typo in decision tree

2019-12-06 09:11:10 +01:00
parent ac26951bd1
commit 6a7f015f11
12 changed files with 42 additions and 42 deletions
@@ -297,7 +297,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Dec 5, 2019</h4></center> <!-- date -->
+<center><h4>Dec 6, 2019</h4></center> <!-- date -->
 <br>
 <p>

@@ -282,7 +282,7 @@ MathJax.Hub.Config({

 <p>
 Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with
-a decision tree wth different depths and perform a bootstrap aggregate (in this case we as many bootstraps as data points \( n \)).
+a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points \( n \)).
 <p>

 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
@@ -315,7 +315,7 @@ bagged trees will look quite similar to each other. Hence the
 predictions from the bagged trees will be highly correlated.
 Unfortunately, averaging many highly correlated quantities does not
 lead to as large of a reduction in variance as averaging many
-uncorrelated quanti- ties. In particular, this means that bagging will
+uncorrelated quantities. In particular, this means that bagging will
 not lead to a substantial reduction in variance over a single tree in
 this setting.

@@ -285,21 +285,21 @@ The algorithm described here can be applied to both classification and regressio
 We will grow of forest of say \( M \) trees.

 <ol>
-<li> For \( m=1:M \) we</li>
+<li> For \( b=1:B \)</li>

 <ul>
  <li> Draw a bootstrap sample of from the training data organized in our \( \boldsymbol{X} \) matrix.</li>
-  <li> We grow then a random forest tree \( T_m \) based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached</li>
+  <li> We grow then a random forest tree \( T_b \) based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached</li>

 <ol>
-   <li> we select \( m \le p \) varibales at random from the \( p \) predictors/features</li>
+   <li> we select \( m \le p \) variables at random from the \( p \) predictors/features</li>
   <li> pick the best split point among the \( m \) features using either the CART algorithm or the ID3 for classification and create a new node</li>
   <li> split the node into daughter nodes</li>
 </ol>

 </ul>

-<li> Output then the ensemble of trees \( \{T_m\}_1^{M} \) and make predictions for either a regression type of problem or a classification type of problem.</li> 
+<li> Output then the ensemble of trees \( \{T_b\}_1^{B} \) and make predictions for either a regression type of problem or a classification type of problem.</li> 
 </ol>

 <p>
@@ -297,7 +297,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Dec 5, 2019</h4></center> <!-- date -->
+<center><h4>Dec 6, 2019</h4></center> <!-- date -->
 <br>
 <p>

@@ -148,7 +148,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>&nbsp;<br>
-<center><h4>Dec 5, 2019</h4></center> <!-- date -->
+<center><h4>Dec 6, 2019</h4></center> <!-- date -->
 <br>
 <p>

@@ -1784,7 +1784,7 @@ plt.show()

 <p>
 Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with
-a decision tree wth different depths and perform a bootstrap aggregate (in this case we as many bootstraps as data points \( n \)).
+a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points \( n \)).
 <p>

 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -1889,7 +1889,7 @@ bagged trees will look quite similar to each other. Hence the
 predictions from the bagged trees will be highly correlated.
 Unfortunately, averaging many highly correlated quantities does not
 lead to as large of a reduction in variance as averaging many
-uncorrelated quanti- ties. In particular, this means that bagging will
+uncorrelated quantities. In particular, this means that bagging will
 not lead to a substantial reduction in variance over a single tree in
 this setting.
 </section>
@@ -1903,17 +1903,17 @@ The algorithm described here can be applied to both classification and regressio
 We will grow of forest of say \( M \) trees.

 <ol>
-<p><li> For \( m=1:M \) we</li>
+<p><li> For \( b=1:B \)</li>

 <ul>

 <p><li> Draw a bootstrap sample of from the training data organized in our \( \boldsymbol{X} \) matrix.</li>

-<p><li> We grow then a random forest tree \( T_m \) based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached</li>
+<p><li> We grow then a random forest tree \( T_b \) based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached</li>

 <ol>

-<p><li> we select \( m \le p \) varibales at random from the \( p \) predictors/features</li>
+<p><li> we select \( m \le p \) variables at random from the \( p \) predictors/features</li>

 <p><li> pick the best split point among the \( m \) features using either the CART algorithm or the ID3 for classification and create a new node</li>

@@ -1921,7 +1921,7 @@ We will grow of forest of say \( M \) trees.
 </ol>
 <p>
 </ul>
-<p><li> Output then the ensemble of trees \( \{T_m\}_1^{M} \) and make predictions for either a regression type of problem or a classification type of problem.</li> 
+<p><li> Output then the ensemble of trees \( \{T_b\}_1^{B} \) and make predictions for either a regression type of problem or a classification type of problem.</li> 
 </ol>
 </section>

@@ -223,7 +223,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Dec 5, 2019</h4></center> <!-- date -->
+<center><h4>Dec 6, 2019</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1806,7 +1806,7 @@ plt.show()

 <p>
 Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with
-a decision tree wth different depths and perform a bootstrap aggregate (in this case we as many bootstraps as data points \( n \)).
+a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points \( n \)).
 <p>

 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -1908,7 +1908,7 @@ bagged trees will look quite similar to each other. Hence the
 predictions from the bagged trees will be highly correlated.
 Unfortunately, averaging many highly correlated quantities does not
 lead to as large of a reduction in variance as averaging many
-uncorrelated quanti- ties. In particular, this means that bagging will
+uncorrelated quantities. In particular, this means that bagging will
 not lead to a substantial reduction in variance over a single tree in
 this setting.

@@ -1922,21 +1922,21 @@ The algorithm described here can be applied to both classification and regressio
 We will grow of forest of say \( M \) trees.

 <ol>
-<li> For \( m=1:M \) we</li>
+<li> For \( b=1:B \)</li>

 <ul>
  <li> Draw a bootstrap sample of from the training data organized in our \( \boldsymbol{X} \) matrix.</li>
-  <li> We grow then a random forest tree \( T_m \) based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached</li>
+  <li> We grow then a random forest tree \( T_b \) based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached</li>

 <ol>
-   <li> we select \( m \le p \) varibales at random from the \( p \) predictors/features</li>
+   <li> we select \( m \le p \) variables at random from the \( p \) predictors/features</li>
   <li> pick the best split point among the \( m \) features using either the CART algorithm or the ID3 for classification and create a new node</li>
   <li> split the node into daughter nodes</li>
 </ol>

 </ul>

-<li> Output then the ensemble of trees \( \{T_m\}_1^{M} \) and make predictions for either a regression type of problem or a classification type of problem.</li> 
+<li> Output then the ensemble of trees \( \{T_b\}_1^{B} \) and make predictions for either a regression type of problem or a classification type of problem.</li> 
 </ol>

 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -228,7 +228,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Dec 5, 2019</h4></center> <!-- date -->
+<center><h4>Dec 6, 2019</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1811,7 +1811,7 @@ plt<span style="color: #666666">.</span>show()

 <p>
 Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with
-a decision tree wth different depths and perform a bootstrap aggregate (in this case we as many bootstraps as data points \( n \)).
+a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points \( n \)).
 <p>

 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
@@ -1913,7 +1913,7 @@ bagged trees will look quite similar to each other. Hence the
 predictions from the bagged trees will be highly correlated.
 Unfortunately, averaging many highly correlated quantities does not
 lead to as large of a reduction in variance as averaging many
-uncorrelated quanti- ties. In particular, this means that bagging will
+uncorrelated quantities. In particular, this means that bagging will
 not lead to a substantial reduction in variance over a single tree in
 this setting.

@@ -1927,21 +1927,21 @@ The algorithm described here can be applied to both classification and regressio
 We will grow of forest of say \( M \) trees.

 <ol>
-<li> For \( m=1:M \) we</li>
+<li> For \( b=1:B \)</li>

 <ul>
  <li> Draw a bootstrap sample of from the training data organized in our \( \boldsymbol{X} \) matrix.</li>
-  <li> We grow then a random forest tree \( T_m \) based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached</li>
+  <li> We grow then a random forest tree \( T_b \) based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached</li>

 <ol>
-   <li> we select \( m \le p \) varibales at random from the \( p \) predictors/features</li>
+   <li> we select \( m \le p \) variables at random from the \( p \) predictors/features</li>
   <li> pick the best split point among the \( m \) features using either the CART algorithm or the ID3 for classification and create a new node</li>
   <li> split the node into daughter nodes</li>
 </ol>

 </ul>

-<li> Output then the ensemble of trees \( \{T_m\}_1^{M} \) and make predictions for either a regression type of problem or a classification type of problem.</li> 
+<li> Output then the ensemble of trees \( \{T_b\}_1^{B} \) and make predictions for either a regression type of problem or a classification type of problem.</li> 
 </ol>

 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -10,7 +10,7 @@
    "<!-- Author: -->  \n",
    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
    "\n",
-    "Date: **Dec 5, 2019**\n",
+    "Date: **Dec 6, 2019**\n",
    "\n",
    "Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
    "\n",
@@ -1827,7 +1827,7 @@
    "## Making your own Bootstrap: Changing the Level of the Decision Tree\n",
    "\n",
    "Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with\n",
-    "a decision tree wth different depths and perform a bootstrap aggregate (in this case we as many bootstraps as data points $n$)."
+    "a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points $n$)."
   ]
  },
  {
@@ -1944,7 +1944,7 @@
    "predictions from the bagged trees will be highly correlated.\n",
    "Unfortunately, averaging many highly correlated quantities does not\n",
    "lead to as large of a reduction in variance as averaging many\n",
-    "uncorrelated quanti- ties. In particular, this means that bagging will\n",
+    "uncorrelated quantities. In particular, this means that bagging will\n",
    "not lead to a substantial reduction in variance over a single tree in\n",
    "this setting.\n",
    "\n",
@@ -1953,13 +1953,13 @@
    "The algorithm described here can be applied to both classification and regression problems.\n",
    "\n",
    "We will grow of forest of say $M$ trees.\n",
-    "1. For $m=1:M$ we\n",
+    "1. For $b=1:B$\n",
    "\n",
    "  * Draw a bootstrap sample of from the training data organized in our $\\boldsymbol{X}$ matrix.\n",
    "\n",
-    "  * We grow then a random forest tree $T_m$ based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached\n",
+    "  * We grow then a random forest tree $T_b$ based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached\n",
    "\n",
-    "1. we select $m \\le p$ varibales at random from the $p$ predictors/features\n",
+    "1. we select $m \\le p$ variables at random from the $p$ predictors/features\n",
    "\n",
    "2. pick the best split point among the $m$ features using either the CART algorithm or the ID3 for classification and create a new node\n",
    "\n",
@@ -1967,7 +1967,7 @@
    "\n",
    "\n",
    "\n",
-    "4. Output then the ensemble of trees $\\{T_m\\}_1^{M}$ and make predictions for either a regression type of problem or a classification type of problem. \n",
+    "4. Output then the ensemble of trees $\\{T_b\\}_1^{B}$ and make predictions for either a regression type of problem or a classification type of problem. \n",
    "\n",
    "## Random Forests Compared with other Methods on the Cancer Data"
   ]
@@ -1449,7 +1449,7 @@ plt.show()
 =====  Making your own Bootstrap: Changing the Level of the Decision Tree =====

 Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with
-a decision tree wth different depths and perform a bootstrap aggregate (in this case we as many bootstraps as data points $n$).
+a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points $n$).
 !bc pycod

 import matplotlib.pyplot as plt
@@ -1550,7 +1550,7 @@ bagged trees will look quite similar to each other. Hence the
 predictions from the bagged trees will be highly correlated.
 Unfortunately, averaging many highly correlated quantities does not
 lead to as large of a reduction in variance as averaging many
-uncorrelated quanti- ties. In particular, this means that bagging will
+uncorrelated quantities. In particular, this means that bagging will
 not lead to a substantial reduction in variance over a single tree in
 this setting.

@@ -1560,13 +1560,13 @@ this setting.
 The algorithm described here can be applied to both classification and regression problems.

 We will grow of forest of say $M$ trees.
-o For $m=1:M$ we
+o For $b=1:B$
  * Draw a bootstrap sample of from the training data organized in our $\bm{X}$ matrix.
-  * We grow then a random forest tree $T_m$ based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached
-    o we select $m \le p$ varibales at random from the $p$ predictors/features
+  * We grow then a random forest tree $T_b$ based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached
+    o we select $m \le p$ variables at random from the $p$ predictors/features
    o pick the best split point among the $m$ features using either the CART algorithm or the ID3 for classification and create a new node
    o split the node into daughter nodes
-o Output then the ensemble of trees $\{T_m\}_1^{M}$ and make predictions for either a regression type of problem or a classification type of problem. 
+o Output then the ensemble of trees $\{T_b\}_1^{B}$ and make predictions for either a regression type of problem or a classification type of problem.