and Iterative Fitting </h2>
|
||||
|
||||
<p>To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.</p>
|
||||
|
||||
<p>For simplicity we assume also that our functions \( b(x;\gamma)=1+\gamma x \). </p>
|
||||
|
||||
<p>This means that for every iteration \( m \), we need to optimize</p>
|
||||
|
||||
$$
|
||||
(\beta_m,\gamma_m) = \mathrm{argmin}_{\beta,\lambda}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2=\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(1+\gamma x_i))^2.
|
||||
$$
|
||||
|
||||
<p>We start our iteration by simply setting \( f_0(x)=0 \).
|
||||
Taking the derivatives with respect to \( \beta \) and \( \gamma \) we obtain
|
||||
</p>
|
||||
$$
|
||||
\frac{\partial {\cal C}}{\partial \beta} = -2\sum_{i}(1+\gamma x_i)(y_i-\beta(1+\gamma x_i))=0,
|
||||
$$
|
||||
|
||||
<p>and</p>
|
||||
$$
|
||||
\frac{\partial {\cal C}}{\partial \gamma} =-2\sum_{i}\beta x_i(y_i-\beta(1+\gamma x_i))=0.
|
||||
$$
|
||||
|
||||
<p>We can then rewrite these equations as (defining \( \boldsymbol{w}=\boldsymbol{e}+\gamma \boldsymbol{x}) \) with \( \boldsymbol{e} \) being the unit vector)</p>
|
||||
$$
|
||||
\gamma \boldsymbol{w}^T(\boldsymbol{y}-\beta\gamma \boldsymbol{w})=0,
|
||||
$$
|
||||
|
||||
<p>which gives us \( \beta = \boldsymbol{w}^T\boldsymbol{y}/(\boldsymbol{w}^T\boldsymbol{w}) \). Similarly we have </p>
|
||||
$$
|
||||
\beta\gamma \boldsymbol{x}^T(\boldsymbol{y}-\beta(1+\gamma \boldsymbol{x}))=0,
|
||||
$$
|
||||
|
||||
<p>which leads to \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\boldsymbol{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
|
||||
for \( \beta \) gives us an equation for \( \gamma \). This is a non-linear equation in the unknown \( \gamma \) and has to be solved numerically.
|
||||
</p>
|
||||
|
||||
<p>The solution to these two equations gives us in turn \( \beta_1 \) and \( \gamma_1 \) leading to the new expression for \( f_1(x) \) as
|
||||
\( f_1(x) = \beta_1(1+\gamma_1x) \). Doing this \( M \) times results in our final estimate for the function \( f \).
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="iterative-fitting-classification-and-adaboost">Iterative Fitting, Classification and AdaBoost </h2>
|
||||
|
||||
<p>Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
|
||||
observations. We define a classification function \( G(x) \) which produces a prediction taking one or the other of the two values
|
||||
\( \{-1,1\} \).
|
||||
</p>
|
||||
|
||||
<p>The error rate of the training sample is then</p>
|
||||
|
||||
$$
|
||||
\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i)).
|
||||
$$
|
||||
|
||||
<p>The iterative procedure starts with defining a weak classifier whose
|
||||
error rate is barely better than random guessing. The iterative
|
||||
procedure in boosting is to sequentially apply a weak
|
||||
classification algorithm to repeatedly modified versions of the data
|
||||
producing a sequence of weak classifiers \( G_m(x) \).
|
||||
</p>
|
||||
|
||||
<p>Here we will express our function \( f(x) \) in terms of \( G(x) \). That is</p>
|
||||
$$
|
||||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||||
$$
|
||||
|
||||
<p>will be a function of </p>
|
||||
$$
|
||||
G_M(x) = \mathrm{sign} \sum_{i=1}^M \alpha_m G_m(x).
|
||||
$$
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="adaptive-boosting-adaboost">Adaptive Boosting, AdaBoost </h2>
|
||||
|
||||
<p>In our iterative procedure we define thus</p>
|
||||
$$
|
||||
f_m(x) = f_{m-1}(x)+\beta_mG_m(x).
|
||||
$$
|
||||
|
||||
<p>The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the
|
||||
exponential cost/loss function defined as
|
||||
</p>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{(-y_i(f_{m-1}(x_i)+\beta G(x_i))}.
|
||||
$$
|
||||
|
||||
<p>We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in the regression case.
|
||||
This is normally done in two steps. Let us however first rewrite the cost function as
|
||||
</p>
|
||||
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{(-y_i\beta G(x_i))},
|
||||
$$
|
||||
|
||||
<p>where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \).</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="building-up-adaboost">Building up AdaBoost </h2>
|
||||
|
||||
<p>First, for any \( \beta > 0 \), we optimize \( G \) by setting</p>
|
||||
$$
|
||||
G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)),
|
||||
$$
|
||||
|
||||
<p>which is the classifier that minimizes the weighted error rate in predicting \( y \).</p>
|
||||
|
||||
<p>We can do this by rewriting</p>
|
||||
$$
|
||||
\exp{-(\beta)}\sum_{y_i=G(x_i)}w_i^m+\exp{(\beta)}\sum_{y_i\ne G(x_i)}w_i^m,
|
||||
$$
|
||||
|
||||
<p>which can be rewritten as</p>
|
||||
$$
|
||||
(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{(-\beta)}\sum_{i=0}^{n-1}w_i^m=0,
|
||||
$$
|
||||
|
||||
<p>which leads to</p>
|
||||
$$
|
||||
\beta_m = \frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}},
|
||||
$$
|
||||
|
||||
<p>where we have redefined the error as </p>
|
||||
$$
|
||||
\mathrm{\overline{err}}_m=\frac{1}{n}\frac{\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i)}{\sum_{i=0}^{n-1}w_i^m},
|
||||
$$
|
||||
|
||||
<p>which leads to an update of</p>
|
||||
$$
|
||||
f_m(x) = f_{m-1}(x) +\beta_m G_m(x).
|
||||
$$
|
||||
|
||||
<p>This leads to the new weights</p>
|
||||
$$
|
||||
w_i^{m+1} = w_i^m \exp{(-y_i\beta_m G_m(x_i))}
|
||||
$$
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="adaptive-boosting-adaboost-basic-algorithm">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
|
||||
<p>The algorithm here is rather straightforward. Assume that our weak
|
||||
classifier is a decision tree and we consider a binary set of outputs
|
||||
with \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
|
||||
observations. Our design matrix is given in terms of the
|
||||
feature/predictor vectors
|
||||
\( \boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1}] \). Finally, we define also a
|
||||
classifier determined by our data via a function \( G(x) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \).
|
||||
</p>
|
||||
|
||||
<p>We have already defined the misclassification error \( \mathrm{err} \) as</p>
|
||||
$$
|
||||
\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i)),
|
||||
$$
|
||||
|
||||
<p>where the function \( I() \) is one if we misclassify and zero if we classify correctly. </p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="basic-steps-of-adaboost">Basic Steps of AdaBoost </h2>
|
||||
|
||||
<p>With the above definitions we are now ready to set up the algorithm for AdaBoost.
|
||||
The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.
|
||||
</p>
|
||||
<ol>
|
||||
<li> We start by initializing all weights to \( w_i = 1/n \), with \( i=0,1,2,\dots n-1 \). It is easy to see that we must have \( \sum_{i=0}^{n-1}w_i = 1 \).</li>
|
||||
<li> We rewrite the misclassification error as</li>
|
||||
</ol>
|
||||
$$
|
||||
\mathrm{\overline{err}}_m=\frac{\sum_{i=0}^{n-1}w_i^m I(y_i\ne G(x_i))}{\sum_{i=0}^{n-1}w_i},
|
||||
$$
|
||||
|
||||
<ol>
|
||||
<li> Then we start looping over all attempts at classifying, namely we start an iterative process for \( m=1:M \), where \( M \) is the final number of classifications. Our given classifier could for example be a plain decision tree.
|
||||
<ol type="a"></li>
|
||||
<li> Fit then a given classifier to the training set using the weights \( w_i \).</li>
|
||||
<li> Compute then \( \mathrm{err} \) and figure out which events are classified properly and which are classified wrongly.</li>
|
||||
<li> Define a quantity \( \alpha_{m} = \log{(1-\mathrm{\overline{err}}_m)/\mathrm{\overline{err}}_m} \)</li>
|
||||
<li> Set the new weights to \( w_i = w_i\times \exp{(\alpha_m I(y_i\ne G(x_i)} \).</li>
|
||||
</ol>
|
||||
<li> Compute the new classifier \( G(x)= \sum_{i=0}^{n-1}\alpha_m I(y_i\ne G(x_i) \).</li>
|
||||
</ol>
|
||||
<p>For the iterations with \( m \le 2 \) the weights are modified
|
||||
individually at each steps. The observations which were misclassified
|
||||
at iteration \( m-1 \) have a weight which is larger than those which were
|
||||
classified properly. As this proceeds, the observations which were
|
||||
difficult to classifiy correctly are given a larger influence. Each
|
||||
new classification step \( m \) is then forced to concentrate on those
|
||||
observations that are missed in the previous iterations.
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="adaboost-examples">AdaBoost Examples </h2>
|
||||
|
||||
<p>Using <b>Scikit-Learn</b> it is easy to apply the adaptive boosting algorithm, as done here.</p>
|
||||
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #eeeedd">
|
||||
<pre style="line-height: 125%;"><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.ensemble</span> <span style="color: #8B008B; font-weight: bold">import</span> AdaBoostClassifier
|
||||
|
||||
ada_clf = AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth=<span style="color: #B452CD">1</span>), n_estimators=<span style="color: #B452CD">200</span>,
|
||||
algorithm=<span style="color: #CD5555">"SAMME.R"</span>, learning_rate=<span style="color: #B452CD">0.5</span>, random_state=<span style="color: #B452CD">42</span>)
|
||||
ada_clf.fit(X_train, y_train)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.ensemble</span> <span style="color: #8B008B; font-weight: bold">import</span> AdaBoostClassifier
|
||||
|
||||
ada_clf = AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth=<span style="color: #B452CD">1</span>), n_estimators=<span style="color: #B452CD">200</span>,
|
||||
algorithm=<span style="color: #CD5555">"SAMME.R"</span>, learning_rate=<span style="color: #B452CD">0.5</span>, random_state=<span style="color: #B452CD">42</span>)
|
||||
ada_clf.fit(X_train_scaled, y_train)
|
||||
y_pred = ada_clf.predict(X_test_scaled)
|
||||
skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=<span style="color: #8B008B; font-weight: bold">True</span>)
|
||||
plt.show()
|
||||
y_probas = ada_clf.predict_proba(X_test_scaled)
|
||||
skplt.metrics.plot_roc(y_test, y_probas)
|
||||
plt.show()
|
||||
skplt.metrics.plot_cumulative_gain(y_test, y_probas)
|
||||
plt.show()
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
<center style="font-size:80%">
|
||||
<!-- copyright --> © 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
|
||||
|
||||
@@ -301,7 +301,38 @@ div.toc p,a {
|
||||
('Compare Bagging on Trees with Random Forests',
|
||||
2,
|
||||
None,
|
||||
'compare-bagging-on-trees-with-random-forests')]}
|
||||
'compare-bagging-on-trees-with-random-forests'),
|
||||
("Boosting, a Bird's Eye View",
|
||||
2,
|
||||
None,
|
||||
'boosting-a-bird-s-eye-view'),
|
||||
('What is boosting? Additive Modelling/Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'what-is-boosting-additive-modelling-iterative-fitting'),
|
||||
('Iterative Fitting, Regression and Squared-error Cost Function',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-regression-and-squared-error-cost-function'),
|
||||
('Squared-Error Example and Iterative Fitting',
|
||||
2,
|
||||
None,
|
||||
'squared-error-example-and-iterative-fitting'),
|
||||
('Iterative Fitting, Classification and AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'iterative-fitting-classification-and-adaboost'),
|
||||
('Adaptive Boosting, AdaBoost',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost'),
|
||||
('Building up AdaBoost', 2, None, 'building-up-adaboost'),
|
||||
('Adaptive boosting: AdaBoost, Basic Algorithm',
|
||||
2,
|
||||
None,
|
||||
'adaptive-boosting-adaboost-basic-algorithm'),
|
||||
('Basic Steps of AdaBoost', 2, None, 'basic-steps-of-adaboost'),
|
||||
('AdaBoost Examples', 2, None, 'adaboost-examples')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -339,7 +370,7 @@ MathJax.Hub.Config({
|
||||
</center>
|
||||
<br>
|
||||
<center>
|
||||
<h4>Nov 3, 2022</h4>
|
||||
<h4>Nov 4, 2022</h4>
|
||||
</center> <!-- date -->
|
||||
<br>
|
||||
|
||||
@@ -2526,6 +2557,330 @@ np<span style="color: #666666">.</span>sum(y_pred <span style="color: #666666">=
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="boosting-a-bird-s-eye-view">Boosting, a Bird's Eye View </h2>
|
||||
|
||||
<p>The basic idea is to combine weak classifiers in order to create a good
|
||||
classifier. With a weak classifier we often intend a classifier which
|
||||
produces results which are only slightly better than we would get by
|
||||
random guesses.
|
||||
</p>
|
||||
|
||||
<p>This is done by applying in an iterative way a weak (or a standard
|
||||
classifier like decision trees) to modify the data. In each iteration
|
||||
we emphasize those observations which are misclassified by weighting
|
||||
them with a factor.
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="what-is-boosting-additive-modelling-iterative-fitting">What is boosting? Additive Modelling/Iterative Fitting </h2>
|
||||
|
||||
<p>Boosting is a way of fitting an additive expansion in a set of
|
||||
elementary basis functions like for example some simple polynomials.
|
||||
Assume for example that we have a function
|
||||
</p>
|
||||
$$
|
||||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||||
$$
|
||||
|
||||
<p>where \( \beta_m \) are the expansion parameters to be determined in a
|
||||
minimization process and \( b(x;\gamma_m) \) are some simple functions of
|
||||
the multivariable parameter \( x \) which is characterized by the
|
||||
parameters \( \gamma_m \).
|
||||
</p>
|
||||
|
||||
<p>As an example, consider the Sigmoid function we used in logistic
|
||||
regression. In that case, we can translate the function
|
||||
\( b(x;\gamma_m) \) into the Sigmoid function
|
||||
</p>
|
||||
|
||||
$$
|
||||
\sigma(t) = \frac{1}{1+\exp{(-t)}},
|
||||
$$
|
||||
|
||||
<p>where \( t=\gamma_0+\gamma_1 x \) and the parameters \( \gamma_0 \) and
|
||||
\( \gamma_1 \) were determined by the Logistic Regression fitting
|
||||
algorithm.
|
||||
</p>
|
||||
|
||||
<p>As another example, consider the cost function we defined for linear regression</p>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
|
||||
$$
|
||||
|
||||
<p>In this case the function \( f(x) \) was replaced by the design matrix
|
||||
\( \boldsymbol{X} \) and the unknown linear regression parameters \( \boldsymbol{\beta} \),
|
||||
that is \( \boldsymbol{f}=\boldsymbol{X}\boldsymbol{\beta} \). In linear regression we can
|
||||
simply invert a matrix and obtain the parameters \( \beta \) by
|
||||
</p>
|
||||
|
||||
$$
|
||||
\boldsymbol{\beta}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}.
|
||||
$$
|
||||
|
||||
<p>In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters \( \beta_m \) and \( \gamma_m \).</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="iterative-fitting-regression-and-squared-error-cost-function">Iterative Fitting, Regression and Squared-error Cost Function </h2>
|
||||
|
||||
<p>The way we proceed is as follows (here we specialize to the squared-error cost function)</p>
|
||||
|
||||
<ol>
|
||||
<li> Establish a cost function, here \( {\cal C}(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f_M(x_i))^2 \) with \( f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m) \).</li>
|
||||
<li> Initialize with a guess \( f_0(x) \). It could be one or even zero or some random numbers.</li>
|
||||
<li> For \( m=1:M \)
|
||||
<ol type="a"></li>
|
||||
<li> minimize \( \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2 \) wrt \( \gamma \) and \( \beta \)</li>
|
||||
<li> This gives the optimal values \( \beta_m \) and \( \gamma_m \)</li>
|
||||
<li> Determine then the new values \( f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m) \)</li>
|
||||
</ol>
|
||||
</ol>
|
||||
<p>We could use any of the algorithms we have discussed till now. If we
|
||||
use trees, \( \gamma \) parameterizes the split variables and split points
|
||||
at the internal nodes, and the predictions at the terminal nodes.
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="squared-error-example-and-iterative-fitting">Squared-Error Example and Iterative Fitting </h2>
|
||||
|
||||
<p>To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.</p>
|
||||
|
||||
<p>For simplicity we assume also that our functions \( b(x;\gamma)=1+\gamma x \). </p>
|
||||
|
||||
<p>This means that for every iteration \( m \), we need to optimize</p>
|
||||
|
||||
$$
|
||||
(\beta_m,\gamma_m) = \mathrm{argmin}_{\beta,\lambda}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2=\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(1+\gamma x_i))^2.
|
||||
$$
|
||||
|
||||
<p>We start our iteration by simply setting \( f_0(x)=0 \).
|
||||
Taking the derivatives with respect to \( \beta \) and \( \gamma \) we obtain
|
||||
</p>
|
||||
$$
|
||||
\frac{\partial {\cal C}}{\partial \beta} = -2\sum_{i}(1+\gamma x_i)(y_i-\beta(1+\gamma x_i))=0,
|
||||
$$
|
||||
|
||||
<p>and</p>
|
||||
$$
|
||||
\frac{\partial {\cal C}}{\partial \gamma} =-2\sum_{i}\beta x_i(y_i-\beta(1+\gamma x_i))=0.
|
||||
$$
|
||||
|
||||
<p>We can then rewrite these equations as (defining \( \boldsymbol{w}=\boldsymbol{e}+\gamma \boldsymbol{x}) \) with \( \boldsymbol{e} \) being the unit vector)</p>
|
||||
$$
|
||||
\gamma \boldsymbol{w}^T(\boldsymbol{y}-\beta\gamma \boldsymbol{w})=0,
|
||||
$$
|
||||
|
||||
<p>which gives us \( \beta = \boldsymbol{w}^T\boldsymbol{y}/(\boldsymbol{w}^T\boldsymbol{w}) \). Similarly we have </p>
|
||||
$$
|
||||
\beta\gamma \boldsymbol{x}^T(\boldsymbol{y}-\beta(1+\gamma \boldsymbol{x}))=0,
|
||||
$$
|
||||
|
||||
<p>which leads to \( \gamma =(\boldsymbol{x}^T\boldsymbol{y}-\beta\boldsymbol{x}^T\boldsymbol{e})/(\beta\boldsymbol{x}^T\boldsymbol{x}) \). Inserting
|
||||
for \( \beta \) gives us an equation for \( \gamma \). This is a non-linear equation in the unknown \( \gamma \) and has to be solved numerically.
|
||||
</p>
|
||||
|
||||
<p>The solution to these two equations gives us in turn \( \beta_1 \) and \( \gamma_1 \) leading to the new expression for \( f_1(x) \) as
|
||||
\( f_1(x) = \beta_1(1+\gamma_1x) \). Doing this \( M \) times results in our final estimate for the function \( f \).
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="iterative-fitting-classification-and-adaboost">Iterative Fitting, Classification and AdaBoost </h2>
|
||||
|
||||
<p>Let us consider a binary classification problem with two outcomes \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
|
||||
observations. We define a classification function \( G(x) \) which produces a prediction taking one or the other of the two values
|
||||
\( \{-1,1\} \).
|
||||
</p>
|
||||
|
||||
<p>The error rate of the training sample is then</p>
|
||||
|
||||
$$
|
||||
\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i)).
|
||||
$$
|
||||
|
||||
<p>The iterative procedure starts with defining a weak classifier whose
|
||||
error rate is barely better than random guessing. The iterative
|
||||
procedure in boosting is to sequentially apply a weak
|
||||
classification algorithm to repeatedly modified versions of the data
|
||||
producing a sequence of weak classifiers \( G_m(x) \).
|
||||
</p>
|
||||
|
||||
<p>Here we will express our function \( f(x) \) in terms of \( G(x) \). That is</p>
|
||||
$$
|
||||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||||
$$
|
||||
|
||||
<p>will be a function of </p>
|
||||
$$
|
||||
G_M(x) = \mathrm{sign} \sum_{i=1}^M \alpha_m G_m(x).
|
||||
$$
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="adaptive-boosting-adaboost">Adaptive Boosting, AdaBoost </h2>
|
||||
|
||||
<p>In our iterative procedure we define thus</p>
|
||||
$$
|
||||
f_m(x) = f_{m-1}(x)+\beta_mG_m(x).
|
||||
$$
|
||||
|
||||
<p>The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the
|
||||
exponential cost/loss function defined as
|
||||
</p>
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}\exp{(-y_i(f_{m-1}(x_i)+\beta G(x_i))}.
|
||||
$$
|
||||
|
||||
<p>We optimize \( \beta \) and \( G \) for each value of \( m=1:M \) as we did in the regression case.
|
||||
This is normally done in two steps. Let us however first rewrite the cost function as
|
||||
</p>
|
||||
|
||||
$$
|
||||
C(\boldsymbol{y},\boldsymbol{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{(-y_i\beta G(x_i))},
|
||||
$$
|
||||
|
||||
<p>where we have defined \( w_i^m= \exp{(-y_if_{m-1}(x_i))} \).</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="building-up-adaboost">Building up AdaBoost </h2>
|
||||
|
||||
<p>First, for any \( \beta > 0 \), we optimize \( G \) by setting</p>
|
||||
$$
|
||||
G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)),
|
||||
$$
|
||||
|
||||
<p>which is the classifier that minimizes the weighted error rate in predicting \( y \).</p>
|
||||
|
||||
<p>We can do this by rewriting</p>
|
||||
$$
|
||||
\exp{-(\beta)}\sum_{y_i=G(x_i)}w_i^m+\exp{(\beta)}\sum_{y_i\ne G(x_i)}w_i^m,
|
||||
$$
|
||||
|
||||
<p>which can be rewritten as</p>
|
||||
$$
|
||||
(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{(-\beta)}\sum_{i=0}^{n-1}w_i^m=0,
|
||||
$$
|
||||
|
||||
<p>which leads to</p>
|
||||
$$
|
||||
\beta_m = \frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}},
|
||||
$$
|
||||
|
||||
<p>where we have redefined the error as </p>
|
||||
$$
|
||||
\mathrm{\overline{err}}_m=\frac{1}{n}\frac{\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i)}{\sum_{i=0}^{n-1}w_i^m},
|
||||
$$
|
||||
|
||||
<p>which leads to an update of</p>
|
||||
$$
|
||||
f_m(x) = f_{m-1}(x) +\beta_m G_m(x).
|
||||
$$
|
||||
|
||||
<p>This leads to the new weights</p>
|
||||
$$
|
||||
w_i^{m+1} = w_i^m \exp{(-y_i\beta_m G_m(x_i))}
|
||||
$$
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="adaptive-boosting-adaboost-basic-algorithm">Adaptive boosting: AdaBoost, Basic Algorithm </h2>
|
||||
|
||||
<p>The algorithm here is rather straightforward. Assume that our weak
|
||||
classifier is a decision tree and we consider a binary set of outputs
|
||||
with \( y_i \in \{-1,1\} \) and \( i=0,1,2,\dots,n-1 \) as our set of
|
||||
observations. Our design matrix is given in terms of the
|
||||
feature/predictor vectors
|
||||
\( \boldsymbol{X}=[\boldsymbol{x}_0\boldsymbol{x}_1\dots\boldsymbol{x}_{p-1}] \). Finally, we define also a
|
||||
classifier determined by our data via a function \( G(x) \). This function tells us how well we are able to classify our outputs/targets \( \boldsymbol{y} \).
|
||||
</p>
|
||||
|
||||
<p>We have already defined the misclassification error \( \mathrm{err} \) as</p>
|
||||
$$
|
||||
\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i)),
|
||||
$$
|
||||
|
||||
<p>where the function \( I() \) is one if we misclassify and zero if we classify correctly. </p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="basic-steps-of-adaboost">Basic Steps of AdaBoost </h2>
|
||||
|
||||
<p>With the above definitions we are now ready to set up the algorithm for AdaBoost.
|
||||
The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.
|
||||
</p>
|
||||
<ol>
|
||||
<li> We start by initializing all weights to \( w_i = 1/n \), with \( i=0,1,2,\dots n-1 \). It is easy to see that we must have \( \sum_{i=0}^{n-1}w_i = 1 \).</li>
|
||||
<li> We rewrite the misclassification error as</li>
|
||||
</ol>
|
||||
$$
|
||||
\mathrm{\overline{err}}_m=\frac{\sum_{i=0}^{n-1}w_i^m I(y_i\ne G(x_i))}{\sum_{i=0}^{n-1}w_i},
|
||||
$$
|
||||
|
||||
<ol>
|
||||
<li> Then we start looping over all attempts at classifying, namely we start an iterative process for \( m=1:M \), where \( M \) is the final number of classifications. Our given classifier could for example be a plain decision tree.
|
||||
<ol type="a"></li>
|
||||
<li> Fit then a given classifier to the training set using the weights \( w_i \).</li>
|
||||
<li> Compute then \( \mathrm{err} \) and figure out which events are classified properly and which are classified wrongly.</li>
|
||||
<li> Define a quantity \( \alpha_{m} = \log{(1-\mathrm{\overline{err}}_m)/\mathrm{\overline{err}}_m} \)</li>
|
||||
<li> Set the new weights to \( w_i = w_i\times \exp{(\alpha_m I(y_i\ne G(x_i)} \).</li>
|
||||
</ol>
|
||||
<li> Compute the new classifier \( G(x)= \sum_{i=0}^{n-1}\alpha_m I(y_i\ne G(x_i) \).</li>
|
||||
</ol>
|
||||
<p>For the iterations with \( m \le 2 \) the weights are modified
|
||||
individually at each steps. The observations which were misclassified
|
||||
at iteration \( m-1 \) have a weight which is larger than those which were
|
||||
classified properly. As this proceeds, the observations which were
|
||||
difficult to classifiy correctly are given a larger influence. Each
|
||||
new classification step \( m \) is then forced to concentrate on those
|
||||
observations that are missed in the previous iterations.
|
||||
</p>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="adaboost-examples">AdaBoost Examples </h2>
|
||||
|
||||
<p>Using <b>Scikit-Learn</b> it is easy to apply the adaptive boosting algorithm, as done here.</p>
|
||||
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class="highlight" style="background: #f8f8f8">
|
||||
<pre style="line-height: 125%;"><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> AdaBoostClassifier
|
||||
|
||||
ada_clf <span style="color: #666666">=</span> AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth<span style="color: #666666">=1</span>), n_estimators<span style="color: #666666">=200</span>,
|
||||
algorithm<span style="color: #666666">=</span><span style="color: #BA2121">"SAMME.R"</span>, learning_rate<span style="color: #666666">=0.5</span>, random_state<span style="color: #666666">=42</span>)
|
||||
ada_clf<span style="color: #666666">.</span>fit(X_train, y_train)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.ensemble</span> <span style="color: #008000; font-weight: bold">import</span> AdaBoostClassifier
|
||||
|
||||
ada_clf <span style="color: #666666">=</span> AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth<span style="color: #666666">=1</span>), n_estimators<span style="color: #666666">=200</span>,
|
||||
algorithm<span style="color: #666666">=</span><span style="color: #BA2121">"SAMME.R"</span>, learning_rate<span style="color: #666666">=0.5</span>, random_state<span style="color: #666666">=42</span>)
|
||||
ada_clf<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
y_pred <span style="color: #666666">=</span> ada_clf<span style="color: #666666">.</span>predict(X_test_scaled)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_confusion_matrix(y_test, y_pred, normalize<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
y_probas <span style="color: #666666">=</span> ada_clf<span style="color: #666666">.</span>predict_proba(X_test_scaled)
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_roc(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
skplt<span style="color: #666666">.</span>metrics<span style="color: #666666">.</span>plot_cumulative_gain(y_test, y_probas)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="output_wrapper">
|
||||
<div class="output">
|
||||
<div class="output_area">
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
<center style="font-size:80%">
|
||||
<!-- copyright --> © 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
|
||||
|
||||
Binary file not shown.
+867
-113
File diff suppressed because it is too large
Load Diff
@@ -1692,3 +1692,328 @@ np.sum(y_pred == y_pred_rf) / len(y_pred)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
!split
|
||||
===== Boosting, a Bird's Eye View =====
|
||||
|
||||
The basic idea is to combine weak classifiers in order to create a good
|
||||
classifier. With a weak classifier we often intend a classifier which
|
||||
produces results which are only slightly better than we would get by
|
||||
random guesses.
|
||||
|
||||
This is done by applying in an iterative way a weak (or a standard
|
||||
classifier like decision trees) to modify the data. In each iteration
|
||||
we emphasize those observations which are misclassified by weighting
|
||||
them with a factor.
|
||||
|
||||
|
||||
!split
|
||||
===== What is boosting? Additive Modelling/Iterative Fitting =====
|
||||
|
||||
Boosting is a way of fitting an additive expansion in a set of
|
||||
elementary basis functions like for example some simple polynomials.
|
||||
Assume for example that we have a function
|
||||
!bt
|
||||
\[
|
||||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||||
\]
|
||||
!et
|
||||
|
||||
where $\beta_m$ are the expansion parameters to be determined in a
|
||||
minimization process and $b(x;\gamma_m)$ are some simple functions of
|
||||
the multivariable parameter $x$ which is characterized by the
|
||||
parameters $\gamma_m$.
|
||||
|
||||
As an example, consider the Sigmoid function we used in logistic
|
||||
regression. In that case, we can translate the function
|
||||
$b(x;\gamma_m)$ into the Sigmoid function
|
||||
|
||||
|
||||
!bt
|
||||
\[
|
||||
\sigma(t) = \frac{1}{1+\exp{(-t)}},
|
||||
\]
|
||||
!et
|
||||
|
||||
where $t=\gamma_0+\gamma_1 x$ and the parameters $\gamma_0$ and
|
||||
$\gamma_1$ were determined by the Logistic Regression fitting
|
||||
algorithm.
|
||||
|
||||
As another example, consider the cost function we defined for linear regression
|
||||
!bt
|
||||
\[
|
||||
C(\bm{y},\bm{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
|
||||
\]
|
||||
!et
|
||||
|
||||
In this case the function $f(x)$ was replaced by the design matrix
|
||||
$\bm{X}$ and the unknown linear regression parameters $\bm{\beta}$,
|
||||
that is $\bm{f}=\bm{X}\bm{\beta}$. In linear regression we can
|
||||
simply invert a matrix and obtain the parameters $\beta$ by
|
||||
|
||||
!bt
|
||||
\[
|
||||
\bm{\beta}=\left(\bm{X}^T\bm{X}\right)^{-1}\bm{X}^T\bm{y}.
|
||||
\]
|
||||
!et
|
||||
|
||||
In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters $\beta_m$ and $\gamma_m$.
|
||||
|
||||
|
||||
!split
|
||||
===== Iterative Fitting, Regression and Squared-error Cost Function =====
|
||||
|
||||
The way we proceed is as follows (here we specialize to the squared-error cost function)
|
||||
|
||||
o Establish a cost function, here ${\cal C}(\bm{y},\bm{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f_M(x_i))^2$ with $f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m)$.
|
||||
o Initialize with a guess $f_0(x)$. It could be one or even zero or some random numbers.
|
||||
o For $m=1:M$
|
||||
o minimize $\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2$ wrt $\gamma$ and $\beta$
|
||||
o This gives the optimal values $\beta_m$ and $\gamma_m$
|
||||
o Determine then the new values $f_m(x)=f_{m-1}(x) +\beta_m b(x;\gamma_m)$
|
||||
|
||||
We could use any of the algorithms we have discussed till now. If we
|
||||
use trees, $\gamma$ parameterizes the split variables and split points
|
||||
at the internal nodes, and the predictions at the terminal nodes.
|
||||
|
||||
|
||||
!split
|
||||
===== Squared-Error Example and Iterative Fitting =====
|
||||
|
||||
To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.
|
||||
|
||||
For simplicity we assume also that our functions $b(x;\gamma)=1+\gamma x$.
|
||||
|
||||
This means that for every iteration $m$, we need to optimize
|
||||
|
||||
!bt
|
||||
\[
|
||||
(\beta_m,\gamma_m) = \mathrm{argmin}_{\beta,\lambda}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta b(x;\gamma))^2=\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\beta(1+\gamma x_i))^2.
|
||||
\]
|
||||
!et
|
||||
|
||||
We start our iteration by simply setting $f_0(x)=0$.
|
||||
Taking the derivatives with respect to $\beta$ and $\gamma$ we obtain
|
||||
!bt
|
||||
\[
|
||||
\frac{\partial {\cal C}}{\partial \beta} = -2\sum_{i}(1+\gamma x_i)(y_i-\beta(1+\gamma x_i))=0,
|
||||
\]
|
||||
!et
|
||||
and
|
||||
!bt
|
||||
\[
|
||||
\frac{\partial {\cal C}}{\partial \gamma} =-2\sum_{i}\beta x_i(y_i-\beta(1+\gamma x_i))=0.
|
||||
\]
|
||||
!et
|
||||
We can then rewrite these equations as (defining $\bm{w}=\bm{e}+\gamma \bm{x})$ with $\bm{e}$ being the unit vector)
|
||||
!bt
|
||||
\[
|
||||
\gamma \bm{w}^T(\bm{y}-\beta\gamma \bm{w})=0,
|
||||
\]
|
||||
!et
|
||||
which gives us $\beta = \bm{w}^T\bm{y}/(\bm{w}^T\bm{w})$. Similarly we have
|
||||
!bt
|
||||
\[
|
||||
\beta\gamma \bm{x}^T(\bm{y}-\beta(1+\gamma \bm{x}))=0,
|
||||
\]
|
||||
!et
|
||||
|
||||
which leads to $\gamma =(\bm{x}^T\bm{y}-\beta\bm{x}^T\bm{e})/(\beta\bm{x}^T\bm{x})$. Inserting
|
||||
for $\beta$ gives us an equation for $\gamma$. This is a non-linear equation in the unknown $\gamma$ and has to be solved numerically.
|
||||
|
||||
The solution to these two equations gives us in turn $\beta_1$ and $\gamma_1$ leading to the new expression for $f_1(x)$ as
|
||||
$f_1(x) = \beta_1(1+\gamma_1x)$. Doing this $M$ times results in our final estimate for the function $f$.
|
||||
|
||||
|
||||
|
||||
!split
|
||||
===== Iterative Fitting, Classification and AdaBoost =====
|
||||
|
||||
Let us consider a binary classification problem with two outcomes $y_i \in \{-1,1\}$ and $i=0,1,2,\dots,n-1$ as our set of
|
||||
observations. We define a classification function $G(x)$ which produces a prediction taking one or the other of the two values
|
||||
$\{-1,1\}$.
|
||||
|
||||
The error rate of the training sample is then
|
||||
|
||||
!bt
|
||||
\[
|
||||
\mathrm{\overline{err}}=\frac{1}{n} \sum_{i=0}^{n-1} I(y_i\ne G(x_i)).
|
||||
\]
|
||||
!et
|
||||
|
||||
The iterative procedure starts with defining a weak classifier whose
|
||||
error rate is barely better than random guessing. The iterative
|
||||
procedure in boosting is to sequentially apply a weak
|
||||
classification algorithm to repeatedly modified versions of the data
|
||||
producing a sequence of weak classifiers $G_m(x)$.
|
||||
|
||||
Here we will express our function $f(x)$ in terms of $G(x)$. That is
|
||||
!bt
|
||||
\[
|
||||
f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m),
|
||||
\]
|
||||
!et
|
||||
will be a function of
|
||||
!bt
|
||||
\[
|
||||
G_M(x) = \mathrm{sign} \sum_{i=1}^M \alpha_m G_m(x).
|
||||
\]
|
||||
!et
|
||||
|
||||
|
||||
|
||||
!split
|
||||
===== Adaptive Boosting, AdaBoost =====
|
||||
|
||||
In our iterative procedure we define thus
|
||||
!bt
|
||||
\[
|
||||
f_m(x) = f_{m-1}(x)+\beta_mG_m(x).
|
||||
\]
|
||||
!et
|
||||
|
||||
The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the
|
||||
exponential cost/loss function defined as
|
||||
!bt
|
||||
\[
|
||||
C(\bm{y},\bm{f}) = \sum_{i=0}^{n-1}\exp{(-y_i(f_{m-1}(x_i)+\beta G(x_i))}.
|
||||
\]
|
||||
!et
|
||||
|
||||
We optimize $\beta$ and $G$ for each value of $m=1:M$ as we did in the regression case.
|
||||
This is normally done in two steps. Let us however first rewrite the cost function as
|
||||
|
||||
!bt
|
||||
\[
|
||||
C(\bm{y},\bm{f}) = \sum_{i=0}^{n-1}w_i^{m}\exp{(-y_i\beta G(x_i))},
|
||||
\]
|
||||
!et
|
||||
where we have defined $w_i^m= \exp{(-y_if_{m-1}(x_i))}$.
|
||||
|
||||
!split
|
||||
===== Building up AdaBoost =====
|
||||
|
||||
First, for any $\beta > 0$, we optimize $G$ by setting
|
||||
!bt
|
||||
\[
|
||||
G_m(x) = \mathrm{sign} \sum_{i=0}^{n-1} w_i^m I(y_i \ne G_(x_i)),
|
||||
\]
|
||||
!et
|
||||
which is the classifier that minimizes the weighted error rate in predicting $y$.
|
||||
|
||||
We can do this by rewriting
|
||||
!bt
|
||||
\[
|
||||
\exp{-(\beta)}\sum_{y_i=G(x_i)}w_i^m+\exp{(\beta)}\sum_{y_i\ne G(x_i)}w_i^m,
|
||||
\]
|
||||
!et
|
||||
which can be rewritten as
|
||||
!bt
|
||||
\[
|
||||
(\exp{(\beta)}-\exp{-(\beta)})\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i))+\exp{(-\beta)}\sum_{i=0}^{n-1}w_i^m=0,
|
||||
\]
|
||||
!et
|
||||
which leads to
|
||||
!bt
|
||||
\[
|
||||
\beta_m = \frac{1}{2}\log{\frac{1-\mathrm{\overline{err}}}{\mathrm{\overline{err}}}},
|
||||
\]
|
||||
!et
|
||||
where we have redefined the error as
|
||||
!bt
|
||||
\[
|
||||
\mathrm{\overline{err}}_m=\frac{1}{n}\frac{\sum_{i=0}^{n-1}w_i^mI(y_i\ne G(x_i)}{\sum_{i=0}^{n-1}w_i^m},
|
||||
\]
|
||||
!et
|
||||
which leads to an update of
|
||||
!bt
|
||||
\[
|
||||
f_m(x) = f_{m-1}(x) +\beta_m G_m(x).
|
||||
\]
|
||||
!et
|
||||
This leads to the new weights
|
||||
!bt
|
||||
\[
|
||||
w_i^{m+1} = w_i^m \exp{(-y_i\beta_m G_m(x_i))}
|
||||
\]
|
||||
!et
|
||||
|
||||
|
||||
!split
|
||||
===== Adaptive boosting: AdaBoost, Basic Algorithm =====
|
||||
|
||||
The algorithm here is rather straightforward. Assume that our weak
|
||||
classifier is a decision tree and we consider a binary set of outputs
|
||||
with $y_i \in \{-1,1\}$ and $i=0,1,2,\dots,n-1$ as our set of
|
||||
observations. Our design matrix is given in terms of the
|
||||
feature/predictor vectors
|
||||
$\bm{X}=[\bm{x}_0\bm{x}_1\dots\bm{x}_{p-1}]$. Finally, we define also a
|
||||
classifier determined by our data via a function $G(x)$. This function tells us how well we are able to classify our outputs/targets $\bm{y}$.
|
||||
|
||||
We have already defined the misclassification error $\mathrm{err}$ as
|
||||
!bt
|
||||
\[
|
||||
\mathrm{err}=\frac{1}{n}\sum_{i=0}^{n-1}I(y_i\ne G(x_i)),
|
||||
\]
|
||||
!et
|
||||
where the function $I()$ is one if we misclassify and zero if we classify correctly.
|
||||
|
||||
!split
|
||||
===== Basic Steps of AdaBoost =====
|
||||
|
||||
With the above definitions we are now ready to set up the algorithm for AdaBoost.
|
||||
The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.
|
||||
o We start by initializing all weights to $w_i = 1/n$, with $i=0,1,2,\dots n-1$. It is easy to see that we must have $\sum_{i=0}^{n-1}w_i = 1$.
|
||||
o We rewrite the misclassification error as
|
||||
!bt
|
||||
\[
|
||||
\mathrm{\overline{err}}_m=\frac{\sum_{i=0}^{n-1}w_i^m I(y_i\ne G(x_i))}{\sum_{i=0}^{n-1}w_i},
|
||||
\]
|
||||
!et
|
||||
o Then we start looping over all attempts at classifying, namely we start an iterative process for $m=1:M$, where $M$ is the final number of classifications. Our given classifier could for example be a plain decision tree.
|
||||
o Fit then a given classifier to the training set using the weights $w_i$.
|
||||
o Compute then $\mathrm{err}$ and figure out which events are classified properly and which are classified wrongly.
|
||||
o Define a quantity $\alpha_{m} = \log{(1-\mathrm{\overline{err}}_m)/\mathrm{\overline{err}}_m}$
|
||||
o Set the new weights to $w_i = w_i\times \exp{(\alpha_m I(y_i\ne G(x_i)}$.
|
||||
o Compute the new classifier $G(x)= \sum_{i=0}^{n-1}\alpha_m I(y_i\ne G(x_i)$.
|
||||
|
||||
For the iterations with $m \le 2$ the weights are modified
|
||||
individually at each steps. The observations which were misclassified
|
||||
at iteration $m-1$ have a weight which is larger than those which were
|
||||
classified properly. As this proceeds, the observations which were
|
||||
difficult to classifiy correctly are given a larger influence. Each
|
||||
new classification step $m$ is then forced to concentrate on those
|
||||
observations that are missed in the previous iterations.
|
||||
|
||||
|
||||
|
||||
!split
|
||||
===== AdaBoost Examples =====
|
||||
|
||||
Using _Scikit-Learn_ it is easy to apply the adaptive boosting algorithm, as done here.
|
||||
|
||||
!bc pycod
|
||||
from sklearn.ensemble import AdaBoostClassifier
|
||||
|
||||
ada_clf = AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth=1), n_estimators=200,
|
||||
algorithm="SAMME.R", learning_rate=0.5, random_state=42)
|
||||
ada_clf.fit(X_train, y_train)
|
||||
|
||||
from sklearn.ensemble import AdaBoostClassifier
|
||||
|
||||
ada_clf = AdaBoostClassifier(
|
||||
DecisionTreeClassifier(max_depth=1), n_estimators=200,
|
||||
algorithm="SAMME.R", learning_rate=0.5, random_state=42)
|
||||
ada_clf.fit(X_train_scaled, y_train)
|
||||
y_pred = ada_clf.predict(X_test_scaled)
|
||||
skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
|
||||
plt.show()
|
||||
y_probas = ada_clf.predict_proba(X_test_scaled)
|
||||
skplt.metrics.plot_roc(y_test, y_probas)
|
||||
plt.show()
|
||||
skplt.metrics.plot_cumulative_gain(y_test, y_probas)
|
||||
plt.show()
|
||||
!ec
|
||||
|
||||
|
||||
Reference in New Issue
Block a user