diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html index 270401bc0..6180ddc0b 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html @@ -297,7 +297,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 5, 2019

+

Dec 6, 2019


diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs040.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs040.html index f7d02c5d9..5b8c37cd4 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs040.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs040.html @@ -282,7 +282,7 @@ MathJax.Hub.Config({

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 \( n \)).

diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs041.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs041.html index 0d8d8cac3..0cdba8e3c 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs041.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs041.html @@ -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. diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs042.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs042.html index 33bb1e112..d4c0e951a 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs042.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs042.html @@ -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.

    -
  1. For \( m=1:M \) we
    2. +
  2. For \( b=1:B \)
    3. -
  3. 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.
    4. +
  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.

diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html index 270401bc0..6180ddc0b 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html @@ -297,7 +297,7 @@ MathJax.Hub.Config({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 5, 2019

+

Dec 6, 2019


diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html index 1169dea27..64b17ab31 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html @@ -148,7 +148,7 @@ MathJax.Hub.Config({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

 
-

Dec 5, 2019

+

Dec 6, 2019


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

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 \( n \)).

@@ -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. @@ -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.

    -

  1. For \( m=1:M \) we
    2. +

  2. For \( b=1:B \)
    3. -

  3. 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.
    4. +

  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.
diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html index 627c7f756..cc7d97d36 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html @@ -223,7 +223,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 5, 2019

+

Dec 6, 2019












@@ -1806,7 +1806,7 @@ plt.show()

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 \( n \)).

@@ -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.

    -
  1. For \( m=1:M \) we
    2. +
  2. For \( b=1:B \)
    3. -
  3. 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.
    4. +
  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.










diff --git a/doc/pub/DecisionTrees/html/DecisionTrees.html b/doc/pub/DecisionTrees/html/DecisionTrees.html index 339c930bf..4c136f88f 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees.html @@ -228,7 +228,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 5, 2019

+

Dec 6, 2019












@@ -1811,7 +1811,7 @@ plt.show()

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 \( n \)).

@@ -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.

    -
  1. For \( m=1:M \) we
    2. +
  2. For \( b=1:B \)
    3. -
  3. 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.
    4. +
  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.










diff --git a/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb b/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb index 1885b3cc2..2a7a30dba 100644 --- a/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb +++ b/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb @@ -10,7 +10,7 @@ " \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" ] diff --git a/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz b/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz index a0743d665..bcf32e0b9 100644 Binary files a/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz and b/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz differ diff --git a/doc/pub/DecisionTrees/pdf/DecisionTrees-minted.pdf b/doc/pub/DecisionTrees/pdf/DecisionTrees-minted.pdf index a60a2f889..52ca6827c 100644 Binary files a/doc/pub/DecisionTrees/pdf/DecisionTrees-minted.pdf and b/doc/pub/DecisionTrees/pdf/DecisionTrees-minted.pdf differ diff --git a/doc/src/DecisionTrees/DecisionTrees.do.txt b/doc/src/DecisionTrees/DecisionTrees.do.txt index bf8941655..bc4b03864 100644 --- a/doc/src/DecisionTrees/DecisionTrees.do.txt +++ b/doc/src/DecisionTrees/DecisionTrees.do.txt @@ -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.