added video on bootstrap
This commit is contained in:
Morten Hjorth-Jensen
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
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2,
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None,
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'other-measures-in-classification-studies-cancer-data-again'),
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('Friday September 25', 2, None, 'friday-september-25'),
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('Optimization, the central part of any Machine Learning '
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'algortithm',
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2,
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@@ -210,19 +209,18 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
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</ul>
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</li>
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@@ -277,7 +275,7 @@ MathJax.Hub.Config({
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<li><a href="._week38-bs008.html">9</a></li>
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<li><a href="._week38-bs009.html">10</a></li>
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<li><a href="">...</a></li>
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||||
<li><a href="._week38-bs042.html">43</a></li>
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<li><a href="._week38-bs041.html">42</a></li>
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<li><a href="._week38-bs001.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
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2,
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None,
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||||
'other-measures-in-classification-studies-cancer-data-again'),
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||||
('Friday September 25', 2, None, 'friday-september-25'),
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||||
('Optimization, the central part of any Machine Learning '
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||||
'algortithm',
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2,
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@@ -210,19 +209,18 @@ MathJax.Hub.Config({
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||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
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||||
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</ul>
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</li>
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@@ -238,7 +236,7 @@ MathJax.Hub.Config({
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<ul>
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<li> Lab Wednesday and Thursday: work on project 1</li>
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<li> Thursday: Summary of regression methods, cross-validation and discussion of project 1. Start Logistic Regression <a href="https://youtu.be/sdt_BFla8uA" target="_self">Video of lecture</a></li>
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<li> Thursday: Summary of regression methods, cross-validation and discussion of project 1. Start Logistic Regression <a href="https://youtu.be/sdt_BFla8uA" target="_self">Video of lecture</a> <a href="https://www.youtube.com/watch?v=Xz0x-8-cgaQ" target="_self">Video on Bootstrapping</a></li>
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<li> Friday: Classification problems and Logistic Regression, from binary cases to several categories. Start optimization methods</li>
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<li> Reading recommendations:
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<ol type="a"></li>
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@@ -264,7 +262,7 @@ MathJax.Hub.Config({
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<li><a href="._week38-bs009.html">10</a></li>
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<li><a href="._week38-bs010.html">11</a></li>
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<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
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||||
<li><a href="._week38-bs041.html">42</a></li>
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||||
<li><a href="._week38-bs002.html">»</a></li>
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||||
</ul>
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||||
<!-- ------------------- end of main content --------------- -->
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@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
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||||
2,
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||||
None,
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||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
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||||
'algortithm',
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2,
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@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
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||||
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</ul>
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||||
</li>
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||||
@@ -305,7 +303,7 @@ $$
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<li><a href="._week38-bs010.html">11</a></li>
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||||
<li><a href="._week38-bs011.html">12</a></li>
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||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs003.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -270,7 +268,7 @@ cross-validation (LOOCV).
|
||||
<li><a href="._week38-bs011.html">12</a></li>
|
||||
<li><a href="._week38-bs012.html">13</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs004.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -274,7 +272,7 @@ $$
|
||||
<li><a href="._week38-bs012.html">13</a></li>
|
||||
<li><a href="._week38-bs013.html">14</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs005.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -270,7 +268,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week38-bs013.html">14</a></li>
|
||||
<li><a href="._week38-bs014.html">15</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs006.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -370,7 +368,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week38-bs014.html">15</a></li>
|
||||
<li><a href="._week38-bs015.html">16</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs007.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -271,7 +269,7 @@ simple recipe for fitting our data.
|
||||
<li><a href="._week38-bs015.html">16</a></li>
|
||||
<li><a href="._week38-bs016.html">17</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs008.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -277,7 +275,7 @@ failure etc.
|
||||
<li><a href="._week38-bs016.html">17</a></li>
|
||||
<li><a href="._week38-bs017.html">18</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs009.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -276,7 +274,7 @@ models, as we will see later.
|
||||
<li><a href="._week38-bs017.html">18</a></li>
|
||||
<li><a href="._week38-bs018.html">19</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs010.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -284,7 +282,7 @@ $$
|
||||
<li><a href="._week38-bs018.html">19</a></li>
|
||||
<li><a href="._week38-bs019.html">20</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs011.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -281,7 +279,7 @@ $$
|
||||
<li><a href="._week38-bs019.html">20</a></li>
|
||||
<li><a href="._week38-bs020.html">21</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs012.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -281,7 +279,7 @@ the probability of a given category. This leads us to the logistic function.
|
||||
<li><a href="._week38-bs020.html">21</a></li>
|
||||
<li><a href="._week38-bs021.html">22</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs013.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -340,7 +338,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week38-bs021.html">22</a></li>
|
||||
<li><a href="._week38-bs022.html">23</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs014.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -312,7 +310,7 @@ representing the probability for finding a value of \( y_i \) with a given
|
||||
<li><a href="._week38-bs022.html">23</a></li>
|
||||
<li><a href="._week38-bs023.html">24</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs015.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -279,7 +277,7 @@ $$
|
||||
<li><a href="._week38-bs023.html">24</a></li>
|
||||
<li><a href="._week38-bs024.html">25</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs016.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -340,7 +338,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week38-bs024.html">25</a></li>
|
||||
<li><a href="._week38-bs025.html">26</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs017.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -277,7 +275,7 @@ $$
|
||||
<li><a href="._week38-bs025.html">26</a></li>
|
||||
<li><a href="._week38-bs026.html">27</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs018.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -280,7 +278,7 @@ $$
|
||||
<li><a href="._week38-bs026.html">27</a></li>
|
||||
<li><a href="._week38-bs027.html">28</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs019.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -277,7 +275,7 @@ in practice we often supplement the cross-entropy with additional regularization
|
||||
<li><a href="._week38-bs027.html">28</a></li>
|
||||
<li><a href="._week38-bs028.html">29</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs020.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -279,7 +277,7 @@ $$
|
||||
<li><a href="._week38-bs028.html">29</a></li>
|
||||
<li><a href="._week38-bs029.html">30</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs021.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -280,7 +278,7 @@ $$
|
||||
<li><a href="._week38-bs029.html">30</a></li>
|
||||
<li><a href="._week38-bs030.html">31</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs022.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -272,7 +270,7 @@ $$
|
||||
<li><a href="._week38-bs030.html">31</a></li>
|
||||
<li><a href="._week38-bs031.html">32</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs023.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -284,7 +282,7 @@ $$
|
||||
<li><a href="._week38-bs031.html">32</a></li>
|
||||
<li><a href="._week38-bs032.html">33</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs024.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -296,7 +294,7 @@ methods</a>.
|
||||
<li><a href="._week38-bs032.html">33</a></li>
|
||||
<li><a href="._week38-bs033.html">34</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs025.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -261,7 +259,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week38-bs033.html">34</a></li>
|
||||
<li><a href="._week38-bs034.html">35</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs026.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -314,7 +312,7 @@ logreg<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
<li><a href="._week38-bs034.html">35</a></li>
|
||||
<li><a href="._week38-bs035.html">36</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs027.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -321,7 +319,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week38-bs035.html">36</a></li>
|
||||
<li><a href="._week38-bs036.html">37</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs028.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -329,7 +327,7 @@ applications. This will be discussed later this semester (<a href="https://compp
|
||||
<li><a href="._week38-bs036.html">37</a></li>
|
||||
<li><a href="._week38-bs037.html">38</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs029.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -327,7 +325,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week38-bs037.html">38</a></li>
|
||||
<li><a href="._week38-bs038.html">39</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs030.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -234,7 +232,19 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0030"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="friday-september-25" class="anchor">Friday September 25 </h2>
|
||||
<h2 id="optimization-the-central-part-of-any-machine-learning-algortithm" class="anchor">Optimization, the central part of any Machine Learning algortithm </h2>
|
||||
|
||||
<a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/OverarchingAimsWeek39.mp4?vrtx=view-as-webpage" target="_self">Overview Video, why do we care about gradient methods?</a>
|
||||
|
||||
<p>Almost every problem in machine learning and data science starts with
|
||||
a dataset \( X \), a model \( g(\beta) \), which is a function of the
|
||||
parameters \( \beta \) and a cost function \( C(X, g(\beta)) \) that allows
|
||||
us to judge how well the model \( g(\beta) \) explains the observations
|
||||
\( X \). The model is fit by finding the values of \( \beta \) that minimize
|
||||
the cost function. Ideally we would be able to solve for \( \beta \)
|
||||
analytically, however this is not possible in general and we must use
|
||||
some approximative/numerical method to compute the minimum.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -261,7 +271,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week38-bs038.html">39</a></li>
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs031.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -234,20 +232,25 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0031"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="optimization-the-central-part-of-any-machine-learning-algortithm" class="anchor">Optimization, the central part of any Machine Learning algortithm </h2>
|
||||
<h2 id="revisiting-our-logistic-regression-case" class="anchor">Revisiting our Logistic Regression case </h2>
|
||||
|
||||
<a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/OverarchingAimsWeek39.mp4?vrtx=view-as-webpage" target="_self">Overview Video, why do we care about gradient methods?</a>
|
||||
|
||||
<p>Almost every problem in machine learning and data science starts with
|
||||
a dataset \( X \), a model \( g(\beta) \), which is a function of the
|
||||
parameters \( \beta \) and a cost function \( C(X, g(\beta)) \) that allows
|
||||
us to judge how well the model \( g(\beta) \) explains the observations
|
||||
\( X \). The model is fit by finding the values of \( \beta \) that minimize
|
||||
the cost function. Ideally we would be able to solve for \( \beta \)
|
||||
analytically, however this is not possible in general and we must use
|
||||
some approximative/numerical method to compute the minimum.
|
||||
<p>In our discussion on Logistic Regression we studied the
|
||||
case of
|
||||
two classes, with \( y_i \) either
|
||||
\( 0 \) or \( 1 \). Furthermore we assumed also that we have only two
|
||||
parameters \( \beta \) in our fitting, that is we
|
||||
defined probabilities
|
||||
</p>
|
||||
|
||||
$$
|
||||
\begin{align*}
|
||||
p(y_i=1|x_i,\boldsymbol{\beta}) &= \frac{\exp{(\beta_0+\beta_1x_i)}}{1+\exp{(\beta_0+\beta_1x_i)}},\nonumber\\
|
||||
p(y_i=0|x_i,\boldsymbol{\beta}) &= 1 - p(y_i=1|x_i,\boldsymbol{\beta}),
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
<p>where \( \boldsymbol{\beta} \) are the weights we wish to extract from data, in our case \( \beta_0 \) and \( \beta_1 \). </p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -273,7 +276,7 @@ some approximative/numerical method to compute the minimum.
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs032.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -234,24 +232,28 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0032"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="revisiting-our-logistic-regression-case" class="anchor">Revisiting our Logistic Regression case </h2>
|
||||
<h2 id="the-equations-to-solve" class="anchor">The equations to solve </h2>
|
||||
|
||||
<p>In our discussion on Logistic Regression we studied the
|
||||
case of
|
||||
two classes, with \( y_i \) either
|
||||
\( 0 \) or \( 1 \). Furthermore we assumed also that we have only two
|
||||
parameters \( \beta \) in our fitting, that is we
|
||||
defined probabilities
|
||||
<p>Our compact equations used a definition of a vector \( \boldsymbol{y} \) with \( n \)
|
||||
elements \( y_i \), an \( n\times p \) matrix \( \boldsymbol{X} \) which contains the
|
||||
\( x_i \) values and a vector \( \boldsymbol{p} \) of fitted probabilities
|
||||
\( p(y_i\vert x_i,\boldsymbol{\beta}) \). We rewrote in a more compact form
|
||||
the first derivative of the cost function as
|
||||
</p>
|
||||
|
||||
$$
|
||||
\begin{align*}
|
||||
p(y_i=1|x_i,\boldsymbol{\beta}) &= \frac{\exp{(\beta_0+\beta_1x_i)}}{1+\exp{(\beta_0+\beta_1x_i)}},\nonumber\\
|
||||
p(y_i=0|x_i,\boldsymbol{\beta}) &= 1 - p(y_i=1|x_i,\boldsymbol{\beta}),
|
||||
\end{align*}
|
||||
\frac{\partial \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}} = -\boldsymbol{X}^T\left(\boldsymbol{y}-\boldsymbol{p}\right).
|
||||
$$
|
||||
|
||||
<p>where \( \boldsymbol{\beta} \) are the weights we wish to extract from data, in our case \( \beta_0 \) and \( \beta_1 \). </p>
|
||||
<p>If we in addition define a diagonal matrix \( \boldsymbol{W} \) with elements
|
||||
\( p(y_i\vert x_i,\boldsymbol{\beta})(1-p(y_i\vert x_i,\boldsymbol{\beta}) \), we can obtain a compact expression of the second derivative as
|
||||
</p>
|
||||
|
||||
$$
|
||||
\frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T} = \boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X}.
|
||||
$$
|
||||
|
||||
<p>This defines what is called the Hessian matrix.</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -277,8 +279,6 @@ $$
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs033.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -234,28 +232,25 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0033"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="the-equations-to-solve" class="anchor">The equations to solve </h2>
|
||||
<h2 id="solving-using-newton-raphson-s-method" class="anchor">Solving using Newton-Raphson's method </h2>
|
||||
|
||||
<p>Our compact equations used a definition of a vector \( \boldsymbol{y} \) with \( n \)
|
||||
elements \( y_i \), an \( n\times p \) matrix \( \boldsymbol{X} \) which contains the
|
||||
\( x_i \) values and a vector \( \boldsymbol{p} \) of fitted probabilities
|
||||
\( p(y_i\vert x_i,\boldsymbol{\beta}) \). We rewrote in a more compact form
|
||||
the first derivative of the cost function as
|
||||
</p>
|
||||
<p>If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the matrices that define the first and second derivatives. </p>
|
||||
|
||||
<p>Our iterative scheme is then given by</p>
|
||||
|
||||
$$
|
||||
\frac{\partial \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}} = -\boldsymbol{X}^T\left(\boldsymbol{y}-\boldsymbol{p}\right).
|
||||
\boldsymbol{\beta}^{\mathrm{new}} = \boldsymbol{\beta}^{\mathrm{old}}-\left(\frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T}\right)^{-1}_{\boldsymbol{\beta}^{\mathrm{old}}}\times \left(\frac{\partial \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}}\right)_{\boldsymbol{\beta}^{\mathrm{old}}},
|
||||
$$
|
||||
|
||||
<p>If we in addition define a diagonal matrix \( \boldsymbol{W} \) with elements
|
||||
\( p(y_i\vert x_i,\boldsymbol{\beta})(1-p(y_i\vert x_i,\boldsymbol{\beta}) \), we can obtain a compact expression of the second derivative as
|
||||
</p>
|
||||
<p>or in matrix form as</p>
|
||||
|
||||
$$
|
||||
\frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T} = \boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X}.
|
||||
\boldsymbol{\beta}^{\mathrm{new}} = \boldsymbol{\beta}^{\mathrm{old}}-\left(\boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X} \right)^{-1}\times \left(-\boldsymbol{X}^T(\boldsymbol{y}-\boldsymbol{p}) \right)_{\boldsymbol{\beta}^{\mathrm{old}}}.
|
||||
$$
|
||||
|
||||
<p>This defines what is called the Hessian matrix.</p>
|
||||
<p>The right-hand side is computed with the old values of \( \beta \). </p>
|
||||
|
||||
<p>If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement. </p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -280,7 +275,6 @@ $$
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs034.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -234,25 +232,18 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0034"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="solving-using-newton-raphson-s-method" class="anchor">Solving using Newton-Raphson's method </h2>
|
||||
<h2 id="brief-reminder-on-newton-raphson-s-method" class="anchor">Brief reminder on Newton-Raphson's method </h2>
|
||||
|
||||
<p>If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the matrices that define the first and second derivatives. </p>
|
||||
<p>Let us quickly remind ourselves how we derive the above method.</p>
|
||||
|
||||
<p>Our iterative scheme is then given by</p>
|
||||
|
||||
$$
|
||||
\boldsymbol{\beta}^{\mathrm{new}} = \boldsymbol{\beta}^{\mathrm{old}}-\left(\frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T}\right)^{-1}_{\boldsymbol{\beta}^{\mathrm{old}}}\times \left(\frac{\partial \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}}\right)_{\boldsymbol{\beta}^{\mathrm{old}}},
|
||||
$$
|
||||
|
||||
<p>or in matrix form as</p>
|
||||
|
||||
$$
|
||||
\boldsymbol{\beta}^{\mathrm{new}} = \boldsymbol{\beta}^{\mathrm{old}}-\left(\boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X} \right)^{-1}\times \left(-\boldsymbol{X}^T(\boldsymbol{y}-\boldsymbol{p}) \right)_{\boldsymbol{\beta}^{\mathrm{old}}}.
|
||||
$$
|
||||
|
||||
<p>The right-hand side is computed with the old values of \( \beta \). </p>
|
||||
|
||||
<p>If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement. </p>
|
||||
<p>Perhaps the most celebrated of all one-dimensional root-finding
|
||||
routines is Newton's method, also called the Newton-Raphson
|
||||
method. This method requires the evaluation of both the
|
||||
function \( f \) and its derivative \( f' \) at arbitrary points.
|
||||
If you can only calculate the derivative
|
||||
numerically and/or your function is not of the smooth type, we
|
||||
normally discourage the use of this method.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -276,7 +267,6 @@ $$
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs035.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -234,19 +232,39 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0035"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="brief-reminder-on-newton-raphson-s-method" class="anchor">Brief reminder on Newton-Raphson's method </h2>
|
||||
<h2 id="the-equations" class="anchor">The equations </h2>
|
||||
|
||||
<p>Let us quickly remind ourselves how we derive the above method.</p>
|
||||
|
||||
<p>Perhaps the most celebrated of all one-dimensional root-finding
|
||||
routines is Newton's method, also called the Newton-Raphson
|
||||
method. This method requires the evaluation of both the
|
||||
function \( f \) and its derivative \( f' \) at arbitrary points.
|
||||
If you can only calculate the derivative
|
||||
numerically and/or your function is not of the smooth type, we
|
||||
normally discourage the use of this method.
|
||||
<p>The Newton-Raphson formula consists geometrically of extending the
|
||||
tangent line at a current point until it crosses zero, then setting
|
||||
the next guess to the abscissa of that zero-crossing. The mathematics
|
||||
behind this method is rather simple. Employing a Taylor expansion for
|
||||
\( x \) sufficiently close to the solution \( s \), we have
|
||||
</p>
|
||||
|
||||
$$
|
||||
f(s)=0=f(x)+(s-x)f'(x)+\frac{(s-x)^2}{2}f''(x) +\dots.
|
||||
\tag{2}
|
||||
$$
|
||||
|
||||
<p>For small enough values of the function and for well-behaved
|
||||
functions, the terms beyond linear are unimportant, hence we obtain
|
||||
</p>
|
||||
|
||||
$$
|
||||
f(x)+(s-x)f'(x)\approx 0,
|
||||
$$
|
||||
|
||||
<p>yielding</p>
|
||||
$$
|
||||
s\approx x-\frac{f(x)}{f'(x)}.
|
||||
$$
|
||||
|
||||
<p>Having in mind an iterative procedure, it is natural to start iterating with</p>
|
||||
$$
|
||||
x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}.
|
||||
$$
|
||||
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -268,7 +286,6 @@ normally discourage the use of this method.
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs036.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -234,39 +232,21 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0036"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="the-equations" class="anchor">The equations </h2>
|
||||
<h2 id="simple-geometric-interpretation" class="anchor">Simple geometric interpretation </h2>
|
||||
|
||||
<p>The Newton-Raphson formula consists geometrically of extending the
|
||||
tangent line at a current point until it crosses zero, then setting
|
||||
the next guess to the abscissa of that zero-crossing. The mathematics
|
||||
behind this method is rather simple. Employing a Taylor expansion for
|
||||
\( x \) sufficiently close to the solution \( s \), we have
|
||||
<p>The above is Newton-Raphson's method. It has a simple geometric
|
||||
interpretation, namely \( x_{n+1} \) is the point where the tangent from
|
||||
\( (x_n,f(x_n)) \) crosses the \( x \)-axis. Close to the solution,
|
||||
Newton-Raphson converges fast to the desired result. However, if we
|
||||
are far from a root, where the higher-order terms in the series are
|
||||
important, the Newton-Raphson formula can give grossly inaccurate
|
||||
results. For instance, the initial guess for the root might be so far
|
||||
from the true root as to let the search interval include a local
|
||||
maximum or minimum of the function. If an iteration places a trial
|
||||
guess near such a local extremum, so that the first derivative nearly
|
||||
vanishes, then Newton-Raphson may fail totally
|
||||
</p>
|
||||
|
||||
$$
|
||||
f(s)=0=f(x)+(s-x)f'(x)+\frac{(s-x)^2}{2}f''(x) +\dots.
|
||||
\tag{2}
|
||||
$$
|
||||
|
||||
<p>For small enough values of the function and for well-behaved
|
||||
functions, the terms beyond linear are unimportant, hence we obtain
|
||||
</p>
|
||||
|
||||
$$
|
||||
f(x)+(s-x)f'(x)\approx 0,
|
||||
$$
|
||||
|
||||
<p>yielding</p>
|
||||
$$
|
||||
s\approx x-\frac{f(x)}{f'(x)}.
|
||||
$$
|
||||
|
||||
<p>Having in mind an iterative procedure, it is natural to start iterating with</p>
|
||||
$$
|
||||
x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}.
|
||||
$$
|
||||
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -287,7 +267,6 @@ $$
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs037.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -234,19 +232,57 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0037"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="simple-geometric-interpretation" class="anchor">Simple geometric interpretation </h2>
|
||||
<h2 id="extending-to-more-than-one-variable" class="anchor">Extending to more than one variable </h2>
|
||||
|
||||
<p>The above is Newton-Raphson's method. It has a simple geometric
|
||||
interpretation, namely \( x_{n+1} \) is the point where the tangent from
|
||||
\( (x_n,f(x_n)) \) crosses the \( x \)-axis. Close to the solution,
|
||||
Newton-Raphson converges fast to the desired result. However, if we
|
||||
are far from a root, where the higher-order terms in the series are
|
||||
important, the Newton-Raphson formula can give grossly inaccurate
|
||||
results. For instance, the initial guess for the root might be so far
|
||||
from the true root as to let the search interval include a local
|
||||
maximum or minimum of the function. If an iteration places a trial
|
||||
guess near such a local extremum, so that the first derivative nearly
|
||||
vanishes, then Newton-Raphson may fail totally
|
||||
<p>Newton's method can be generalized to systems of several non-linear equations
|
||||
and variables. Consider the case with two equations
|
||||
</p>
|
||||
$$
|
||||
\begin{array}{cc} f_1(x_1,x_2) &=0\\
|
||||
f_2(x_1,x_2) &=0,\end{array}
|
||||
$$
|
||||
|
||||
<p>which we Taylor expand to obtain</p>
|
||||
|
||||
$$
|
||||
\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1
|
||||
\partial f_1/\partial x_1+h_2
|
||||
\partial f_1/\partial x_2+\dots\\
|
||||
0=f_2(x_1+h_1,x_2+h_2)=&f_2(x_1,x_2)+h_1
|
||||
\partial f_2/\partial x_1+h_2
|
||||
\partial f_2/\partial x_2+\dots
|
||||
\end{array}.
|
||||
$$
|
||||
|
||||
<p>Defining the Jacobian matrix \( {\bf \boldsymbol{J}} \) we have</p>
|
||||
$$
|
||||
{\bf \boldsymbol{J}}=\left( \begin{array}{cc}
|
||||
\partial f_1/\partial x_1 & \partial f_1/\partial x_2 \\
|
||||
\partial f_2/\partial x_1 &\partial f_2/\partial x_2
|
||||
\end{array} \right),
|
||||
$$
|
||||
|
||||
<p>we can rephrase Newton's method as</p>
|
||||
$$
|
||||
\left(\begin{array}{c} x_1^{n+1} \\ x_2^{n+1} \end{array} \right)=
|
||||
\left(\begin{array}{c} x_1^{n} \\ x_2^{n} \end{array} \right)+
|
||||
\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right),
|
||||
$$
|
||||
|
||||
<p>where we have defined</p>
|
||||
$$
|
||||
\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right)=
|
||||
-{\bf \boldsymbol{J}}^{-1}
|
||||
\left(\begin{array}{c} f_1(x_1^{n},x_2^{n}) \\ f_2(x_1^{n},x_2^{n}) \end{array} \right).
|
||||
$$
|
||||
|
||||
<p>We need thus to compute the inverse of the Jacobian matrix and it
|
||||
is to understand that difficulties may
|
||||
arise in case \( {\bf \boldsymbol{J}} \) is nearly singular.
|
||||
</p>
|
||||
|
||||
<p>It is rather straightforward to extend the above scheme to systems of
|
||||
more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -268,7 +304,6 @@ vanishes, then Newton-Raphson may fail totally
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs038.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -234,57 +232,24 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0038"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="extending-to-more-than-one-variable" class="anchor">Extending to more than one variable </h2>
|
||||
<h2 id="steepest-descent" class="anchor">Steepest descent </h2>
|
||||
|
||||
<p>Newton's method can be generalized to systems of several non-linear equations
|
||||
and variables. Consider the case with two equations
|
||||
</p>
|
||||
$$
|
||||
\begin{array}{cc} f_1(x_1,x_2) &=0\\
|
||||
f_2(x_1,x_2) &=0,\end{array}
|
||||
$$
|
||||
|
||||
<p>which we Taylor expand to obtain</p>
|
||||
|
||||
$$
|
||||
\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1
|
||||
\partial f_1/\partial x_1+h_2
|
||||
\partial f_1/\partial x_2+\dots\\
|
||||
0=f_2(x_1+h_1,x_2+h_2)=&f_2(x_1,x_2)+h_1
|
||||
\partial f_2/\partial x_1+h_2
|
||||
\partial f_2/\partial x_2+\dots
|
||||
\end{array}.
|
||||
$$
|
||||
|
||||
<p>Defining the Jacobian matrix \( {\bf \boldsymbol{J}} \) we have</p>
|
||||
$$
|
||||
{\bf \boldsymbol{J}}=\left( \begin{array}{cc}
|
||||
\partial f_1/\partial x_1 & \partial f_1/\partial x_2 \\
|
||||
\partial f_2/\partial x_1 &\partial f_2/\partial x_2
|
||||
\end{array} \right),
|
||||
$$
|
||||
|
||||
<p>we can rephrase Newton's method as</p>
|
||||
$$
|
||||
\left(\begin{array}{c} x_1^{n+1} \\ x_2^{n+1} \end{array} \right)=
|
||||
\left(\begin{array}{c} x_1^{n} \\ x_2^{n} \end{array} \right)+
|
||||
\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right),
|
||||
$$
|
||||
|
||||
<p>where we have defined</p>
|
||||
$$
|
||||
\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right)=
|
||||
-{\bf \boldsymbol{J}}^{-1}
|
||||
\left(\begin{array}{c} f_1(x_1^{n},x_2^{n}) \\ f_2(x_1^{n},x_2^{n}) \end{array} \right).
|
||||
$$
|
||||
|
||||
<p>We need thus to compute the inverse of the Jacobian matrix and it
|
||||
is to understand that difficulties may
|
||||
arise in case \( {\bf \boldsymbol{J}} \) is nearly singular.
|
||||
<p>The basic idea of gradient descent is
|
||||
that a function \( F(\mathbf{x}) \),
|
||||
\( \mathbf{x} \equiv (x_1,\cdots,x_n) \), decreases fastest if one goes from \( \bf {x} \) in the
|
||||
direction of the negative gradient \( -\nabla F(\mathbf{x}) \).
|
||||
</p>
|
||||
|
||||
<p>It is rather straightforward to extend the above scheme to systems of
|
||||
more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function.
|
||||
<p>It can be shown that if </p>
|
||||
$$
|
||||
\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k),
|
||||
$$
|
||||
|
||||
<p>with \( \gamma_k > 0 \).</p>
|
||||
|
||||
<p>For \( \gamma_k \) small enough, then \( F(\mathbf{x}_{k+1}) \leq
|
||||
F(\mathbf{x}_k) \). This means that for a sufficiently small \( \gamma_k \)
|
||||
we are always moving towards smaller function values, i.e a minimum.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -305,7 +270,6 @@ more than two non-linear equations. In our case, the Jacobian matrix is given by
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs039.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -233,25 +231,21 @@ MathJax.Hub.Config({
|
||||
<div class="container">
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0039"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="steepest-descent" class="anchor">Steepest descent </h2>
|
||||
<!-- !split -->
|
||||
<h2 id="more-on-steepest-descent" class="anchor">More on Steepest descent </h2>
|
||||
|
||||
<p>The basic idea of gradient descent is
|
||||
that a function \( F(\mathbf{x}) \),
|
||||
\( \mathbf{x} \equiv (x_1,\cdots,x_n) \), decreases fastest if one goes from \( \bf {x} \) in the
|
||||
direction of the negative gradient \( -\nabla F(\mathbf{x}) \).
|
||||
<p>The previous observation is the basis of the method of steepest
|
||||
descent, which is also referred to as just gradient descent (GD). One
|
||||
starts with an initial guess \( \mathbf{x}_0 \) for a minimum of \( F \) and
|
||||
computes new approximations according to
|
||||
</p>
|
||||
|
||||
<p>It can be shown that if </p>
|
||||
$$
|
||||
\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k),
|
||||
\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k), \ \ k \geq 0.
|
||||
$$
|
||||
|
||||
<p>with \( \gamma_k > 0 \).</p>
|
||||
|
||||
<p>For \( \gamma_k \) small enough, then \( F(\mathbf{x}_{k+1}) \leq
|
||||
F(\mathbf{x}_k) \). This means that for a sufficiently small \( \gamma_k \)
|
||||
we are always moving towards smaller function values, i.e a minimum.
|
||||
<p>The parameter \( \gamma_k \) is often referred to as the step length or
|
||||
the learning rate within the context of Machine Learning.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -271,7 +265,6 @@ we are always moving towards smaller function values, i.e a minimum.
|
||||
<li class="active"><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs040.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -234,20 +232,27 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0040"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="more-on-steepest-descent" class="anchor">More on Steepest descent </h2>
|
||||
<h2 id="the-ideal" class="anchor">The ideal </h2>
|
||||
|
||||
<p>The previous observation is the basis of the method of steepest
|
||||
descent, which is also referred to as just gradient descent (GD). One
|
||||
starts with an initial guess \( \mathbf{x}_0 \) for a minimum of \( F \) and
|
||||
computes new approximations according to
|
||||
<p>Ideally the sequence \( \{\mathbf{x}_k \}_{k=0} \) converges to a global
|
||||
minimum of the function \( F \). In general we do not know if we are in a
|
||||
global or local minimum. In the special case when \( F \) is a convex
|
||||
function, all local minima are also global minima, so in this case
|
||||
gradient descent can converge to the global solution. The advantage of
|
||||
this scheme is that it is conceptually simple and straightforward to
|
||||
implement. However the method in this form has some severe
|
||||
limitations:
|
||||
</p>
|
||||
|
||||
$$
|
||||
\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k), \ \ k \geq 0.
|
||||
$$
|
||||
<p>In machine learing we are often faced with non-convex high dimensional
|
||||
cost functions with many local minima. Since GD is deterministic we
|
||||
will get stuck in a local minimum, if the method converges, unless we
|
||||
have a very good intial guess. This also implies that the scheme is
|
||||
sensitive to the chosen initial condition.
|
||||
</p>
|
||||
|
||||
<p>The parameter \( \gamma_k \) is often referred to as the step length or
|
||||
the learning rate within the context of Machine Learning.
|
||||
<p>Note that the gradient is a function of \( \mathbf{x} =
|
||||
(x_1,\cdots,x_n) \) which makes it expensive to compute numerically.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -266,7 +271,6 @@ the learning rate within the context of Machine Learning.
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li class="active"><a href="._week38-bs040.html">41</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -234,27 +232,20 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
<a name="part0041"></a>
|
||||
<!-- !split -->
|
||||
<h2 id="the-ideal" class="anchor">The ideal </h2>
|
||||
<h2 id="the-sensitiveness-of-the-gradient-descent" class="anchor">The sensitiveness of the gradient descent </h2>
|
||||
|
||||
<p>Ideally the sequence \( \{\mathbf{x}_k \}_{k=0} \) converges to a global
|
||||
minimum of the function \( F \). In general we do not know if we are in a
|
||||
global or local minimum. In the special case when \( F \) is a convex
|
||||
function, all local minima are also global minima, so in this case
|
||||
gradient descent can converge to the global solution. The advantage of
|
||||
this scheme is that it is conceptually simple and straightforward to
|
||||
implement. However the method in this form has some severe
|
||||
limitations:
|
||||
<p>The gradient descent method
|
||||
is sensitive to the choice of learning rate \( \gamma_k \). This is due
|
||||
to the fact that we are only guaranteed that \( F(\mathbf{x}_{k+1}) \leq
|
||||
F(\mathbf{x}_k) \) for sufficiently small \( \gamma_k \). The problem is to
|
||||
determine an optimal learning rate. If the learning rate is chosen too
|
||||
small the method will take a long time to converge and if it is too
|
||||
large we can experience erratic behavior.
|
||||
</p>
|
||||
|
||||
<p>In machine learing we are often faced with non-convex high dimensional
|
||||
cost functions with many local minima. Since GD is deterministic we
|
||||
will get stuck in a local minimum, if the method converges, unless we
|
||||
have a very good intial guess. This also implies that the scheme is
|
||||
sensitive to the chosen initial condition.
|
||||
</p>
|
||||
|
||||
<p>Note that the gradient is a function of \( \mathbf{x} =
|
||||
(x_1,\cdots,x_n) \) which makes it expensive to compute numerically.
|
||||
<p>Many of these shortcomings can be alleviated by introducing
|
||||
randomness. One such method is that of Stochastic Gradient Descent
|
||||
(SGD), see below.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -272,8 +263,6 @@ sensitive to the chosen initial condition.
|
||||
<li><a href="._week38-bs039.html">40</a></li>
|
||||
<li><a href="._week38-bs040.html">41</a></li>
|
||||
<li class="active"><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs042.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
</div> <!-- end container -->
|
||||
|
||||
@@ -112,7 +112,6 @@ doconce format html week38.do.txt --html_style=bootstrap --pygments_html_style=d
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -210,19 +209,18 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs027.html#using-the-correlation-matrix" style="font-size: 80%;">Using the correlation matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs028.html#discussing-the-correlation-data" style="font-size: 80%;">Discussing the correlation data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs029.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;">Other measures in classification studies: Cancer Data again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#friday-september-25" style="font-size: 80%;">Friday September 25</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs042.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs030.html#optimization-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs031.html#revisiting-our-logistic-regression-case" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs032.html#the-equations-to-solve" style="font-size: 80%;">The equations to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs033.html#solving-using-newton-raphson-s-method" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs034.html#brief-reminder-on-newton-raphson-s-method" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs035.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs036.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs037.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs038.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs039.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs040.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week38-bs041.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -277,7 +275,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week38-bs008.html">9</a></li>
|
||||
<li><a href="._week38-bs009.html">10</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week38-bs042.html">43</a></li>
|
||||
<li><a href="._week38-bs041.html">42</a></li>
|
||||
<li><a href="._week38-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -199,7 +199,7 @@ MathJax.Hub.Config({
|
||||
|
||||
<ul>
|
||||
<p><li> Lab Wednesday and Thursday: work on project 1</li>
|
||||
<p><li> Thursday: Summary of regression methods, cross-validation and discussion of project 1. Start Logistic Regression <a href="https://youtu.be/sdt_BFla8uA" target="_blank">Video of lecture</a></li>
|
||||
<p><li> Thursday: Summary of regression methods, cross-validation and discussion of project 1. Start Logistic Regression <a href="https://youtu.be/sdt_BFla8uA" target="_blank">Video of lecture</a> <a href="https://www.youtube.com/watch?v=Xz0x-8-cgaQ" target="_blank">Video on Bootstrapping</a></li>
|
||||
<p><li> Friday: Classification problems and Logistic Regression, from binary cases to several categories. Start optimization methods</li>
|
||||
<p><li> Reading recommendations:
|
||||
<ol type="a"></li>
|
||||
@@ -1328,10 +1328,6 @@ plt.show()
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="friday-september-25">Friday September 25 </h2>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2 id="optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm </h2>
|
||||
|
||||
|
||||
@@ -113,7 +113,6 @@ div.toc p,a {
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -194,7 +193,7 @@ MathJax.Hub.Config({
|
||||
|
||||
<ul>
|
||||
<li> Lab Wednesday and Thursday: work on project 1</li>
|
||||
<li> Thursday: Summary of regression methods, cross-validation and discussion of project 1. Start Logistic Regression <a href="https://youtu.be/sdt_BFla8uA" target="_blank">Video of lecture</a></li>
|
||||
<li> Thursday: Summary of regression methods, cross-validation and discussion of project 1. Start Logistic Regression <a href="https://youtu.be/sdt_BFla8uA" target="_blank">Video of lecture</a> <a href="https://www.youtube.com/watch?v=Xz0x-8-cgaQ" target="_blank">Video on Bootstrapping</a></li>
|
||||
<li> Friday: Classification problems and Logistic Regression, from binary cases to several categories. Start optimization methods</li>
|
||||
<li> Reading recommendations:
|
||||
<ol type="a"></li>
|
||||
@@ -1243,9 +1242,6 @@ plt.show()
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="friday-september-25">Friday September 25 </h2>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm </h2>
|
||||
|
||||
|
||||
@@ -190,7 +190,6 @@ div.toc p,a {
|
||||
2,
|
||||
None,
|
||||
'other-measures-in-classification-studies-cancer-data-again'),
|
||||
('Friday September 25', 2, None, 'friday-september-25'),
|
||||
('Optimization, the central part of any Machine Learning '
|
||||
'algortithm',
|
||||
2,
|
||||
@@ -271,7 +270,7 @@ MathJax.Hub.Config({
|
||||
|
||||
<ul>
|
||||
<li> Lab Wednesday and Thursday: work on project 1</li>
|
||||
<li> Thursday: Summary of regression methods, cross-validation and discussion of project 1. Start Logistic Regression <a href="https://youtu.be/sdt_BFla8uA" target="_blank">Video of lecture</a></li>
|
||||
<li> Thursday: Summary of regression methods, cross-validation and discussion of project 1. Start Logistic Regression <a href="https://youtu.be/sdt_BFla8uA" target="_blank">Video of lecture</a> <a href="https://www.youtube.com/watch?v=Xz0x-8-cgaQ" target="_blank">Video on Bootstrapping</a></li>
|
||||
<li> Friday: Classification problems and Logistic Regression, from binary cases to several categories. Start optimization methods</li>
|
||||
<li> Reading recommendations:
|
||||
<ol type="a"></li>
|
||||
@@ -1320,9 +1319,6 @@ plt<span style="color: #666666">.</span>show()
|
||||
</div>
|
||||
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="friday-september-25">Friday September 25 </h2>
|
||||
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
<h2 id="optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm </h2>
|
||||
|
||||
|
||||
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-148
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Load Diff
@@ -12,6 +12,7 @@ DATE: September 22 and 23
|
||||
* Lab Wednesday and Thursday: work on project 1
|
||||
* Thursday: Summary of regression methods, cross-validation and discussion of project 1. Start Logistic Regression
|
||||
"Video of lecture":"https://youtu.be/sdt_BFla8uA"
|
||||
"Video on Bootstrapping":"https://www.youtube.com/watch?v=Xz0x-8-cgaQ"
|
||||
* Friday: Classification problems and Logistic Regression, from binary cases to several categories. Start optimization methods
|
||||
|
||||
* Reading recommendations:
|
||||
@@ -906,11 +907,6 @@ plt.show()
|
||||
!ec
|
||||
|
||||
|
||||
!split
|
||||
===== Friday September 25 =====
|
||||
|
||||
|
||||
|
||||
|
||||
!split
|
||||
===== Optimization, the central part of any Machine Learning algortithm =====
|
||||
|
||||
Reference in New Issue
Block a user