From 9fc81885cbae0fdcf1dcec27f2a31462cf36728c Mon Sep 17 00:00:00 2001 From: mhjensen Date: Thu, 31 Oct 2019 06:51:29 +0100 Subject: [PATCH] typos --- .../html/._DecisionTrees-bs000.html | 148 +++-- .../html/._DecisionTrees-bs001.html | 148 +++-- .../html/._DecisionTrees-bs002.html | 151 +++--- .../html/._DecisionTrees-bs003.html | 162 +++--- .../html/._DecisionTrees-bs004.html | 168 +++--- .../html/._DecisionTrees-bs005.html | 248 ++++++--- .../html/._DecisionTrees-bs006.html | 254 +++------ .../html/._DecisionTrees-bs007.html | 179 +++--- .../html/._DecisionTrees-bs008.html | 202 ++++--- .../html/._DecisionTrees-bs009.html | 204 +++---- .../html/._DecisionTrees-bs010.html | 184 ++++--- .../html/._DecisionTrees-bs011.html | 192 ++++--- .../html/._DecisionTrees-bs012.html | 182 +++---- .../html/._DecisionTrees-bs013.html | 179 +++--- .../html/._DecisionTrees-bs014.html | 206 +++---- .../html/._DecisionTrees-bs015.html | 221 ++++---- .../html/._DecisionTrees-bs016.html | 179 +++--- .../html/._DecisionTrees-bs017.html | 213 ++++---- .../html/._DecisionTrees-bs018.html | 241 +++++---- .../html/._DecisionTrees-bs019.html | 268 ++++----- .../html/._DecisionTrees-bs020.html | 238 ++++---- .../html/._DecisionTrees-bs021.html | 356 ++++++++---- .../html/._DecisionTrees-bs022.html | 392 ++++---------- .../html/._DecisionTrees-bs023.html | 245 +++++---- .../html/._DecisionTrees-bs024.html | 220 +++----- .../html/._DecisionTrees-bs025.html | 180 +++--- .../html/._DecisionTrees-bs026.html | 230 +++++--- .../html/._DecisionTrees-bs027.html | 232 +++----- .../html/._DecisionTrees-bs028.html | 167 +++--- .../html/._DecisionTrees-bs029.html | 171 +++--- .../html/._DecisionTrees-bs030.html | 179 +++--- .../html/._DecisionTrees-bs031.html | 186 +++---- .../html/._DecisionTrees-bs032.html | 204 ++++--- .../html/._DecisionTrees-bs033.html | 222 ++++---- .../html/._DecisionTrees-bs034.html | 199 +++---- .../html/._DecisionTrees-bs035.html | 209 ++++--- .../html/._DecisionTrees-bs036.html | 222 ++++---- .../html/._DecisionTrees-bs037.html | 212 +++----- .../DecisionTrees/html/DecisionTrees-bs.html | 148 +++-- .../html/DecisionTrees-reveal.html | 381 ++++++------- .../html/DecisionTrees-solarized.html | 457 ++++++++-------- doc/pub/DecisionTrees/html/DecisionTrees.html | 511 +++++++++--------- .../DecisionTrees/ipynb/DecisionTrees.ipynb | 81 +-- .../ipynb/ipynb-DecisionTrees-src.tar.gz | Bin 194 -> 194 bytes .../pdf/DecisionTrees-minted.pdf | Bin 283918 -> 267962 bytes doc/src/DecisionTrees/DecisionTrees.do.txt | 10 +- 46 files changed, 4629 insertions(+), 4952 deletions(-) diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html index 4591c0dc0..ab79ad196 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs000.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - 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    A typical Decision Tree with its pertinent Jargon, Classification Problem

    -

    -In the figure here we present a decision tree obtained from a classification problem -

    @@ -206,7 +197,7 @@ In the figure here we present a decision tree obtained from a classification pro

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    A typical Decision Tree with its pertinent Jargon, Regeression Problem

    +

    General Features

    -In the figure we present a decision tree obtained from a simple regression problem +The overarching approach to decision trees is a top-down approach. + +

    + +This process is then repeated for the subtree rooted at the new +node.

    @@ -207,7 +211,7 @@ In the figure we present a decision tree obtained from a simple regression prob

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html index b35e3c6ad..9436cee23 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs004.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -183,20 +177,20 @@ MathJax.Hub.Config({ -

    General Features

    +

    How do we set it up?

    -The overarching approach to decision trees is a top-down approach. +In simplified terms, the process of training a decision tree and +predicting the target features of query instances is as follows: -

    +
      +
    1. Present a dataset containing of a number of training instances characterized by a number of descriptive features and a target feature
      2. +
    2. Train the decision tree model by continuously splitting the target feature along the values of the descriptive features using a measure of information gain during the training process
      3. +
    3. Grow the tree until we accomplish a stopping criteria create leaf nodes which represent the predictions we want to make for new query instances
      4. +
    4. Show query instances to the tree and run down the tree until we arrive at leaf nodes
      5. +
    -This process is then repeated for the subtree rooted at the new -node. +Then we are essentially done!

    @@ -218,7 +212,7 @@ node.

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html index 7f7d52061..fd649d68c 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs005.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -183,21 +177,99 @@ MathJax.Hub.Config({ -

    How do we set it up?

    - +

    Decision trees and Regression

    -In simplified terms, the process of training a decision tree and -predicting the target features of query instances is as follows: -

      -
    1. Present a dataset containing of a number of training instances characterized by a number of descriptive features and a target feature
      2. -
    2. Train the decision tree model by continuously splitting the target feature along the values of the descriptive features using a measure of information gain during the training process
      3. -
    3. Grow the tree until we accomplish a stopping criteria create leaf nodes which represent the predictions we want to make for new query instances
      4. -
    4. Show query instances to the tree and run down the tree until we arrive at leaf nodes
      5. -
    + +
    import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.preprocessing import PolynomialFeatures
+from sklearn.linear_model import LinearRegression
 
-Then we are essentially done!
+steps=250
 
+distance=0
+x=0
+distance_list=[]
+steps_list=[]
+while x<steps:
+    distance+=np.random.randint(-1,2)
+    distance_list.append(distance)
+    x+=1
+    steps_list.append(x)
+plt.plot(steps_list,distance_list, color='green', label="Random Walk Data")
+
+steps_list=np.asarray(steps_list)
+distance_list=np.asarray(distance_list)
+
+X=steps_list[:,np.newaxis]
+
+#Polynomial fits
+
+#Degree 2
+poly_features=PolynomialFeatures(degree=2, include_bias=False)
+X_poly=poly_features.fit_transform(X)
+
+lin_reg=LinearRegression()
+poly_fit=lin_reg.fit(X_poly,distance_list)
+b=lin_reg.coef_
+c=lin_reg.intercept_
+print ("2nd degree coefficients:")
+print ("zero power: ",c)
+print ("first power: ", b[0])
+print ("second power: ",b[1])
+
+z = np.arange(0, steps, .01)
+z_mod=b[1]*z**2+b[0]*z+c
+
+fit_mod=b[1]*X**2+b[0]*X+c
+plt.plot(z, z_mod, color='r', label="2nd Degree Fit")
+plt.title("Polynomial Regression")
+
+plt.xlabel("Steps")
+plt.ylabel("Distance")
+
+#Degree 10
+poly_features10=PolynomialFeatures(degree=10, include_bias=False)
+X_poly10=poly_features10.fit_transform(X)
+
+poly_fit10=lin_reg.fit(X_poly10,distance_list)
+
+y_plot=poly_fit10.predict(X_poly10)
+plt.plot(X, y_plot, color='black', label="10th Degree Fit")
+
+plt.legend()
+plt.show()
+
+
+#Decision Tree Regression
+from sklearn.tree import DecisionTreeRegressor
+regr_1=DecisionTreeRegressor(max_depth=2)
+regr_2=DecisionTreeRegressor(max_depth=5)
+regr_3=DecisionTreeRegressor(max_depth=7)
+regr_1.fit(X, distance_list)
+regr_2.fit(X, distance_list)
+regr_3.fit(X, distance_list)
+
+X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]
+y_1 = regr_1.predict(X_test)
+y_2 = regr_2.predict(X_test)
+y_3=regr_3.predict(X_test)
+
+# Plot the results
+plt.figure()
+plt.scatter(X, distance_list, s=2.5, c="black", label="data")
+plt.plot(X_test, y_1, color="red",
+         label="max_depth=2", linewidth=2)
+plt.plot(X_test, y_2, color="green", label="max_depth=5", linewidth=2)
+plt.plot(X_test, y_3, color="m", label="max_depth=7", linewidth=2)
+
+plt.xlabel("Data")
+plt.ylabel("Darget")
+plt.title("Decision Tree Regression")
+plt.legend()
+plt.show()
+

    @@ -219,7 +291,7 @@ Then we are essentially done!

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html index 151427dea..8dbb32a53 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs006.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -183,99 +177,31 @@ MathJax.Hub.Config({ -

    Decision trees and Regression

    +

    Building a tree, regression

    +

    +There are mainly two steps - -

    import numpy as np
-import matplotlib.pyplot as plt
-from sklearn.preprocessing import PolynomialFeatures
-from sklearn.linear_model import LinearRegression
+
      
+
    1.  We split the predictor space (the set of possible values \( x_1,x_2,\dots, x_p \)) into \( J \) distinct and non-non-overlapping regions, \( R_1,R_2,\dots,R_J \).
      2.   
+
    2.  For every observation that falls into the region \( R_j \) , we make the same prediction, which is simply the mean of the response values for the training observations in \( R_j \).
      3. 
+
    
 
-steps=250
+How do we construct the regions \( R_1,\dots,R_J \)?  In theory, the
+regions could have any shape. However, we choose to divide the
+predictor space into high-dimensional rectangles, or boxes, for
+simplicity and for ease of interpretation of the resulting predictive
+model. The goal is to find boxes \( R_1,\dots,R_J \) that minimize the
+MSE, given by
 
-distance=0
-x=0
-distance_list=[]
-steps_list=[]
-while x<steps:
-    distance+=np.random.randint(-1,2)
-    distance_list.append(distance)
-    x+=1
-    steps_list.append(x)
-plt.plot(steps_list,distance_list, color='green', label="Random Walk Data")
+$$
+\sum_{j=1}^J\sum_{i\in R_j}(y_i-\overline{y}_{R_j})^2,
+$$
 
-steps_list=np.asarray(steps_list)
-distance_list=np.asarray(distance_list)
+
    
+where \( \overline{y}_{R_j} \)  is the mean response for the training observations 
+within box \( j \).
 
-X=steps_list[:,np.newaxis]
-
-#Polynomial fits
-
-#Degree 2
-poly_features=PolynomialFeatures(degree=2, include_bias=False)
-X_poly=poly_features.fit_transform(X)
-
-lin_reg=LinearRegression()
-poly_fit=lin_reg.fit(X_poly,distance_list)
-b=lin_reg.coef_
-c=lin_reg.intercept_
-print ("2nd degree coefficients:")
-print ("zero power: ",c)
-print ("first power: ", b[0])
-print ("second power: ",b[1])
-
-z = np.arange(0, steps, .01)
-z_mod=b[1]*z**2+b[0]*z+c
-
-fit_mod=b[1]*X**2+b[0]*X+c
-plt.plot(z, z_mod, color='r', label="2nd Degree Fit")
-plt.title("Polynomial Regression")
-
-plt.xlabel("Steps")
-plt.ylabel("Distance")
-
-#Degree 10
-poly_features10=PolynomialFeatures(degree=10, include_bias=False)
-X_poly10=poly_features10.fit_transform(X)
-
-poly_fit10=lin_reg.fit(X_poly10,distance_list)
-
-y_plot=poly_fit10.predict(X_poly10)
-plt.plot(X, y_plot, color='black', label="10th Degree Fit")
-
-plt.legend()
-plt.show()
-
-
-#Decision Tree Regression
-from sklearn.tree import DecisionTreeRegressor
-regr_1=DecisionTreeRegressor(max_depth=2)
-regr_2=DecisionTreeRegressor(max_depth=5)
-regr_3=DecisionTreeRegressor(max_depth=7)
-regr_1.fit(X, distance_list)
-regr_2.fit(X, distance_list)
-regr_3.fit(X, distance_list)
-
-X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]
-y_1 = regr_1.predict(X_test)
-y_2 = regr_2.predict(X_test)
-y_3=regr_3.predict(X_test)
-
-# Plot the results
-plt.figure()
-plt.scatter(X, distance_list, s=2.5, c="black", label="data")
-plt.plot(X_test, y_1, color="red",
-         label="max_depth=2", linewidth=2)
-plt.plot(X_test, y_2, color="green", label="max_depth=5", linewidth=2)
-plt.plot(X_test, y_3, color="m", label="max_depth=7", linewidth=2)
-
-plt.xlabel("Data")
-plt.ylabel("Darget")
-plt.title("Decision Tree Regression")
-plt.legend()
-plt.show()
-

    @@ -298,7 +224,7 @@ plt.show()

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html index fcc3f8e61..2dc0ce343 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs007.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -183,30 +177,21 @@ MathJax.Hub.Config({ -

    Building a tree, regression

    +

    A top-down approach, recursive binary splitting

    -There are mainly two steps - -

      -
    1. We split the predictor space (the set of possible values \( x_1,x_2,\dots, x_p \)) into \( J \) distinct and non-non-overlapping regions, \( R_1,R_2,\dots,R_J \).
      2. -
    2. For every observation that falls into the region \( R_j \) , we make the same prediction, which is simply the mean of the response values for the training observations in \( R_j \).
      3. -
    - -How do we construct the regions \( R_1,\dots,R_J \)? In theory, the -regions could have any shape. However, we choose to divide the -predictor space into high-dimensional rectangles, or boxes, for -simplicity and for ease of interpretation of the resulting predictive -model. The goal is to find boxes \( R_1,\dots,R_J \) that minimize the -MSE, given by - -$$ -\sum_{j=1}^J\sum_{i\in R_j}(y_i-\overline{y}_{R_j})^2, -$$ +Unfortunately, it is computationally infeasible to consider every +possible partition of the feature space into \( J \) boxes. The common +strategy is to take a top-down approach

    -where \( \overline{y}_{R_j} \) is the mean response for the training observations -within box \( j \). +The approach is top-down because it begins at the top of the tree (all +observations belong to a single region) and then successively splits +the predictor space; each split is indicated via two new branches +further down on the tree. It is greedy because at each step of the +tree-building process, the best split is made at that particular step, +rather than looking ahead and picking a split that will lead to a +better tree in some future step.

    @@ -231,7 +216,7 @@ within box \( j \).

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html index c8533f1f2..b474f598a 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs008.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -183,21 +177,53 @@ MathJax.Hub.Config({ -

    A top-down approach, recursive binary splitting

    +

    Making a tree

    -Unfortunately, it is computationally infeasible to consider every -possible partition of the feature space into \( J \) boxes. The common -strategy is to take a top-down approach +In order to implement the recursive binary splitting we start by selecting +the predictor \( x_j \) and a cutpoint \( s \) that splits the predictor space into two regions \( R_1 \) and \( R_2 \) +$$ +\left\{X\vert x_j < s\right\}, +$$ + +and +$$ +\left\{X\vert x_j \geq s\right\}, +$$ + +so that we obtain the lowest MSE, that is +$$ +\sum_{i:x_i\in R_j}(y_i-\overline{y}_{R_1})^2+\sum_{i:x_i\in R_2}(y_i-\overline{y}_{R_2})^2, +$$

    -The approach is top-down because it begins at the top of the tree (all -observations belong to a single region) and then successively splits -the predictor space; each split is indicated via two new branches -further down on the tree. It is greedy because at each step of the -tree-building process, the best split is made at that particular step, -rather than looking ahead and picking a split that will lead to a -better tree in some future step. +which we want to minimize by considering all predictors +\( x_1,x_2,\dots,x_p \). We consider also all possible values of \( s \) for +each predictor. These values could be determined by randomly assigned +numbers or by starting at the midpoint and then proceed till we find +an optimal value. + +

    +For any \( j \) and \( s \), we define the pair of half-planes where +\( \overline{y}_{R_1} \) is the mean response for the training +observations in \( R_1(j,s) \), and \( \overline{y}_{R_2} \) is the mean +response for the training observations in \( R_2(j,s) \). + +

    +Finding the values of \( j \) and \( s \) that minimize the above equation can be +done quite quickly, especially when the number of features \( p \) is not +too large. + +

    +Next, we repeat the process, looking +for the best predictor and best cutpoint in order to split the data +further so as to minimize the MSE within each of the resulting +regions. However, this time, instead of splitting the entire predictor +space, we split one of the two previously identified regions. We now +have three regions. Again, we look to split one of these three regions +further, so as to minimize the MSE. The process continues until a +stopping criterion is reached; for instance, we may continue until no +region contains more than five observations.

    @@ -223,7 +249,7 @@ better tree in some future step.

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html index 525fffcfd..2693c87e2 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs009.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -181,55 +175,23 @@ MathJax.Hub.Config({

     

     

     

    - + -

    Making a tree

    +

    Pruning the tree

    -In order to implement the recursive binary splitting we start by selecting -the predictor \( x_j \) and a cutpoint \( s \) that splits the predictor space into two regions \( R_1 \) and \( R_2 \) -$$ -\left\{X\vert x_j < s\right\}, -$$ - -and -$$ -\left\{X\vert x_j \geq s\right\}, -$$ - -so that we obtain the lowest MSE, that is -$$ -\sum_{i:x_i\in R_j}(y_i-\overline{y}_{R_1})^2+\sum_{i:x_i\in R_2}(y_i-\overline{y}_{R_2})^2, -$$ +The above procedure is rather straightforward, but leads often to +overfitting and unnecessarily large and complicated trees. The basic +idea is to grow a large tree \( T_0 \) and then prune it back in order to +obtain a subtree. A smaller tree with fewer splits (fewer regions) can +lead to smaller variance and better interpretation at the cost of a +little more bias.

    -which we want to minimize by considering all predictors -\( x_1,x_2,\dots,x_p \). We consider also all possible values of \( s \) for -each predictor. These values could be determined by randomly assigned -numbers or by starting at the midpoint and then proceed till we find -an optimal value. - -

    -For any \( j \) and \( s \), we define the pair of half-planes where -\( \overline{y}_{R_1} \) is the mean response for the training -observations in \( R_1(j,s) \), and \( \overline{y}_{R_2} \) is the mean -response for the training observations in \( R_2(j,s) \). - -

    -Finding the values of \( j \) and \( s \) that minimize the above equation can be -done quite quickly, especially when the number of features \( p \) is not -too large. - -

    -Next, we repeat the process, looking -for the best predictor and best cutpoint in order to split the data -further so as to minimize the MSE within each of the resulting -regions. However, this time, instead of splitting the entire predictor -space, we split one of the two previously identified regions. We now -have three regions. Again, we look to split one of these three regions -further, so as to minimize the MSE. The process continues until a -stopping criterion is reached; for instance, we may continue until no -region contains more than five observations. +The so-called Cost complexity pruning algorithm gives us a +way to do just this. Rather than considering every possible subtree, +we consider a sequence of trees indexed by a nonnegative tuning +parameter \( \alpha \).

    @@ -256,7 +218,7 @@ region contains more than five observations.

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html index 83fbc8ee0..45d1809cc 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs010.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -181,23 +175,35 @@ MathJax.Hub.Config({

     

     

     

    - + -

    Pruning the tree

    +

    Cost complexity pruning

    +For each value of \( \alpha \) there corresponds a subtree \( T \in T_0 \) such that +$$ +\sum_{m=1}^{\overline{T}}\sum_{i:x_i\in R_m}(y_i-\overline{y}_{R_m})^2+\alpha\overline{T}, +$$ + +is as small as possible. Here \( \overline{T} \) is +the number of terminal nodes of the tree \( T \) , \( R_m \) is the +rectangle (i.e. the subset of predictor space) corresponding to the \( m \)-th terminal node.

    -The above procedure is rather straightforward, but leads often to -overfitting and unnecessarily large and complicated trees. The basic -idea is to grow a large tree \( T_0 \) and then prune it back in order to -obtain a subtree. A smaller tree with fewer splits (fewer regions) can -lead to smaller variance and better interpretation at the cost of a -little more bias. +The tuning parameter \( \alpha \) controls a trade-off between the subtree’s +com- plexity and its fit to the training data. When \( \alpha = 0 \), then the +subtree \( T \) will simply equal \( T_0 \), +because then the above equation just measures the +training error. +However, as \( \alpha \) increases, there is a price to pay for +having a tree with many terminal nodes. The above equation will +tend to be minimized for a smaller subtree.

    -The so-called Cost complexity pruning algorithm gives us a -way to do just this. Rather than considering every possible subtree, -we consider a sequence of trees indexed by a nonnegative tuning -parameter \( \alpha \). +It turns out that as we increase \( \alpha \) from zero +branches get pruned from the tree in a nested and predictable fashion, +so obtaining the whole sequence of subtrees as a function of \( \alpha \) is +easy. We can select a value of \( \alpha \) using a validation set or using +cross-validation. We then return to the full data set and obtain the +subtree corresponding to \( \alpha \).

    @@ -225,7 +231,7 @@ parameter \( \alpha \).

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html index 87d3174c7..0c22a2e10 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs011.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -183,33 +177,29 @@ MathJax.Hub.Config({ -

    Cost complexity pruning

    -For each value of \( \alpha \) there corresponds a subtree \( T \in T_0 \) such that -$$ -\sum_{m=1}^{\overline{T}}\sum_{i:x_i\in R_m}(y_i-\overline{y}_{R_m})^2+\alpha\overline{T}, -$$ - -is as small as possible. Here \( \overline{T} \) is -the number of terminal nodes of the tree \( T \) , \( R_m \) is the -rectangle (i.e. the subset of predictor space) corresponding to the \( m \)-th terminal node. +

    Schematic Regression Procedure

    -The tuning parameter \( \alpha \) controls a trade-off between the subtree’s -com- plexity and its fit to the training data. When \( \alpha = 0 \), then the -subtree \( T \) will simply equal \( T_0 \), -because then the above equation just measures the -training error. -However, as \( \alpha \) increases, there is a price to pay for -having a tree with many terminal nodes. The above equation will -tend to be minimized for a smaller subtree. +

    +
    +

    + +

      +
    1. Use recursive binary splitting to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.
      2. +
    2. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of \( \alpha \).
      3. +
    3. Use for example \( K \)-fold cross-validation to choose \( \alpha \). Divide the training observations into \( K \) folds. For each \( k=1,2,\dots,K \) we:
      4. + +
        +
      • repeat steps 1 and 2 on all but the \( k \)-th fold of the training data.
        • +
      • Then we valuate the mean squared prediction error on the data in the left-out \( k \)-th fold, as a function of \( \alpha \).
        • +
      • Finally we average the results for each value of \( \alpha \), and pick \( \alpha \) to minimize the average error.
        • +
      + +
    4. Return the subtree from Step 2 that corresponds to the chosen value of \( \alpha \).
      5. +
    +
    +
    -

    -It turns out that as we increase \( \alpha \) from zero -branches get pruned from the tree in a nested and predictable fashion, -so obtaining the whole sequence of subtrees as a function of \( \alpha \) is -easy. We can select a value of \( \alpha \) using a validation set or using -cross-validation. We then return to the full data set and obtain the -subtree corresponding to \( \alpha \).

    @@ -237,7 +227,7 @@ subtree corresponding to \( \alpha \).

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html index d322da06d..12d8e3914 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs012.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -183,29 +177,21 @@ MathJax.Hub.Config({ -

    Schematic Regression Procedure

    +

    A Classification Tree

    -

    -
    -

    - -

      -
    1. Use recursive binary splitting to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.
      2. -
    2. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of \( \alpha \).
      3. -
    3. Use for example \( K \)-fold cross-validation to choose \( \alpha \). Divide the training observations into \( K \) folds. For each \( k=1,2,\dots,K \) we:
      4. - -
        -
      • repeat steps 1 and 2 on all but the \( k \)-th fold of the training data.
        • -
      • Then we valuate the mean squared prediction error on the data in the left-out \( k \)-th fold, as a function of \( \alpha \).
        • -
      • Finally we average the results for each value of \( \alpha \), and pick \( \alpha \) to minimize the average error.
        • -
      - -
    4. Return the subtree from Step 2 that corresponds to the chosen value of \( \alpha \).
      5. -
    -
    -
    - +A classification tree is very similar to a regression tree, except +that it is used to predict a qualitative response rather than a +quantitative one. Recall that for a regression tree, the predicted +response for an observation is given by the mean response of the +training observations that belong to the same terminal node. In +contrast, for a classification tree, we predict that each observation +belongs to the most commonly occurring class of training observations +in the region to which it belongs. In interpreting the results of a +classification tree, we are often interested not only in the class +prediction corresponding to a particular terminal node region, but +also in the class proportions among the training observations that +fall into that region.

    @@ -233,7 +219,7 @@ MathJax.Hub.Config({

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html index bdf58e375..9d076f512 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs013.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -183,21 +177,26 @@ MathJax.Hub.Config({ -

    A Classification Tree

    +

    Growing a classification tree

    -A classification tree is very similar to a regression tree, except -that it is used to predict a qualitative response rather than a -quantitative one. Recall that for a regression tree, the predicted -response for an observation is given by the mean response of the -training observations that belong to the same terminal node. In -contrast, for a classification tree, we predict that each observation -belongs to the most commonly occurring class of training observations -in the region to which it belongs. In interpreting the results of a -classification tree, we are often interested not only in the class -prediction corresponding to a particular terminal node region, but -also in the class proportions among the training observations that -fall into that region. +The task of growing a +classification tree is quite similar to the task of growing a +regression tree. Just as in the regression setting, we use recursive +binary splitting to grow a classification tree. However, in the +classification setting, the MSE cannot be used as a criterion for making +the binary splits. A natural alternative to MSE is the classification +error rate. Since we plan to assign an observation in a given region +to the most commonly occurring error rate class of training +observations in that region, the classification error rate is simply +the fraction of the training observations in that region that do not +belong to the most common class. + +

    +When building a classification tree, either the Gini index or the +entropy are typically used to evaluate the quality of a particular +split, since these two approaches are more sensitive to node purity +than is the classification error rate.

    @@ -225,7 +224,7 @@ fall into that region.

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html index 3743f474b..7222f2a52 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs014.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -183,26 +177,52 @@ MathJax.Hub.Config({ -

    Growing a classification tree

    +

    Classification tree, how to split nodes

    -The task of growing a -classification tree is quite similar to the task of growing a -regression tree. Just as in the regression setting, we use recursive -binary splitting to grow a classification tree. However, in the -classification setting, the MSE cannot be used as a criterion for making -the binary splits. A natural alternative to MSE is the classification -error rate. Since we plan to assign an observation in a given region -to the most commonly occurring error rate class of training -observations in that region, the classification error rate is simply -the fraction of the training observations in that region that do not -belong to the most common class. +If our targets are the outcome of a classification process that takes +for example \( k=1,2,\dots,K \) values, the only thing we need to think of +is to set up the splitting criteria for each node.

    -When building a classification tree, either the Gini index or the -entropy are typically used to evaluate the quality of a particular -split, since these two approaches are more sensitive to node purity -than is the classification error rate. +We define a PDF \( p_{mk} \) that represents the number of observations of +a class \( k \) in a region \( R_m \) with \( N_m \) observations. We represent +this likelihood function in terms of the proportion \( I(y_i=k) \) of +observations of this class in the region \( R_m \) as + +$$ +p_{mk} = \frac{1}{N_m}\sum_{x_i\in R_m}I(y_i=k). +$$ + +

    +We let \( p_{mk} \) represent the majority class of observations in region +\( m \). The three most common ways of splitting a node are given by + +

    + +$$ +p_{mk} = \frac{1}{N_m}\sum_{x_i\in R_m}I(y_i\ne k) = 1-p_{mk}. +$$ + + + + +$$ +g = \sum_{k=1}^K p_{mk}(1-p_{mk}). +$$ + + + + +$$ +s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}. +$$

    @@ -230,7 +250,7 @@ than is the classification error rate.

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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html index 09645870c..e0f137c13 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs015.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -183,53 +177,44 @@ MathJax.Hub.Config({ -

    Classification tree, how to split nodes

    - +

    Visualizing the Tree, Classification

    -If our targets are the outcome of a classification process that takes -for example \( k=1,2,\dots,K \) values, the only thing we need to think of -is to set up the splitting criteria for each node. -

    -We define a PDF \( p_{mk} \) that represents the number of observations of -a class \( k \) in a region \( R_m \) with \( N_m \) observations. We represent -this likelihood function in terms of the proportion \( I(y_i=k) \) of -observations of this class in the region \( R_m \) as + +

    import os
+from sklearn.datasets import load_breast_cancer
+from sklearn.tree import DecisionTreeClassifier
+from sklearn.model_selection import train_test_split
+from sklearn.metrics import confusion_matrix
+from sklearn.tree import export_graphviz
 
-$$
-p_{mk} = \frac{1}{N_m}\sum_{x_i\in R_m}I(y_i=k).
-$$
-
-
    
-We let \( p_{mk} \) represent the majority class of observations in region
-\( m \). The three most common ways of splitting a node are given by
-
-
      
-
    •  Misclassification error
      •  
-
    
-
-$$
-p_{mk} = \frac{1}{N_m}\sum_{x_i\in R_m}I(y_i\ne k) = 1-p_{mk}.
-$$
+from IPython.display import Image 
+from pydot import graph_from_dot_data
+import pandas as pd
+import numpy as np
 
 
-
      
-
    •  Gini index \( g \)
      • 
-
    
-
-$$
-g = \sum_{k=1}^K p_{mk}(1-p_{mk}).
-$$
-
-
-
      
-
    •  Information entropy or just entropy \( s \)
      • 
-
    
-
-$$
-s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}.
-$$
+cancer = load_breast_cancer()
+X = pd.DataFrame(cancer.data, columns=cancer.feature_names)
+print(X)
+y = pd.Categorical.from_codes(cancer.target, cancer.target_names)
+y = pd.get_dummies(y)
+print(y)
+X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)
+tree_clf = DecisionTreeClassifier(max_depth=5)
+tree_clf.fit(X_train, y_train)
 
+export_graphviz(
+    tree_clf,
+    out_file="DataFiles/cancer.dot",
+    feature_names=cancer.feature_names,
+    class_names=cancer.target_names,
+    rounded=True,
+    filled=True
+)
+cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'
+os.system(cmd)
+

    @@ -256,7 +241,7 @@ $$

  • 24
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    • -
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    • diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html index 31ddce3f4..9bd180251 100644 --- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html +++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs016.html @@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec1'), - ('A typical Decision Tree with its pertinent Jargon, Regeression ' - 'Problem', - 2, - None, - '___sec2'), - ('General Features', 2, None, '___sec3'), - ('How do we set it up?', 2, None, '___sec4'), - ('Decision trees and Regression', 2, None, '___sec5'), - ('Building a tree, regression', 2, None, '___sec6'), + ('General Features', 2, None, '___sec2'), + ('How do we set it up?', 2, None, '___sec3'), + ('Decision trees and Regression', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), ('A top-down approach, recursive binary splitting', 2, None, - '___sec7'), - ('Making a tree', 2, None, '___sec8'), - ('Pruning the tree', 2, None, '___sec9'), - ('Cost complexity pruning', 2, None, '___sec10'), - ('Schematic Regression Procedure', 2, None, '___sec11'), - ('A Classification Tree', 2, None, '___sec12'), - ('Growing a classification tree', 2, None, '___sec13'), - ('Classification tree, how to split nodes', 2, None, '___sec14'), - ('Visualizing the Tree, Classification', 2, None, '___sec15'), - ('Visualizing the Tree, The Moons', 2, None, '___sec16'), - ('Computing the Gini index', 2, None, '___sec17'), - ('Simple Python Code to read in Data', 2, None, '___sec18'), - ('Computing the Gini Factor', 2, None, '___sec19'), - ('Entropy and the ID3 algorithm', 2, None, '___sec20'), - ('Implementing the ID3 Algorithm', 2, None, '___sec21'), + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('Schematic Regression Procedure', 2, None, '___sec10'), + ('A Classification Tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Classification tree, how to split nodes', 2, None, '___sec13'), + ('Visualizing the Tree, Classification', 2, None, '___sec14'), + ('Visualizing the Tree, The Moons', 2, None, '___sec15'), + ('Computing the Gini index', 2, None, '___sec16'), + ('Simple Python Code to read in Data', 2, None, '___sec17'), + ('Computing the Gini Factor', 2, None, '___sec18'), + ('Entropy and the ID3 algorithm', 2, None, '___sec19'), + ('Implementing the ID3 Algorithm', 2, None, '___sec20'), ('Cancer Data again now with Decision Trees and other Methods', 2, None, - '___sec22'), - ('Another example, the moons again', 2, None, '___sec23'), - ('Playing around with regions', 2, None, '___sec24'), - ('Regression trees', 2, None, '___sec25'), - ('Final regressor code', 2, None, '___sec26'), - ('Pros and cons of trees, pros', 2, None, '___sec27'), - ('Disadvantages', 2, None, '___sec28'), - ('Bagging', 2, None, '___sec29'), - ('More bagging', 2, None, '___sec30'), - ('Simple example, head or tail', 2, None, '___sec31'), - ('Bagging Example', 2, None, '___sec32'), - ('Random forests', 2, None, '___sec33'), - ('A simple scikit-learn example', 2, None, '___sec34'), - ('Please, not the moons again!', 2, None, '___sec35'), - ('Bagging examples', 2, None, '___sec36'), - ('Then random forests', 2, None, '___sec37')]} + '___sec21'), + ('Another example, the moons again', 2, None, '___sec22'), + ('Playing around with regions', 2, None, '___sec23'), + ('Regression trees', 2, None, '___sec24'), + ('Final regressor code', 2, None, '___sec25'), + ('Pros and cons of trees, pros', 2, None, '___sec26'), + ('Disadvantages', 2, None, '___sec27'), + ('Bagging', 2, None, '___sec28'), + ('More bagging', 2, None, '___sec29'), + ('Simple example, head or tail', 2, None, '___sec30'), + ('Bagging Example', 2, None, '___sec31'), + ('Random forests', 2, None, '___sec32'), + ('A simple scikit-learn example', 2, None, '___sec33'), + ('Please, not the moons again!', 2, None, '___sec34'), + ('Bagging examples', 2, None, '___sec35'), + ('Then random forests', 2, None, '___sec36')]} end of tocinfo --> @@ -132,42 +127,41 @@ MathJax.Hub.Config({ @@ -183,42 +177,33 @@ MathJax.Hub.Config({ -

    Visualizing the Tree, Classification

    +

    Visualizing the Tree, The Moons

    -

    import os
-from sklearn.datasets import load_breast_cancer
+
    # Common imports
+import numpy as np
+from sklearn.model_selection import  train_test_split 
 from sklearn.tree import DecisionTreeClassifier
-from sklearn.model_selection import train_test_split
-from sklearn.metrics import confusion_matrix
+from sklearn.datasets import make_moons
 from sklearn.tree import export_graphviz
-
-from IPython.display import Image 
 from pydot import graph_from_dot_data
 import pandas as pd
-import numpy as np
+import os
 
-
-cancer = load_breast_cancer()
-X = pd.DataFrame(cancer.data, columns=cancer.feature_names)
-print(X)
-y = pd.Categorical.from_codes(cancer.target, cancer.target_names)
-y = pd.get_dummies(y)
-print(y)
-X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)
+np.random.seed(42)
+X, y = make_moons(n_samples=100, noise=0.25, random_state=53)
+X_train, X_test, y_train, y_test = train_test_split(X,y,random_state=0)
 tree_clf = DecisionTreeClassifier(max_depth=5)
 tree_clf.fit(X_train, y_train)
 
 export_graphviz(
     tree_clf,
-    out_file="DataFiles/cancer.dot",
-    feature_names=cancer.feature_names,
-    class_names=cancer.target_names,
+    out_file="DataFiles/moons.dot",
     rounded=True,
     filled=True
 )
-cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'
+cmd = 'dot -Tpng DataFiles/moons.dot -o DataFiles/moons.png'
 os.system(cmd)
 
    
 
    
@@ -247,7 +232,7 @@ os.system(cmd)
   
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diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html
index ab845fe0f..799a4b092 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs017.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,35 +177,48 @@ MathJax.Hub.Config({
 
 
 
-
    Visualizing the Tree, The Moons  
    
+
    Computing the Gini index 
    
+
 
    
+The example we will look at is a classical one in many Machine
+Learning applications. Based on various meteorological features, we
+have several so-called attributes which decide whether we at the end
+will do some outdoor activity like skiing, going for a bike ride etc
+etc.  The table here contains the feautures outlook, temperature,
+humidity and wind.  The target or output is whether we ride
+(True=1) or whether we do something else that day (False=0). The
+attributes for each feature are then sunny, overcast and rain for the
+outlook, hot, cold and mild for temperature, high and normal for
+humidity and weak and strong for wind.
 
-
-
    # Common imports
-import numpy as np
-from sklearn.model_selection import  train_test_split 
-from sklearn.tree import DecisionTreeClassifier
-from sklearn.datasets import make_moons
-from sklearn.tree import export_graphviz
-from pydot import graph_from_dot_data
-import pandas as pd
-import os
+
    
+The table here summarizes the various attributes and
 
-np.random.seed(42)
-X, y = make_moons(n_samples=100, noise=0.25, random_state=53)
-X_train, X_test, y_train, y_test = train_test_split(X,y,random_state=0)
-tree_clf = DecisionTreeClassifier(max_depth=5)
-tree_clf.fit(X_train, y_train)
-
-export_graphviz(
-    tree_clf,
-    out_file="DataFiles/moons.dot",
-    rounded=True,
-    filled=True
-)
-cmd = 'dot -Tpng DataFiles/moons.dot -o DataFiles/moons.png'
-os.system(cmd)
-
    
+
    
+  
    
+    
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+    
    Day Outlook  Temperature Humidity  Wind  Ride 
       1          Sunny           Hot                High            Weak          0        
       2          Sunny           Hot                High            Strong        1        
       3          Overcast        Hot                High            Weak          1        
       4          Rain            Mild               High            Weak          1        
       5          Rain            Cool               Normal          Weak          1        
       6          Rain            Cool               Normal          Strong        0        
       7          Overcast        Cool               Normal          Strong        1        
       8          Sunny           Mild               High            Weak          0        
       9          Sunny           Cool               Normal          Weak          1        
       10         Rain            Mild               Normal          Weak          1        
       11         Sunny           Mild               Normal          Strong        1        
       12         Overcast        Mild               High            Strong        1        
       13         Overcast        Hot                Normal          Weak          1        
       14         Rain            Mild               High            Strong        0        
    
+  
     
+
     
 
    
 
    
 
@@ -238,7 +245,7 @@ os.system(cmd)
   
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diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html
index 504c3373f..fd3e369df 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs018.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,48 +177,65 @@ MathJax.Hub.Config({
 
 
 
-
    Computing the Gini index 
    
+
    Simple Python Code to read in Data 
    
 
 
    
-The example we will look at is a classical one in many Machine
-Learning applications. Based on various meteorological features, we
-have several so-called attributes which decide whether we at the end
-will do some outdoor activity like skiing, going for a bike ride etc
-etc.  The table here contains the feautures outlook, temperature,
-humidity and wind.  The target or output is whether we ride
-(True=1) or whether we do something else that day (False=0). The
-attributes for each feature are then sunny, overcast and rain for the
-outlook, hot, cold and mild for temperature, high and normal for
-humidity and weak and strong for wind.
 
-
    
-The table here summarizes the various attributes and
+
+
    # Common imports
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from sklearn.preprocessing import StandardScaler, OneHotEncoder
+from sklearn.compose import ColumnTransformer
+from IPython.display import Image 
+from pydot import graph_from_dot_data
+import os
 
-
    
-  
    
-    
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-    
    Day Outlook  Temperature Humidity  Wind  Ride 
       1          Sunny           Hot                High            Weak          0        
       2          Sunny           Hot                High            Strong        1        
       3          Overcast        Hot                High            Weak          1        
       4          Rain            Mild               High            Weak          1        
       5          Rain            Cool               Normal          Weak          1        
       6          Rain            Cool               Normal          Strong        0        
       7          Overcast        Cool               Normal          Strong        1        
       8          Sunny           Mild               High            Weak          0        
       9          Sunny           Cool               Normal          Weak          1        
       10         Rain            Mild               Normal          Weak          1        
       11         Sunny           Mild               Normal          Strong        1        
       12         Overcast        Mild               High            Strong        1        
       13         Overcast        Hot                Normal          Weak          1        
       14         Rain            Mild               High            Strong        0        
    
-  
     
-
     
+# Where to save the figures and data files
+PROJECT_ROOT_DIR = "Results"
+FIGURE_ID = "Results/FigureFiles"
+DATA_ID = "DataFiles/"
+
+if not os.path.exists(PROJECT_ROOT_DIR):
+    os.mkdir(PROJECT_ROOT_DIR)
+
+if not os.path.exists(FIGURE_ID):
+    os.makedirs(FIGURE_ID)
+
+if not os.path.exists(DATA_ID):
+    os.makedirs(DATA_ID)
+
+def image_path(fig_id):
+    return os.path.join(FIGURE_ID, fig_id)
+
+def data_path(dat_id):
+    return os.path.join(DATA_ID, dat_id)
+
+def save_fig(fig_id):
+    plt.savefig(image_path(fig_id) + ".png", format='png')
+
+infile = open(data_path("ride.csv"),'r')
+
+# Read the experimental data with Pandas
+from IPython.display import display
+ridedata = pd.read_csv(infile,names = ('Outlook','Temperature','Humidity','Wind','Ride'))
+ridedata = pd.DataFrame(ridedata)
+display(ridedata)
+# Features and targets
+X = ridedata.loc[:, ridedata.columns != 'Ride'].values
+display(X)
+y = ridedata.loc[:, ridedata.columns == 'Ride'].values
+display(y)
+# Categorical variables to one-hot's
+onehotencoder = OneHotEncoder(categories="auto")
+
+X = ColumnTransformer([("", onehotencoder)]).fit_transform(X)
+y.shape
+
+display(X)
+display(y)
+
    
 
    
 
    
 
@@ -251,7 +262,7 @@ The table here summarizes the various attributes and
   
  • 27
    • 
   
  • 28
    • 
   
  • ...
    • 
-  
  • 39
    • 
+  
  • 38
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html
index 6cc582f6b..52213c74a 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs019.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,64 +177,80 @@ MathJax.Hub.Config({
 
 
 
-
    Simple Python Code to read in Data 
    
+
    Computing the Gini Factor  
    
+
+
    
+The above functions (gini, entropy and misclassification error) are
+important components of the so-called CART algorithm. We will discuss
+this algorithm below after we have discussed the information gain
+algorithm ID3.
+
+
    
+In the example here we have converted all our attributes into numerical values \( 0,1,2 \) etc.
 
 
    
 
 
-
    # Common imports
-import numpy as np
-import pandas as pd
-import matplotlib.pyplot as plt
-from sklearn.preprocessing import StandardScaler, OneHotEncoder
-from sklearn.compose import ColumnTransformer
-from IPython.display import Image 
-from pydot import graph_from_dot_data
-import os
+
    # Split a dataset based on an attribute and an attribute value
+def test_split(index, value, dataset):
+	left, right = list(), list()
+	for row in dataset:
+		if row[index] < value:
+			left.append(row)
+		else:
+			right.append(row)
+	return left, right
+ 
+# Calculate the Gini index for a split dataset
+def gini_index(groups, classes):
+	# count all samples at split point
+	n_instances = float(sum([len(group) for group in groups]))
+	# sum weighted Gini index for each group
+	gini = 0.0
+	for group in groups:
+		size = float(len(group))
+		# avoid divide by zero
+		if size == 0:
+			continue
+		score = 0.0
+		# score the group based on the score for each class
+		for class_val in classes:
+			p = [row[-1] for row in group].count(class_val) / size
+			score += p * p
+		# weight the group score by its relative size
+		gini += (1.0 - score) * (size / n_instances)
+	return gini
 
-# Where to save the figures and data files
-PROJECT_ROOT_DIR = "Results"
-FIGURE_ID = "Results/FigureFiles"
-DATA_ID = "DataFiles/"
+# Select the best split point for a dataset
+def get_split(dataset):
+	class_values = list(set(row[-1] for row in dataset))
+	b_index, b_value, b_score, b_groups = 999, 999, 999, None
+	for index in range(len(dataset[0])-1):
+		for row in dataset:
+			groups = test_split(index, row[index], dataset)
+			gini = gini_index(groups, class_values)
+			print('X%d < %.3f Gini=%.3f' % ((index+1), row[index], gini))
+			if gini < b_score:
+				b_index, b_value, b_score, b_groups = index, row[index], gini, groups
+	return {'index':b_index, 'value':b_value, 'groups':b_groups}
+ 
+dataset = [[0,0,0,0,0],
+            [0,0,0,1,1],
+            [1,0,0,0,1],
+            [2,1,0,0,1],
+            [2,2,1,0,1],
+            [2,2,1,1,0],
+            [1,2,1,1,1],
+            [0,1,0,0,0],
+            [0,2,1,0,1],
+            [2,1,1,0,1],
+            [0,1,1,1,1],
+            [1,1,0,1,1],
+            [1,0,1,0,1],
+            [2,1,0,1,0]]
 
-if not os.path.exists(PROJECT_ROOT_DIR):
-    os.mkdir(PROJECT_ROOT_DIR)
-
-if not os.path.exists(FIGURE_ID):
-    os.makedirs(FIGURE_ID)
-
-if not os.path.exists(DATA_ID):
-    os.makedirs(DATA_ID)
-
-def image_path(fig_id):
-    return os.path.join(FIGURE_ID, fig_id)
-
-def data_path(dat_id):
-    return os.path.join(DATA_ID, dat_id)
-
-def save_fig(fig_id):
-    plt.savefig(image_path(fig_id) + ".png", format='png')
-
-infile = open(data_path("ride.csv"),'r')
-
-# Read the experimental data with Pandas
-from IPython.display import display
-ridedata = pd.read_csv(infile,names = ('Outlook','Temperature','Humidity','Wind','Ride'))
-ridedata = pd.DataFrame(ridedata)
-display(ridedata)
-# Features and targets
-X = ridedata.loc[:, ridedata.columns != 'Ride'].values
-display(X)
-y = ridedata.loc[:, ridedata.columns == 'Ride'].values
-display(y)
-# Categorical variables to one-hot's
-onehotencoder = OneHotEncoder(categories="auto")
-
-X = ColumnTransformer([("", onehotencoder)]).fit_transform(X)
-y.shape
-
-display(X)
-display(y)
+split = get_split(dataset)
+print('Split: [X%d < %.3f]' % ((split['index']+1), split['value']))
 
    
 
    
 
    
@@ -268,7 +278,7 @@ display(y)
   
  • 28
    • 
   
  • 29
    • 
   
  • ...
    • 
-  
  • 39
    • 
+  
  • 38
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html
index c20d867e3..fc3eaf882 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs020.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,81 +177,39 @@ MathJax.Hub.Config({
 
 
 
-
    Computing the Gini Factor  
    
+
    Entropy and the ID3 algorithm 
    
 
 
    
-The above functions (gini, entropy and misclassification error) are
-important components of the so-called CART algorithm. We will discuss
-this algorithm below after we have discussed the information gain
-algorithm ID3.
+ID3, learns decision trees by constructing
+them topdown, beginning with the question which attribute should be tested at the root of the tree?
+
+
      
+
    1.  Each instance attribute is evaluated using a statistical test to determine how well it alone classifies the training examples.
      2. 
+
    2.  The best attribute is selected and used as the test at the root node of the tree.
      3. 
+
    3.  A descendant of the root node is then created for each possible value of this attribute.
      4. 
+
    4.  Training examples are sorted to the appropriate descendant node.
      5. 
+
    5.  The entire process is then repeated using the training examples associated with each descendant node to select the best attribute to test at that point in the tree.
      6. 
+
    6.  This forms a greedy search for an acceptable decision tree, in which the algorithm never backtracks to reconsider earlier choices.
      7.  
+
    
+
+The ID3 algorithm selects, which attribute to test at each node in the
+tree.
 
 
    
-In the example here we have converted all our attributes into numerical values \( 0,1,2 \) etc.
+We would like to select the attribute that is most useful for classifying
+examples.
 
 
    
+What is a good quantitative measure of the worth of an attribute?
 
-
-
    # Split a dataset based on an attribute and an attribute value
-def test_split(index, value, dataset):
-	left, right = list(), list()
-	for row in dataset:
-		if row[index] < value:
-			left.append(row)
-		else:
-			right.append(row)
-	return left, right
- 
-# Calculate the Gini index for a split dataset
-def gini_index(groups, classes):
-	# count all samples at split point
-	n_instances = float(sum([len(group) for group in groups]))
-	# sum weighted Gini index for each group
-	gini = 0.0
-	for group in groups:
-		size = float(len(group))
-		# avoid divide by zero
-		if size == 0:
-			continue
-		score = 0.0
-		# score the group based on the score for each class
-		for class_val in classes:
-			p = [row[-1] for row in group].count(class_val) / size
-			score += p * p
-		# weight the group score by its relative size
-		gini += (1.0 - score) * (size / n_instances)
-	return gini
+
    
+Information gain measures how well a given attribute separates the
+training examples according to their target classification.
 
-# Select the best split point for a dataset
-def get_split(dataset):
-	class_values = list(set(row[-1] for row in dataset))
-	b_index, b_value, b_score, b_groups = 999, 999, 999, None
-	for index in range(len(dataset[0])-1):
-		for row in dataset:
-			groups = test_split(index, row[index], dataset)
-			gini = gini_index(groups, class_values)
-			print('X%d < %.3f Gini=%.3f' % ((index+1), row[index], gini))
-			if gini < b_score:
-				b_index, b_value, b_score, b_groups = index, row[index], gini, groups
-	return {'index':b_index, 'value':b_value, 'groups':b_groups}
- 
-dataset = [[0,0,0,0,0],
-            [0,0,0,1,1],
-            [1,0,0,0,1],
-            [2,1,0,0,1],
-            [2,2,1,0,1],
-            [2,2,1,1,0],
-            [1,2,1,1,1],
-            [0,1,0,0,0],
-            [0,2,1,0,1],
-            [2,1,1,0,1],
-            [0,1,1,1,1],
-            [1,1,0,1,1],
-            [1,0,1,0,1],
-            [2,1,0,1,0]]
+
    
+The ID3 algorithm uses this information gain measure to select among the candidate
+attributes at each step while growing the tree.
 
-split = get_split(dataset)
-print('Split: [X%d < %.3f]' % ((split['index']+1), split['value']))
-
    
 
    
 
    
 
@@ -284,7 +236,7 @@ split = get_split(dataset)
   
  • 29
    • 
   
  • 30
    • 
   
  • ...
    • 
-  
  • 39
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+  
  • 38
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    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html
index 5bc4ec431..8862b0863 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs021.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,39 +177,199 @@ MathJax.Hub.Config({
 
 
 
-
    Entropy and the ID3 algorithm 
    
+
    Implementing the ID3 Algorithm 
    
 
 
    
-ID3, learns decision trees by constructing
-them topdown, beginning with the question which attribute should be tested at the root of the tree?
 
-
      
-
    1.  Each instance attribute is evaluated using a statistical test to determine how well it alone classifies the training examples.
      2. 
-
    2.  The best attribute is selected and used as the test at the root node of the tree.
      3. 
-
    3.  A descendant of the root node is then created for each possible value of this attribute.
      4. 
-
    4.  Training examples are sorted to the appropriate descendant node.
      5. 
-
    5.  The entire process is then repeated using the training examples associated with each descendant node to select the best attribute to test at that point in the tree.
      6. 
-
    6.  This forms a greedy search for an acceptable decision tree, in which the algorithm never backtracks to reconsider earlier choices.
      7.  
-
    
+
+
    import re
+import math
+from collections import deque
 
-The ID3 algorithm selects, which attribute to test at each node in the
-tree.
+# x is examples in training set
+# y is set of targets
+# label is target attributes
+# Node is a class which has properties values, childs, and next
+# root is top node in the decision tree
 
-
    
-We would like to select the attribute that is most useful for classifying
-examples.
+class Node(object):
+	def __init__(self):
+		self.value = None
+		self.next = None
+		self.childs = None
 
-
    
-What is a good quantitative measure of the worth of an attribute?
+# Simple class of Decision Tree
+# Aimed for who want to learn Decision Tree, so it is not optimized
+class DecisionTree(object):
+	def __init__(self, sample, attributes, labels):
+		self.sample = sample
+		self.attributes = attributes
+		self.labels = labels
+		self.labelCodes = None
+		self.labelCodesCount = None
+		self.initLabelCodes()
+		# print(self.labelCodes)
+		self.root = None
+		self.entropy = self.getEntropy([x for x in range(len(self.labels))])
 
-
    
-Information gain measures how well a given attribute separates the
-training examples according to their target classification.
+	def initLabelCodes(self):
+		self.labelCodes = []
+		self.labelCodesCount = []
+		for l in self.labels:
+			if l not in self.labelCodes:
+				self.labelCodes.append(l)
+				self.labelCodesCount.append(0)
+			self.labelCodesCount[self.labelCodes.index(l)] += 1
 
-
    
-The ID3 algorithm uses this information gain measure to select among the candidate
-attributes at each step while growing the tree.
+	def getLabelCodeId(self, sampleId):
+		return self.labelCodes.index(self.labels[sampleId])
 
+	def getAttributeValues(self, sampleIds, attributeId):
+		vals = []
+		for sid in sampleIds:
+			val = self.sample[sid][attributeId]
+			if val not in vals:
+				vals.append(val)
+		# print(vals)
+		return vals
+
+	def getEntropy(self, sampleIds):
+		entropy = 0
+		labelCount = [0] * len(self.labelCodes)
+		for sid in sampleIds:
+			labelCount[self.getLabelCodeId(sid)] += 1
+		# print("-ge", labelCount)
+		for lv in labelCount:
+			# print(lv)
+			if lv != 0:
+				entropy += -lv/len(sampleIds) * math.log(lv/len(sampleIds), 2)
+			else:
+				entropy += 0
+		return entropy
+
+	def getDominantLabel(self, sampleIds):
+		labelCodesCount = [0] * len(self.labelCodes)
+		for sid in sampleIds:
+			labelCodesCount[self.labelCodes.index(self.labels[sid])] += 1
+		return self.labelCodes[labelCodesCount.index(max(labelCodesCount))]
+
+	def getInformationGain(self, sampleIds, attributeId):
+		gain = self.getEntropy(sampleIds)
+		attributeVals = []
+		attributeValsCount = []
+		attributeValsIds = []
+		for sid in sampleIds:
+			val = self.sample[sid][attributeId]
+			if val not in attributeVals:
+				attributeVals.append(val)
+				attributeValsCount.append(0)
+				attributeValsIds.append([])
+			vid = attributeVals.index(val)
+			attributeValsCount[vid] += 1
+			attributeValsIds[vid].append(sid)
+		# print("-gig", self.attributes[attributeId])
+		for vc, vids in zip(attributeValsCount, attributeValsIds):
+			# print("-gig", vids)
+			gain -= vc/len(sampleIds) * self.getEntropy(vids)
+		return gain
+
+	def getAttributeMaxInformationGain(self, sampleIds, attributeIds):
+		attributesEntropy = [0] * len(attributeIds)
+		for i, attId in zip(range(len(attributeIds)), attributeIds):
+			attributesEntropy[i] = self.getInformationGain(sampleIds, attId)
+		maxId = attributeIds[attributesEntropy.index(max(attributesEntropy))]
+		return self.attributes[maxId], maxId
+
+	def isSingleLabeled(self, sampleIds):
+		label = self.labels[sampleIds[0]]
+		for sid in sampleIds:
+			if self.labels[sid] != label:
+				return False
+		return True
+
+	def getLabel(self, sampleId):
+		return self.labels[sampleId]
+
+	def id3(self):
+		sampleIds = [x for x in range(len(self.sample))]
+		attributeIds = [x for x in range(len(self.attributes))]
+		self.root = self.id3Recv(sampleIds, attributeIds, self.root)
+
+	def id3Recv(self, sampleIds, attributeIds, root):
+		root = Node() # Initialize current root
+		if self.isSingleLabeled(sampleIds):
+			root.value = self.labels[sampleIds[0]]
+			return root
+		# print(attributeIds)
+		if len(attributeIds) == 0:
+			root.value = self.getDominantLabel(sampleIds)
+			return root
+		bestAttrName, bestAttrId = self.getAttributeMaxInformationGain(
+			sampleIds, attributeIds)
+		# print(bestAttrName)
+		root.value = bestAttrName
+		root.childs = []  # Create list of children
+		for value in self.getAttributeValues(sampleIds, bestAttrId):
+			# print(value)
+			child = Node()
+			child.value = value
+			root.childs.append(child)  # Append new child node to current
+									   # root
+			childSampleIds = []
+			for sid in sampleIds:
+				if self.sample[sid][bestAttrId] == value:
+					childSampleIds.append(sid)
+			if len(childSampleIds) == 0:
+				child.next = self.getDominantLabel(sampleIds)
+			else:
+				# print(bestAttrName, bestAttrId)
+				# print(attributeIds)
+				if len(attributeIds) > 0 and bestAttrId in attributeIds:
+					toRemove = attributeIds.index(bestAttrId)
+					attributeIds.pop(toRemove)
+				child.next = self.id3Recv(
+					childSampleIds, attributeIds, child.next)
+		return root
+
+	def printTree(self):
+		if self.root:
+			roots = deque()
+			roots.append(self.root)
+			while len(roots) > 0:
+				root = roots.popleft()
+				print(root.value)
+				if root.childs:
+					for child in root.childs:
+						print('({})'.format(child.value))
+						roots.append(child.next)
+				elif root.next:
+					print(root.next)
+
+
+def test():
+	f = open('DataFiles/rideclass.csv')
+	attributes = f.readline().split(',')
+	attributes = attributes[1:len(attributes)-1]
+	print(attributes)
+	sample = f.readlines()
+	f.close()
+	for i in range(len(sample)):
+		sample[i] = re.sub('\d+,', '', sample[i])
+		sample[i] = sample[i].strip().split(',')
+	labels = []
+	for s in sample:
+		labels.append(s.pop())
+	# print(sample)
+	# print(labels)
+	decisionTree = DecisionTree(sample, attributes, labels)
+	print("System entropy {}".format(decisionTree.entropy))
+	decisionTree.id3()
+	decisionTree.printTree()
+
+
+if __name__ == '__main__':
+	test()
+
    
 
    
 
    
 
@@ -242,7 +396,7 @@ attributes at each step while growing the tree.
   
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    • 
   
  • ...
    • 
-  
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    • 
+  
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    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html
index 25c8cbcc9..0530a3bda 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs022.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,212 +177,52 @@ MathJax.Hub.Config({
 
 
 
-
    Implementing the ID3 Algorithm 
    
-
+
    Cancer Data again now with Decision Trees and other Methods 
    
 
    
-import re
-import math
-from collections import deque
 
-
    
-
-
-
-
-
+
+
    import matplotlib.pyplot as plt
+import numpy as np
+from sklearn.model_selection import  train_test_split 
+from sklearn.datasets import load_breast_cancer
+from sklearn.svm import SVC
+from sklearn.linear_model import LogisticRegression
+from sklearn.tree import DecisionTreeClassifier
 
-
    
-class Node(object):
-	def __init__(self):
-		self.value = None
-		self.next = None
-		self.childs = None
-
-
    
-
-
-class DecisionTree(object):
-	def __init__(self, sample, attributes, labels):
-		self.sample = sample
-		self.attributes = attributes
-		self.labels = labels
-		self.labelCodes = None
-		self.labelCodesCount = None
-		self.initLabelCodes()
-		# print(self.labelCodes)
-		self.root = None
-		self.entropy = self.getEntropy([x for x in range(len(self.labels))])
-
-
    
-	def initLabelCodes(self):
-		self.labelCodes = []
-		self.labelCodesCount = []
-		for l in self.labels:
-			if l not in self.labelCodes:
-				self.labelCodes.append(l)
-				self.labelCodesCount.append(0)
-			self.labelCodesCount[self.labelCodes.index(l)] += 1
-
-
    
-	def getLabelCodeId(self, sampleId):
-		return self.labelCodes.index(self.labels[sampleId])
-
-
    
-	def getAttributeValues(self, sampleIds, attributeId):
-		vals = []
-		for sid in sampleIds:
-			val = self.sample[sid][attributeId]
-			if val not in vals:
-				vals.append(val)
-		# print(vals)
-		return vals
-
-
    
-	def getEntropy(self, sampleIds):
-		entropy = 0
-		labelCount = [0] * len(self.labelCodes)
-		for sid in sampleIds:
-			labelCount[self.getLabelCodeId(sid)] += 1
-		# print("-ge", labelCount)
-		for lv in labelCount:
-			# print(lv)
-			if lv != 0:
-				entropy += -lv/len(sampleIds) * math.log(lv/len(sampleIds), 2)
-			else:
-				entropy += 0
-		return entropy
-
-
    
-	def getDominantLabel(self, sampleIds):
-		labelCodesCount = [0] * len(self.labelCodes)
-		for sid in sampleIds:
-			labelCodesCount[self.labelCodes.index(self.labels[sid])] += 1
-		return self.labelCodes[labelCodesCount.index(max(labelCodesCount))]
-
-
    
-	def getInformationGain(self, sampleIds, attributeId):
-		gain = self.getEntropy(sampleIds)
-		attributeVals = []
-		attributeValsCount = []
-		attributeValsIds = []
-		for sid in sampleIds:
-			val = self.sample[sid][attributeId]
-			if val not in attributeVals:
-				attributeVals.append(val)
-				attributeValsCount.append(0)
-				attributeValsIds.append([])
-			vid = attributeVals.index(val)
-			attributeValsCount[vid] += 1
-			attributeValsIds[vid].append(sid)
-		# print("-gig", self.attributes[attributeId])
-		for vc, vids in zip(attributeValsCount, attributeValsIds):
-			# print("-gig", vids)
-			gain -= vc/len(sampleIds) * self.getEntropy(vids)
-		return gain
-
-
    
-	def getAttributeMaxInformationGain(self, sampleIds, attributeIds):
-		attributesEntropy = [0] * len(attributeIds)
-		for i, attId in zip(range(len(attributeIds)), attributeIds):
-			attributesEntropy[i] = self.getInformationGain(sampleIds, attId)
-		maxId = attributeIds[attributesEntropy.index(max(attributesEntropy))]
-		return self.attributes[maxId], maxId
-
-
    
-	def isSingleLabeled(self, sampleIds):
-		label = self.labels[sampleIds[0]]
-		for sid in sampleIds:
-			if self.labels[sid] != label:
-				return False
-		return True
-
-
    
-	def getLabel(self, sampleId):
-		return self.labels[sampleId]
-
-
    
-	def id3(self):
-		sampleIds = [x for x in range(len(self.sample))]
-		attributeIds = [x for x in range(len(self.attributes))]
-		self.root = self.id3Recv(sampleIds, attributeIds, self.root)
-
-
    
-	def id3Recv(self, sampleIds, attributeIds, root):
-		root = Node() # Initialize current root
-		if self.isSingleLabeled(sampleIds):
-			root.value = self.labels[sampleIds[0]]
-			return root
-		# print(attributeIds)
-		if len(attributeIds) == 0:
-			root.value = self.getDominantLabel(sampleIds)
-			return root
-		bestAttrName, bestAttrId = self.getAttributeMaxInformationGain(
-			sampleIds, attributeIds)
-		# print(bestAttrName)
-		root.value = bestAttrName
-		root.childs = []  # Create list of children
-		for value in self.getAttributeValues(sampleIds, bestAttrId):
-			# print(value)
-			child = Node()
-			child.value = value
-			root.childs.append(child)  # Append new child node to current
-									   # root
-			childSampleIds = []
-			for sid in sampleIds:
-				if self.sample[sid][bestAttrId] == value:
-					childSampleIds.append(sid)
-			if len(childSampleIds) == 0:
-				child.next = self.getDominantLabel(sampleIds)
-			else:
-				# print(bestAttrName, bestAttrId)
-				# print(attributeIds)
-				if len(attributeIds) > 0 and bestAttrId in attributeIds:
-					toRemove = attributeIds.index(bestAttrId)
-					attributeIds.pop(toRemove)
-				child.next = self.id3Recv(
-					childSampleIds, attributeIds, child.next)
-		return root
-
-
    
-	def printTree(self):
-		if self.root:
-			roots = deque()
-			roots.append(self.root)
-			while len(roots) > 0:
-				root = roots.popleft()
-				print(root.value)
-				if root.childs:
-					for child in root.childs:
-						print('({})'.format(child.value))
-						roots.append(child.next)
-				elif root.next:
-					print(root.next)
-
-
    
-def test():
-	f = open('DataFiles/rideclass.csv')
-	attributes = f.readline().split(',')
-	attributes = attributes[1:len(attributes)-1]
-	print(attributes)
-	sample = f.readlines()
-	f.close()
-	for i in range(len(sample)):
-		sample[i] = re.sub('\d+,', '', sample[i])
-		sample[i] = sample[i].strip().split(',')
-	labels = []
-	for s in sample:
-		labels.append(s.pop())
-	# print(sample)
-	# print(labels)
-	decisionTree = DecisionTree(sample, attributes, labels)
-	print("System entropy {}".format(decisionTree.entropy))
-	decisionTree.id3()
-	decisionTree.printTree()
-
-
    
-if __name__ == '__main__':
-	test()
+# Load the data
+cancer = load_breast_cancer()
 
+X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
+print(X_train.shape)
+print(X_test.shape)
+# Logistic Regression
+logreg = LogisticRegression(solver='lbfgs')
+logreg.fit(X_train, y_train)
+print("Test set accuracy with Logistic Regression: {:.2f}".format(logreg.score(X_test,y_test)))
+# Support vector machine
+svm = SVC(gamma='auto', C=100)
+svm.fit(X_train, y_train)
+print("Test set accuracy with SVM: {:.2f}".format(svm.score(X_test,y_test)))
+# Decision Trees
+deep_tree_clf = DecisionTreeClassifier(max_depth=None)
+deep_tree_clf.fit(X_train, y_train)
+print("Test set accuracy with Decision Trees: {:.2f}".format(deep_tree_clf.score(X_test,y_test)))
+#now scale the data
+from sklearn.preprocessing import StandardScaler
+scaler = StandardScaler()
+scaler.fit(X_train)
+X_train_scaled = scaler.transform(X_train)
+X_test_scaled = scaler.transform(X_test)
+# Logistic Regression
+logreg.fit(X_train_scaled, y_train)
+print("Test set accuracy Logistic Regression with scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
+# Support Vector Machine
+svm.fit(X_train_scaled, y_train)
+print("Test set accuracy SVM with scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
+# Decision Trees
+deep_tree_clf.fit(X_train_scaled, y_train)
+print("Test set accuracy with Decision Trees and scaled data: {:.2f}".format(deep_tree_clf.score(X_test_scaled,y_test)))
+
    
 
    
 
    
 
@@ -415,7 +249,7 @@ if __name__ == '__main__':
   
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    • 
   
  • ...
    • 
-  
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diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html
index 6c66fb5e7..e369c4f45 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs023.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,51 +177,74 @@ MathJax.Hub.Config({
 
 
 
-
    Cancer Data again now with Decision Trees and other Methods 
    
+
    Another example, the moons again 
    
 
    
 
 
-
    import matplotlib.pyplot as plt
+
    from __future__ import division, print_function, unicode_literals
+
+# Common imports
 import numpy as np
-from sklearn.model_selection import  train_test_split 
-from sklearn.datasets import load_breast_cancer
+import os
+
+# to make this notebook's output stable across runs
+np.random.seed(42)
+
+# To plot pretty figures
+import matplotlib
+import matplotlib.pyplot as plt
+from matplotlib.colors import ListedColormap
+plt.rcParams['axes.labelsize'] = 14
+plt.rcParams['xtick.labelsize'] = 12
+plt.rcParams['ytick.labelsize'] = 12
+
+
 from sklearn.svm import SVC
-from sklearn.linear_model import LogisticRegression
+from sklearn import datasets
 from sklearn.tree import DecisionTreeClassifier
+from sklearn.datasets import make_moons
+from sklearn.tree import export_graphviz
 
-# Load the data
-cancer = load_breast_cancer()
+Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)
 
-X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
-print(X_train.shape)
-print(X_test.shape)
-# Logistic Regression
-logreg = LogisticRegression(solver='lbfgs')
-logreg.fit(X_train, y_train)
-print("Test set accuracy with Logistic Regression: {:.2f}".format(logreg.score(X_test,y_test)))
-# Support vector machine
-svm = SVC(gamma='auto', C=100)
-svm.fit(X_train, y_train)
-print("Test set accuracy with SVM: {:.2f}".format(svm.score(X_test,y_test)))
-# Decision Trees
-deep_tree_clf = DecisionTreeClassifier(max_depth=None)
-deep_tree_clf.fit(X_train, y_train)
-print("Test set accuracy with Decision Trees: {:.2f}".format(deep_tree_clf.score(X_test,y_test)))
-#now scale the data
-from sklearn.preprocessing import StandardScaler
-scaler = StandardScaler()
-scaler.fit(X_train)
-X_train_scaled = scaler.transform(X_train)
-X_test_scaled = scaler.transform(X_test)
-# Logistic Regression
-logreg.fit(X_train_scaled, y_train)
-print("Test set accuracy Logistic Regression with scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
-# Support Vector Machine
-svm.fit(X_train_scaled, y_train)
-print("Test set accuracy SVM with scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
-# Decision Trees
-deep_tree_clf.fit(X_train_scaled, y_train)
-print("Test set accuracy with Decision Trees and scaled data: {:.2f}".format(deep_tree_clf.score(X_test_scaled,y_test)))
+deep_tree_clf1 = DecisionTreeClassifier(random_state=42)
+deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)
+deep_tree_clf1.fit(Xm, ym)
+deep_tree_clf2.fit(Xm, ym)
+
+
+def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):
+    x1s = np.linspace(axes[0], axes[1], 100)
+    x2s = np.linspace(axes[2], axes[3], 100)
+    x1, x2 = np.meshgrid(x1s, x2s)
+    X_new = np.c_[x1.ravel(), x2.ravel()]
+    y_pred = clf.predict(X_new).reshape(x1.shape)
+    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])
+    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)
+    if not iris:
+        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])
+        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)
+    if plot_training:
+        plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo", label="Iris-Setosa")
+        plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs", label="Iris-Versicolor")
+        plt.plot(X[:, 0][y==2], X[:, 1][y==2], "g^", label="Iris-Virginica")
+        plt.axis(axes)
+    if iris:
+        plt.xlabel("Petal length", fontsize=14)
+        plt.ylabel("Petal width", fontsize=14)
+    else:
+        plt.xlabel(r"$x_1$", fontsize=18)
+        plt.ylabel(r"$x_2$", fontsize=18, rotation=0)
+    if legend:
+        plt.legend(loc="lower right", fontsize=14)
+plt.figure(figsize=(11, 4))
+plt.subplot(121)
+plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)
+plt.title("No restrictions", fontsize=16)
+plt.subplot(122)
+plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)
+plt.title("min_samples_leaf = {}".format(deep_tree_clf2.min_samples_leaf), fontsize=14)
+plt.show()
 
    
 
    
 
    
@@ -255,7 +272,7 @@ deep_tree_clf.fit(X_train_scaled, y_train)
   
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diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html
index 4edb2d51a..b2f7470df 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs024.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,73 +177,29 @@ MathJax.Hub.Config({
 
 
 
-
    Another example, the moons again 
    
+
    Playing around with regions 
    
 
    
 
 
-
    from __future__ import division, print_function, unicode_literals
+
    np.random.seed(6)
+Xs = np.random.rand(100, 2) - 0.5
+ys = (Xs[:, 0] > 0).astype(np.float32) * 2
 
-# Common imports
-import numpy as np
-import os
+angle = np.pi/4
+rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])
+Xsr = Xs.dot(rotation_matrix)
 
-# to make this notebook's output stable across runs
-np.random.seed(42)
+tree_clf_s = DecisionTreeClassifier(random_state=42)
+tree_clf_s.fit(Xs, ys)
+tree_clf_sr = DecisionTreeClassifier(random_state=42)
+tree_clf_sr.fit(Xsr, ys)
 
-# To plot pretty figures
-import matplotlib
-import matplotlib.pyplot as plt
-from matplotlib.colors import ListedColormap
-plt.rcParams['axes.labelsize'] = 14
-plt.rcParams['xtick.labelsize'] = 12
-plt.rcParams['ytick.labelsize'] = 12
-
-
-from sklearn.svm import SVC
-from sklearn import datasets
-from sklearn.tree import DecisionTreeClassifier
-from sklearn.datasets import make_moons
-from sklearn.tree import export_graphviz
-
-Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)
-
-deep_tree_clf1 = DecisionTreeClassifier(random_state=42)
-deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)
-deep_tree_clf1.fit(Xm, ym)
-deep_tree_clf2.fit(Xm, ym)
-
-
-def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):
-    x1s = np.linspace(axes[0], axes[1], 100)
-    x2s = np.linspace(axes[2], axes[3], 100)
-    x1, x2 = np.meshgrid(x1s, x2s)
-    X_new = np.c_[x1.ravel(), x2.ravel()]
-    y_pred = clf.predict(X_new).reshape(x1.shape)
-    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])
-    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)
-    if not iris:
-        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])
-        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)
-    if plot_training:
-        plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo", label="Iris-Setosa")
-        plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs", label="Iris-Versicolor")
-        plt.plot(X[:, 0][y==2], X[:, 1][y==2], "g^", label="Iris-Virginica")
-        plt.axis(axes)
-    if iris:
-        plt.xlabel("Petal length", fontsize=14)
-        plt.ylabel("Petal width", fontsize=14)
-    else:
-        plt.xlabel(r"$x_1$", fontsize=18)
-        plt.ylabel(r"$x_2$", fontsize=18, rotation=0)
-    if legend:
-        plt.legend(loc="lower right", fontsize=14)
 plt.figure(figsize=(11, 4))
 plt.subplot(121)
-plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)
-plt.title("No restrictions", fontsize=16)
+plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)
 plt.subplot(122)
-plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)
-plt.title("min_samples_leaf = {}".format(deep_tree_clf2.min_samples_leaf), fontsize=14)
+plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)
+
 plt.show()
 
    
 
    
@@ -278,7 +228,7 @@ plt.show()
   
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diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html
index 9b12a47de..38e372b68 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs025.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,30 +177,24 @@ MathJax.Hub.Config({
 
 
 
-
    Playing around with regions 
    
+
    Regression trees 
    
 
    
 
 
-
    np.random.seed(6)
-Xs = np.random.rand(100, 2) - 0.5
-ys = (Xs[:, 0] > 0).astype(np.float32) * 2
+
    # Quadratic training set + noise
+np.random.seed(42)
+m = 200
+X = np.random.rand(m, 1)
+y = 4 * (X - 0.5) ** 2
+y = y + np.random.randn(m, 1) / 10
+
    
+
    
 
-angle = np.pi/4
-rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])
-Xsr = Xs.dot(rotation_matrix)
+
+
    from sklearn.tree import DecisionTreeRegressor
 
-tree_clf_s = DecisionTreeClassifier(random_state=42)
-tree_clf_s.fit(Xs, ys)
-tree_clf_sr = DecisionTreeClassifier(random_state=42)
-tree_clf_sr.fit(Xsr, ys)
-
-plt.figure(figsize=(11, 4))
-plt.subplot(121)
-plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)
-plt.subplot(122)
-plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)
-
-plt.show()
+tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)
+tree_reg.fit(X, y)
 
    
 
    
 
    
@@ -234,7 +222,7 @@ plt.show()
   
  • 34
    • 
   
  • 35
    • 
   
  • ...
    • 
-  
  • 39
    • 
+  
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diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html
index 8f217f034..1796e10dd 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs026.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,24 +177,80 @@ MathJax.Hub.Config({
 
 
 
-
    Regression trees 
    
-
    
-
-
-
    # Quadratic training set + noise
-np.random.seed(42)
-m = 200
-X = np.random.rand(m, 1)
-y = 4 * (X - 0.5) ** 2
-y = y + np.random.randn(m, 1) / 10
-
    
+
    Final regressor code 
    
 
    
 
 
 
    from sklearn.tree import DecisionTreeRegressor
 
-tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)
-tree_reg.fit(X, y)
+tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)
+tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)
+tree_reg1.fit(X, y)
+tree_reg2.fit(X, y)
+
+def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel="$y$"):
+    x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)
+    y_pred = tree_reg.predict(x1)
+    plt.axis(axes)
+    plt.xlabel("$x_1$", fontsize=18)
+    if ylabel:
+        plt.ylabel(ylabel, fontsize=18, rotation=0)
+    plt.plot(X, y, "b.")
+    plt.plot(x1, y_pred, "r.-", linewidth=2, label=r"$\hat{y}$")
+
+plt.figure(figsize=(11, 4))
+plt.subplot(121)
+plot_regression_predictions(tree_reg1, X, y)
+for split, style in ((0.1973, "k-"), (0.0917, "k--"), (0.7718, "k--")):
+    plt.plot([split, split], [-0.2, 1], style, linewidth=2)
+plt.text(0.21, 0.65, "Depth=0", fontsize=15)
+plt.text(0.01, 0.2, "Depth=1", fontsize=13)
+plt.text(0.65, 0.8, "Depth=1", fontsize=13)
+plt.legend(loc="upper center", fontsize=18)
+plt.title("max_depth=2", fontsize=14)
+
+plt.subplot(122)
+plot_regression_predictions(tree_reg2, X, y, ylabel=None)
+for split, style in ((0.1973, "k-"), (0.0917, "k--"), (0.7718, "k--")):
+    plt.plot([split, split], [-0.2, 1], style, linewidth=2)
+for split in (0.0458, 0.1298, 0.2873, 0.9040):
+    plt.plot([split, split], [-0.2, 1], "k:", linewidth=1)
+plt.text(0.3, 0.5, "Depth=2", fontsize=13)
+plt.title("max_depth=3", fontsize=14)
+
+plt.show()
+
    
+
    
+
+
+
    tree_reg1 = DecisionTreeRegressor(random_state=42)
+tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)
+tree_reg1.fit(X, y)
+tree_reg2.fit(X, y)
+
+x1 = np.linspace(0, 1, 500).reshape(-1, 1)
+y_pred1 = tree_reg1.predict(x1)
+y_pred2 = tree_reg2.predict(x1)
+
+plt.figure(figsize=(11, 4))
+
+plt.subplot(121)
+plt.plot(X, y, "b.")
+plt.plot(x1, y_pred1, "r.-", linewidth=2, label=r"$\hat{y}$")
+plt.axis([0, 1, -0.2, 1.1])
+plt.xlabel("$x_1$", fontsize=18)
+plt.ylabel("$y$", fontsize=18, rotation=0)
+plt.legend(loc="upper center", fontsize=18)
+plt.title("No restrictions", fontsize=14)
+
+plt.subplot(122)
+plt.plot(X, y, "b.")
+plt.plot(x1, y_pred2, "r.-", linewidth=2, label=r"$\hat{y}$")
+plt.axis([0, 1, -0.2, 1.1])
+plt.xlabel("$x_1$", fontsize=18)
+plt.title("min_samples_leaf={}".format(tree_reg2.min_samples_leaf), fontsize=14)
+
+plt.show()
 
    
 
    
 
    
@@ -228,7 +278,7 @@ tree_reg.fit(X, y)
   
  • 35
    • 
   
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    • 
   
  • ...
    • 
-  
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    • 
+  
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    • 
   
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diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html
index 21cc1bb47..afeb9be33 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs027.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,82 +177,18 @@ MathJax.Hub.Config({
 
 
 
-
    Final regressor code 
    
-
    
+
    Pros and cons of trees, pros 
    
 
-
-
    from sklearn.tree import DecisionTreeRegressor
+
      
+
    •  White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)
      • 
+
    •  Trees are very easy to explain to people. In fact, they are even easier to explain than linear regression!
      • 
+
    •  No feature normalization needed
      • 
+
    •  Tree models can handle both continuous and categorical data (Classification and Regression Trees)
      • 
+
    •  Can model nonlinear relationships
      • 
+
    •  Can model interactions between the different descriptive features
      • 
+
    •  Trees can be displayed graphically, and are easily interpreted even by a non-expert (especially if they are small)
      • 
+
    
 
-tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)
-tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)
-tree_reg1.fit(X, y)
-tree_reg2.fit(X, y)
-
-def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel="$y$"):
-    x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)
-    y_pred = tree_reg.predict(x1)
-    plt.axis(axes)
-    plt.xlabel("$x_1$", fontsize=18)
-    if ylabel:
-        plt.ylabel(ylabel, fontsize=18, rotation=0)
-    plt.plot(X, y, "b.")
-    plt.plot(x1, y_pred, "r.-", linewidth=2, label=r"$\hat{y}$")
-
-plt.figure(figsize=(11, 4))
-plt.subplot(121)
-plot_regression_predictions(tree_reg1, X, y)
-for split, style in ((0.1973, "k-"), (0.0917, "k--"), (0.7718, "k--")):
-    plt.plot([split, split], [-0.2, 1], style, linewidth=2)
-plt.text(0.21, 0.65, "Depth=0", fontsize=15)
-plt.text(0.01, 0.2, "Depth=1", fontsize=13)
-plt.text(0.65, 0.8, "Depth=1", fontsize=13)
-plt.legend(loc="upper center", fontsize=18)
-plt.title("max_depth=2", fontsize=14)
-
-plt.subplot(122)
-plot_regression_predictions(tree_reg2, X, y, ylabel=None)
-for split, style in ((0.1973, "k-"), (0.0917, "k--"), (0.7718, "k--")):
-    plt.plot([split, split], [-0.2, 1], style, linewidth=2)
-for split in (0.0458, 0.1298, 0.2873, 0.9040):
-    plt.plot([split, split], [-0.2, 1], "k:", linewidth=1)
-plt.text(0.3, 0.5, "Depth=2", fontsize=13)
-plt.title("max_depth=3", fontsize=14)
-
-plt.show()
-
    
-
    
-
-
-
    tree_reg1 = DecisionTreeRegressor(random_state=42)
-tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)
-tree_reg1.fit(X, y)
-tree_reg2.fit(X, y)
-
-x1 = np.linspace(0, 1, 500).reshape(-1, 1)
-y_pred1 = tree_reg1.predict(x1)
-y_pred2 = tree_reg2.predict(x1)
-
-plt.figure(figsize=(11, 4))
-
-plt.subplot(121)
-plt.plot(X, y, "b.")
-plt.plot(x1, y_pred1, "r.-", linewidth=2, label=r"$\hat{y}$")
-plt.axis([0, 1, -0.2, 1.1])
-plt.xlabel("$x_1$", fontsize=18)
-plt.ylabel("$y$", fontsize=18, rotation=0)
-plt.legend(loc="upper center", fontsize=18)
-plt.title("No restrictions", fontsize=14)
-
-plt.subplot(122)
-plt.plot(X, y, "b.")
-plt.plot(x1, y_pred2, "r.-", linewidth=2, label=r"$\hat{y}$")
-plt.axis([0, 1, -0.2, 1.1])
-plt.xlabel("$x_1$", fontsize=18)
-plt.title("min_samples_leaf={}".format(tree_reg2.min_samples_leaf), fontsize=14)
-
-plt.show()
-
    
-
    
 
    
 
 
    
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html
index de920c9e4..8646025cb 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs028.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,18 +177,21 @@ MathJax.Hub.Config({
 
 
 
-
    Pros and cons of trees, pros 
    
+
    Disadvantages 
    
 
 
      
-
    •  White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)
      • 
-
    •  Trees are very easy to explain to people. In fact, they are even easier to explain than linear regression!
      • 
-
    •  No feature normalization needed
      • 
-
    •  Tree models can handle both continuous and categorical data (Classification and Regression Trees)
      • 
-
    •  Can model nonlinear relationships
      • 
-
    •  Can model interactions between the different descriptive features
      • 
-
    •  Trees can be displayed graphically, and are easily interpreted even by a non-expert (especially if they are small)
      • 
+
    •  Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches
      • 
+
    •  If continuous features are used the tree may become quite large and hence less interpretable
      • 
+
    •  Decision trees are prone to overfit the training data and hence do not well generalize the data if no stopping criteria or improvements like pruning, boosting or bagging are implemented
      • 
+
    •  Small changes in the data may lead to a completely different tree. This issue can be addressed by using ensemble methods like bagging, boosting or random forests
      • 
+
    •  Unbalanced datasets where some target feature values occur much more frequently than others may lead to biased trees since the frequently occurring feature values are preferred over the less frequently occurring ones.
      •  
+
    •  If the number of features is relatively large (high dimensional) and the number of instances is relatively low, the tree might overfit the data
      • 
+
    •  Features with many levels may be preferred over features with less levels since for them it is more easy to split the dataset such that the sub datasets only contain pure target feature values. This issue can be addressed by preferring for instance the information gain ratio as splitting criteria over information gain
      • 
 
    
 
+However, by aggregating many decision trees, using methods like bagging, random forests, and boosting, the predictive performance of trees can be substantially improved.
+
+
    
 
    
 
 
      
@@ -219,8 +216,6 @@ MathJax.Hub.Config({
   
    • 36
      • 
   
    • 37
      • 
   
    • 38
      • 
-  
    • ...
      • 
-  
    • 39
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html
index 0ccfacfb4..351fcd155 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs029.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,19 +177,21 @@ MathJax.Hub.Config({
 
 
 
-
    Disadvantages 
    
+
    Bagging 
    
 
-
      
-
    •  Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches
      • 
-
    •  If continuous features are used the tree may become quite large and hence less interpretable
      • 
-
    •  Decision trees are prone to overfit the training data and hence do not well generalize the data if no stopping criteria or improvements like pruning, boosting or bagging are implemented
      • 
-
    •  Small changes in the data may lead to a completely different tree. This issue can be addressed by using ensemble methods like bagging, boosting or random forests
      • 
-
    •  Unbalanced datasets where some target feature values occur much more frequently than others may lead to biased trees since the frequently occurring feature values are preferred over the less frequently occurring ones.
      •  
-
    •  If the number of features is relatively large (high dimensional) and the number of instances is relatively low, the tree might overfit the data
      • 
-
    •  Features with many levels may be preferred over features with less levels since for them it is more easy to split the dataset such that the sub datasets only contain pure target feature values. This issue can be addressed by preferring for instance the information gain ratio as splitting criteria over information gain
      • 
-
    
+
    
+The plain decision trees suffer from high
+variance. This means that if we split the training data into two parts
+at random, and fit a decision tree to both halves, the results that we
+get could be quite different. In contrast, a procedure with low
+variance will yield similar results if applied repeatedly to distinct
+data sets; linear regression tends to have low variance, if the ratio
+of \( n \) to \( p \) is moderately large.
 
-However, by aggregating many decision trees, using methods like bagging, random forests, and boosting, the predictive performance of trees can be substantially improved.
+
    
+Bootstrap aggregation, or just bagging, is a
+general-purpose procedure for reducing the variance of a statistical
+learning method.
 
 
    
 
    
@@ -221,7 +217,6 @@ However, by aggregating many decision trees, using methods like bagging, random
   
  • 36
    • 
   
  • 37
    • 
   
  • 38
    • 
-  
  • 39
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html
index 0227cab95..7da1b0026 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs030.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,21 +177,31 @@ MathJax.Hub.Config({
 
 
 
-
    Bagging 
    
+
    More bagging 
    
 
 
    
-The plain decision trees suffer from high
-variance. This means that if we split the training data into two parts
-at random, and fit a decision tree to both halves, the results that we
-get could be quite different. In contrast, a procedure with low
-variance will yield similar results if applied repeatedly to distinct
-data sets; linear regression tends to have low variance, if the ratio
-of \( n \) to \( p \) is moderately large.
+Bagging typically results in improved accuracy
+over prediction using a single tree. Unfortunately, however, it can be
+difficult to interpret the resulting model. Recall that one of the
+advantages of decision trees is the attractive and easily interpreted
+diagram that results.
 
 
    
-Bootstrap aggregation, or just bagging, is a
-general-purpose procedure for reducing the variance of a statistical
-learning method.
+However, when we bag a large number of trees, it is no longer
+possible to represent the resulting statistical learning procedure
+using a single tree, and it is no longer clear which variables are
+most important to the procedure. Thus, bagging improves prediction
+accuracy at the expense of interpretability.  Although the collection
+of bagged trees is much more difficult to interpret than a single
+tree, one can obtain an overall summary of the importance of each
+predictor using the MSE (for bagging regression trees) or the Gini
+index (for bagging classification trees). In the case of bagging
+regression trees, we can record the total amount that the MSE is
+decreased due to splits over a given predictor, averaged over all \( B \) possible
+trees. A large value indicates an important predictor. Similarly, in
+the context of bagging classification trees, we can add up the total
+amount that the Gini index  is decreased by splits over a given
+predictor, averaged over all \( B \) trees.
 
 
    
 
    
@@ -222,7 +226,6 @@ learning method.
   
  • 36
    • 
   
  • 37
    • 
   
  • 38
    • 
-  
  • 39
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html
index 8c89c0702..3a54259db 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs031.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,32 +177,23 @@ MathJax.Hub.Config({
 
 
 
-
    More bagging 
    
-
+
    Simple example, head or tail 
    
 
    
-Bagging typically results in improved accuracy
-over prediction using a single tree. Unfortunately, however, it can be
-difficult to interpret the resulting model. Recall that one of the
-advantages of decision trees is the attractive and easily interpreted
-diagram that results.
-
-
    
-However, when we bag a large number of trees, it is no longer
-possible to represent the resulting statistical learning procedure
-using a single tree, and it is no longer clear which variables are
-most important to the procedure. Thus, bagging improves prediction
-accuracy at the expense of interpretability.  Although the collection
-of bagged trees is much more difficult to interpret than a single
-tree, one can obtain an overall summary of the importance of each
-predictor using the MSE (for bagging regression trees) or the Gini
-index (for bagging classification trees). In the case of bagging
-regression trees, we can record the total amount that the MSE is
-decreased due to splits over a given predictor, averaged over all \( B \) possible
-trees. A large value indicates an important predictor. Similarly, in
-the context of bagging classification trees, we can add up the total
-amount that the Gini index  is decreased by splits over a given
-predictor, averaged over all \( B \) trees.
 
+
+
    heads_proba = 0.51
+coin_tosses = (np.random.rand(10000, 10) < heads_proba).astype(np.int32)
+cumulative_heads_ratio = np.cumsum(coin_tosses, axis=0) / np.arange(1, 10001).reshape(-1, 1)
+plt.figure(figsize=(8,3.5))
+plt.plot(cumulative_heads_ratio)
+plt.plot([0, 10000], [0.51, 0.51], "k--", linewidth=2, label="51%")
+plt.plot([0, 10000], [0.5, 0.5], "k-", label="50%")
+plt.xlabel("Number of coin tosses")
+plt.ylabel("Heads ratio")
+plt.legend(loc="lower right")
+plt.axis([0, 10000, 0.42, 0.58])
+plt.show()
+
    
 
    
 
    
 
@@ -231,7 +216,6 @@ predictor, averaged over all \( B \) trees.
   
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-  
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    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html
index 53e0b096e..6a2a6ac0f 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs032.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,22 +177,53 @@ MathJax.Hub.Config({
 
 
 
-
    Simple example, head or tail 
    
+
    Bagging Example 
    
 
    
 
 
-
    heads_proba = 0.51
-coin_tosses = (np.random.rand(10000, 10) < heads_proba).astype(np.int32)
-cumulative_heads_ratio = np.cumsum(coin_tosses, axis=0) / np.arange(1, 10001).reshape(-1, 1)
-plt.figure(figsize=(8,3.5))
-plt.plot(cumulative_heads_ratio)
-plt.plot([0, 10000], [0.51, 0.51], "k--", linewidth=2, label="51%")
-plt.plot([0, 10000], [0.5, 0.5], "k-", label="50%")
-plt.xlabel("Number of coin tosses")
-plt.ylabel("Heads ratio")
-plt.legend(loc="lower right")
-plt.axis([0, 10000, 0.42, 0.58])
-plt.show()
+
    from sklearn.model_selection import train_test_split
+from sklearn.datasets import make_moons
+
+X, y = make_moons(n_samples=500, noise=0.30, random_state=42)
+X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
+
+from sklearn.ensemble import RandomForestClassifier
+from sklearn.ensemble import VotingClassifier
+from sklearn.linear_model import LogisticRegression
+from sklearn.svm import SVC
+
+log_clf = LogisticRegression(solver="liblinear", random_state=42)
+rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
+svm_clf = SVC(gamma="auto", random_state=42)
+
+voting_clf = VotingClassifier(
+    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
+    voting='hard')
+
+voting_clf.fit(X_train, y_train)
+
+from sklearn.metrics import accuracy_score
+
+for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
+    clf.fit(X_train, y_train)
+    y_pred = clf.predict(X_test)
+    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
+
+log_clf = LogisticRegression(solver="liblinear", random_state=42)
+rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
+svm_clf = SVC(gamma="auto", probability=True, random_state=42)
+
+voting_clf = VotingClassifier(
+    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
+    voting='soft')
+voting_clf.fit(X_train, y_train)
+
+from sklearn.metrics import accuracy_score
+
+for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
+    clf.fit(X_train, y_train)
+    y_pred = clf.predict(X_test)
+    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
 
    
 
    
 
    
@@ -221,7 +246,6 @@ plt.show()
   
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    • 
   
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    • 
   
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-  
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    • 
   
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    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html
index e56a049b4..404065ca8 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs033.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,54 +177,47 @@ MathJax.Hub.Config({
 
 
 
-
    Bagging Example 
    
+
    Random forests 
    
+
 
    
+Random forests provide an improvement over bagged trees by way of a
+small tweak that decorrelates the trees.
 
-
-
    from sklearn.model_selection import train_test_split
-from sklearn.datasets import make_moons
+
    
+As in bagging, we build a
+number of decision trees on bootstrapped training samples. But when
+building these decision trees, each time a split in a tree is
+considered, a random sample of \( m \) predictors is chosen as split
+candidates from the full set of \( p \) predictors. The split is allowed to
+use only one of those \( m \) predictors.
 
-X, y = make_moons(n_samples=500, noise=0.30, random_state=42)
-X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
+
    
+A fresh sample of \( m \) predictors is
+taken at each split, and typically we choose 
 
-from sklearn.ensemble import RandomForestClassifier
-from sklearn.ensemble import VotingClassifier
-from sklearn.linear_model import LogisticRegression
-from sklearn.svm import SVC
+$$
+m\approx \sqrt{p}.
+$$
 
-log_clf = LogisticRegression(solver="liblinear", random_state=42)
-rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
-svm_clf = SVC(gamma="auto", random_state=42)
+
    
+In building a random forest, at
+each split in the tree, the algorithm is not even allowed to consider
+a majority of the available predictors.
 
-voting_clf = VotingClassifier(
-    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
-    voting='hard')
+
    
+The reason for this is rather clever. Suppose that there is one very
+strong predictor in the data set, along with a number of other
+moderately strong predictors. Then in the collection of bagged
+variable importance random forest trees, most or all of the trees will
+use this strong predictor in the top split. Consequently, all of the
+bagged trees will look quite similar to each other. Hence the
+predictions from the bagged trees will be highly correlated.
+Unfortunately, averaging many highly correlated quantities does not
+lead to as large of a reduction in variance as averaging many
+uncorrelated quanti- ties. In particular, this means that bagging will
+not lead to a substantial reduction in variance over a single tree in
+this setting.
 
-voting_clf.fit(X_train, y_train)
-
-from sklearn.metrics import accuracy_score
-
-for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
-    clf.fit(X_train, y_train)
-    y_pred = clf.predict(X_test)
-    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
-
-log_clf = LogisticRegression(solver="liblinear", random_state=42)
-rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)
-svm_clf = SVC(gamma="auto", probability=True, random_state=42)
-
-voting_clf = VotingClassifier(
-    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
-    voting='soft')
-voting_clf.fit(X_train, y_train)
-
-from sklearn.metrics import accuracy_score
-
-for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
-    clf.fit(X_train, y_train)
-    y_pred = clf.predict(X_test)
-    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
-
    
 
    
 
    
 
@@ -251,7 +238,6 @@ voting_clf.fit(X_train, y_train)
   
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diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html
index a6d930144..8babd7241 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs034.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,47 +177,21 @@ MathJax.Hub.Config({
 
 
 
-
    Random forests 
    
-
+
    A simple scikit-learn example 
    
 
    
-Random forests provide an improvement over bagged trees by way of a
-small tweak that decorrelates the trees.
-
-
    
-As in bagging, we build a
-number of decision trees on bootstrapped training samples. But when
-building these decision trees, each time a split in a tree is
-considered, a random sample of \( m \) predictors is chosen as split
-candidates from the full set of \( p \) predictors. The split is allowed to
-use only one of those \( m \) predictors.
-
-
    
-A fresh sample of \( m \) predictors is
-taken at each split, and typically we choose 
-
-$$
-m\approx \sqrt{p}.
-$$
-
-
    
-In building a random forest, at
-each split in the tree, the algorithm is not even allowed to consider
-a majority of the available predictors.
-
-
    
-The reason for this is rather clever. Suppose that there is one very
-strong predictor in the data set, along with a number of other
-moderately strong predictors. Then in the collection of bagged
-variable importance random forest trees, most or all of the trees will
-use this strong predictor in the top split. Consequently, all of the
-bagged trees will look quite similar to each other. Hence the
-predictions from the bagged trees will be highly correlated.
-Unfortunately, averaging many highly correlated quantities does not
-lead to as large of a reduction in variance as averaging many
-uncorrelated quanti- ties. In particular, this means that bagging will
-not lead to a substantial reduction in variance over a single tree in
-this setting.
 
+
+
    from sklearn.ensemble import RandomForestClassifier
+from sklearn.preprocessing import LabelEncoder
+from sklearn.model_selection import cross_validate
+# Data set not specificied
+X = dataset.XXX
+Y = dataset.YYY
+#Instantiate the model with 100 trees and entropy as splitting criteria
+Random_Forest_model = RandomForestClassifier(n_estimators=100,criterion="entropy")
+#Cross validation
+accuracy = cross_validate(Random_Forest_model,X,Y,cv=10)['test_score']
+
    
 
    
 
    
 
@@ -243,7 +211,6 @@ this setting.
   
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    • 
   
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    • 
   
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    • 
-  
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    • 
   
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    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html
index 069858f8e..50cde2289 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs035.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,20 +177,60 @@ MathJax.Hub.Config({
 
 
 
-
    A simple scikit-learn example 
    
+
    Please, not the moons again! 
    
 
    
 
 
-
    from sklearn.ensemble import RandomForestClassifier
-from sklearn.preprocessing import LabelEncoder
-from sklearn.model_selection import cross_validate
-# Data set not specificied
-X = dataset.XXX
-Y = dataset.YYY
-#Instantiate the model with 100 trees and entropy as splitting criteria
-Random_Forest_model = RandomForestClassifier(n_estimators=100,criterion="entropy")
-#Cross validation
-accuracy = cross_validate(Random_Forest_model,X,Y,cv=10)['test_score']
+
    from sklearn.model_selection import train_test_split
+from sklearn.datasets import make_moons
+
+X, y = make_moons(n_samples=500, noise=0.30, random_state=42)
+X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
+from sklearn.ensemble import RandomForestClassifier
+from sklearn.ensemble import VotingClassifier
+from sklearn.linear_model import LogisticRegression
+from sklearn.svm import SVC
+
+log_clf = LogisticRegression(random_state=42)
+rnd_clf = RandomForestClassifier(random_state=42)
+svm_clf = SVC(random_state=42)
+
+voting_clf = VotingClassifier(
+    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
+    voting='hard')
+voting_clf.fit(X_train, y_train)
+
    
+
    
+
+
+
    from sklearn.metrics import accuracy_score
+
+for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
+    clf.fit(X_train, y_train)
+    y_pred = clf.predict(X_test)
+    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
+
    
+
    
+
+
+
    log_clf = LogisticRegression(random_state=42)
+rnd_clf = RandomForestClassifier(random_state=42)
+svm_clf = SVC(probability=True, random_state=42)
+
+voting_clf = VotingClassifier(
+    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
+    voting='soft')
+voting_clf.fit(X_train, y_train)
+
    
+
    
+
+
+
    from sklearn.metrics import accuracy_score
+
+for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
+    clf.fit(X_train, y_train)
+    y_pred = clf.predict(X_test)
+    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
 
    
 
    
 
    
@@ -216,7 +250,6 @@ accuracy = cross_validate(Random_Forest_mode
   
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    • 
   
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    • 
   
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    • 
-  
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    • 
   
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    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html
index e606b8e79..2393ad333 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs036.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,60 +177,63 @@ MathJax.Hub.Config({
 
 
 
-
    Please, not the moons again! 
    
+
    Bagging examples 
    
+
 
    
 
 
-
    from sklearn.model_selection import train_test_split
-from sklearn.datasets import make_moons
+
    from sklearn.ensemble import BaggingClassifier
+from sklearn.tree import DecisionTreeClassifier
 
-X, y = make_moons(n_samples=500, noise=0.30, random_state=42)
-X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
-from sklearn.ensemble import RandomForestClassifier
-from sklearn.ensemble import VotingClassifier
-from sklearn.linear_model import LogisticRegression
-from sklearn.svm import SVC
-
-log_clf = LogisticRegression(random_state=42)
-rnd_clf = RandomForestClassifier(random_state=42)
-svm_clf = SVC(random_state=42)
-
-voting_clf = VotingClassifier(
-    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
-    voting='hard')
-voting_clf.fit(X_train, y_train)
+bag_clf = BaggingClassifier(
+    DecisionTreeClassifier(random_state=42), n_estimators=500,
+    max_samples=100, bootstrap=True, n_jobs=-1, random_state=42)
+bag_clf.fit(X_train, y_train)
+y_pred = bag_clf.predict(X_test)
 
    
 
    
 
 
 
    from sklearn.metrics import accuracy_score
-
-for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
-    clf.fit(X_train, y_train)
-    y_pred = clf.predict(X_test)
-    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
+print(accuracy_score(y_test, y_pred))
 
    
 
    
 
 
-
    log_clf = LogisticRegression(random_state=42)
-rnd_clf = RandomForestClassifier(random_state=42)
-svm_clf = SVC(probability=True, random_state=42)
-
-voting_clf = VotingClassifier(
-    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],
-    voting='soft')
-voting_clf.fit(X_train, y_train)
+
    tree_clf = DecisionTreeClassifier(random_state=42)
+tree_clf.fit(X_train, y_train)
+y_pred_tree = tree_clf.predict(X_test)
+print(accuracy_score(y_test, y_pred_tree))
 
    
 
    
 
 
-
    from sklearn.metrics import accuracy_score
+
    from matplotlib.colors import ListedColormap
 
-for clf in (log_clf, rnd_clf, svm_clf, voting_clf):
-    clf.fit(X_train, y_train)
-    y_pred = clf.predict(X_test)
-    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))
+def plot_decision_boundary(clf, X, y, axes=[-1.5, 2.5, -1, 1.5], alpha=0.5, contour=True):
+    x1s = np.linspace(axes[0], axes[1], 100)
+    x2s = np.linspace(axes[2], axes[3], 100)
+    x1, x2 = np.meshgrid(x1s, x2s)
+    X_new = np.c_[x1.ravel(), x2.ravel()]
+    y_pred = clf.predict(X_new).reshape(x1.shape)
+    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])
+    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)
+    if contour:
+        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])
+        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)
+    plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo", alpha=alpha)
+    plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs", alpha=alpha)
+    plt.axis(axes)
+    plt.xlabel(r"$x_1$", fontsize=18)
+    plt.ylabel(r"$x_2$", fontsize=18, rotation=0)
+plt.figure(figsize=(11,4))
+plt.subplot(121)
+plot_decision_boundary(tree_clf, X, y)
+plt.title("Decision Tree", fontsize=14)
+plt.subplot(122)
+plot_decision_boundary(bag_clf, X, y)
+plt.title("Decision Trees with Bagging", fontsize=14)
+plt.show()
 
    
 
    
 
    
@@ -255,7 +252,6 @@ voting_clf.fit(X_train, y_train)
   
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    • 
   
  • 37
    • 
   
  • 38
    • 
-  
  • 39
    • 
   
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    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html b/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html
index fd4b8a4d6..397c77e98 100644
--- a/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html
+++ b/doc/pub/DecisionTrees/html/._DecisionTrees-bs037.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -183,65 +177,27 @@ MathJax.Hub.Config({
 
 
 
-
    Bagging examples 
    
-
+
    Then random forests 
    
 
    
 
 
-
    from sklearn.ensemble import BaggingClassifier
-from sklearn.tree import DecisionTreeClassifier
+
    bag_clf = BaggingClassifier(
+    DecisionTreeClassifier(splitter="random", max_leaf_nodes=16, random_state=42),
+    n_estimators=500, max_samples=1.0, bootstrap=True, n_jobs=-1, random_state=42)
+
    
+
    
 
-bag_clf = BaggingClassifier(
-    DecisionTreeClassifier(random_state=42), n_estimators=500,
-    max_samples=100, bootstrap=True, n_jobs=-1, random_state=42)
-bag_clf.fit(X_train, y_train)
+
+
    bag_clf.fit(X_train, y_train)
 y_pred = bag_clf.predict(X_test)
+from sklearn.ensemble import RandomForestClassifier
+rnd_clf = RandomForestClassifier(n_estimators=500, max_leaf_nodes=16, n_jobs=-1, random_state=42)
+rnd_clf.fit(X_train, y_train)
+y_pred_rf = rnd_clf.predict(X_test)
+np.sum(y_pred == y_pred_rf) / len(y_pred) 
 
    
 
    
 
-
-
    from sklearn.metrics import accuracy_score
-print(accuracy_score(y_test, y_pred))
-
    
-
    
-
-
-
    tree_clf = DecisionTreeClassifier(random_state=42)
-tree_clf.fit(X_train, y_train)
-y_pred_tree = tree_clf.predict(X_test)
-print(accuracy_score(y_test, y_pred_tree))
-
    
-
    
-
-
-
    from matplotlib.colors import ListedColormap
-
-def plot_decision_boundary(clf, X, y, axes=[-1.5, 2.5, -1, 1.5], alpha=0.5, contour=True):
-    x1s = np.linspace(axes[0], axes[1], 100)
-    x2s = np.linspace(axes[2], axes[3], 100)
-    x1, x2 = np.meshgrid(x1s, x2s)
-    X_new = np.c_[x1.ravel(), x2.ravel()]
-    y_pred = clf.predict(X_new).reshape(x1.shape)
-    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])
-    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)
-    if contour:
-        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])
-        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)
-    plt.plot(X[:, 0][y==0], X[:, 1][y==0], "yo", alpha=alpha)
-    plt.plot(X[:, 0][y==1], X[:, 1][y==1], "bs", alpha=alpha)
-    plt.axis(axes)
-    plt.xlabel(r"$x_1$", fontsize=18)
-    plt.ylabel(r"$x_2$", fontsize=18, rotation=0)
-plt.figure(figsize=(11,4))
-plt.subplot(121)
-plot_decision_boundary(tree_clf, X, y)
-plt.title("Decision Tree", fontsize=14)
-plt.subplot(122)
-plot_decision_boundary(bag_clf, X, y)
-plt.title("Decision Trees with Bagging", fontsize=14)
-plt.show()
-
    
-
    
 
    
 
 
      
@@ -257,8 +213,6 @@ plt.show()
   
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-  
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      • 
 
    
 
 
diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html
index 4591c0dc0..ab79ad196 100644
--- a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html
+++ b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html
@@ -47,52 +47,47 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -132,42 +127,41 @@ MathJax.Hub.Config({
         
       
@@ -226,7 +220,7 @@ MathJax.Hub.Config({
   
  • 9
    • 
   
  • 10
    • 
   
  • ...
    • 
-  
  • 39
    • 
+  
  • 38
    • 
   
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    • 
 
 
diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html
index 2b39f802b..aef2f82ea 100644
--- a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html
+++ b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html
@@ -194,22 +194,11 @@ given some assumptions, make predictions about the target feature value
 
 
    
 
    A typical Decision Tree with its pertinent Jargon, Classification Problem 
    
-
-
    
-In the figure here we present a decision tree obtained from a classification problem
 
    
 
 
 
    
-
    A typical Decision Tree with its pertinent Jargon, Regeression Problem 
    
-
-
    
-In the figure we present a decision tree obtained from a simple regression  problem
-
    
-
-
-
    
-
    General Features 
    
+
    General Features 
    
 
 
    
 The overarching approach to decision trees is a top-down approach.
@@ -228,7 +217,7 @@ node.
 
 
 
    
-
    How do we set it up? 
    
+
    How do we set it up? 
    
 
 
    
 In simplified terms, the process of training a decision tree and
@@ -247,7 +236,7 @@ Then we are essentially done!
 
 
 
    
-
    Decision trees and Regression  
    
+
    Decision trees and Regression  
    
 
    
 
 
@@ -344,7 +333,7 @@ plt.show()
 
 
 
    
-
    Building a tree, regression 
    
+
    Building a tree, regression 
    
 
 
    
 There are mainly two steps
@@ -376,7 +365,7 @@ within box \( j \).
 
 
 
    
-
    A top-down approach, recursive binary splitting 
    
+
    A top-down approach, recursive binary splitting 
    
 
 
    
 Unfortunately, it is computationally infeasible to consider every
@@ -395,7 +384,7 @@ better tree in some future step.
 
 
 
    
-
    Making a tree 
    
+
    Making a tree 
    
 
 
    
 In order to implement the recursive binary splitting we start by selecting
@@ -452,7 +441,7 @@ region contains more than five observations.
 
 
 
    
-
    Pruning the tree 
    
+
    Pruning the tree 
    
 
 
    
 The above procedure is rather straightforward, but leads often to
@@ -471,7 +460,7 @@ parameter \( \alpha \).
 
 
 
    
-
    Cost complexity pruning 
    
+
    Cost complexity pruning 
    
 For each value of \( \alpha \)  there corresponds a subtree \( T \in T_0 \) such that
 
     
    
 $$
@@ -504,7 +493,7 @@ subtree corresponding to \( \alpha \).
 
 
 
    
-
    Schematic Regression Procedure 
    
+
    Schematic Regression Procedure 
    
 
 
    
 
    
@@ -529,7 +518,7 @@ subtree corresponding to \( \alpha \).
 
 
 
    
-
    A Classification Tree 
    
+
    A Classification Tree 
    
 
 
    
 A classification tree is very similar to a regression tree, except
@@ -548,7 +537,7 @@ fall into that region.
 
 
 
    
-
    Growing a classification tree 
    
+
    Growing a classification tree 
    
 
 
    
 The task of growing a
@@ -572,7 +561,7 @@ than is the classification error rate.
 
 
 
    
-
    Classification tree, how to split nodes 
    
+
    Classification tree, how to split nodes 
    
 
 
    
 If our targets are the outcome of a classification process that takes
@@ -627,7 +616,7 @@ $$
 
 
 
    
-
    Visualizing the Tree, Classification 
    
+
    Visualizing the Tree, Classification 
    
 
    
 
 
@@ -669,7 +658,7 @@ os.system(cmd)
 
 
 
    
-
    Visualizing the Tree, The Moons  
    
+
    Visualizing the Tree, The Moons  
    
 
    
 
 
@@ -702,7 +691,7 @@ os.system(cmd)
 
 
 
    
-
    Computing the Gini index 
    
+
    Computing the Gini index 
    
 
 
    
 The example we will look at is a classical one in many Machine
@@ -743,7 +732,7 @@ The table here summarizes the various attributes and
 
 
 
    
-
    Simple Python Code to read in Data 
    
+
    Simple Python Code to read in Data 
    
 
 
    
 
@@ -806,7 +795,7 @@ display(y)
 
 
 
    
-
    Computing the Gini Factor  
    
+
    Computing the Gini Factor  
    
 
 
    
 The above functions (gini, entropy and misclassification error) are
@@ -885,7 +874,7 @@ split = get_split(dataset)
 
 
 
    
-
    Entropy and the ID3 algorithm 
    
+
    Entropy and the ID3 algorithm 
    
 
 
    
 ID3, learns decision trees by constructing
@@ -922,216 +911,204 @@ attributes at each step while growing the tree.
 
 
 
    
-
    Implementing the ID3 Algorithm 
    
+
    Implementing the ID3 Algorithm 
    
 
 
    
-import re
-import math
-from collections import deque
 
-
    
-
-
-
-
-
+
+
    import re
+import math
+from collections import deque
 
-
    
-class Node(object):
-	def __init__(self):
-		self.value = None
-		self.next = None
-		self.childs = None
+# x is examples in training set
+# y is set of targets
+# label is target attributes
+# Node is a class which has properties values, childs, and next
+# root is top node in the decision tree
 
-
    
-
-
-class DecisionTree(object):
-	def __init__(self, sample, attributes, labels):
-		self.sample = sample
-		self.attributes = attributes
-		self.labels = labels
-		self.labelCodes = None
-		self.labelCodesCount = None
-		self.initLabelCodes()
-		# print(self.labelCodes)
-		self.root = None
-		self.entropy = self.getEntropy([x for x in range(len(self.labels))])
+class Node(object):
+	def __init__(self):
+		self.value = None
+		self.next = None
+		self.childs = None
 
-
    
-	def initLabelCodes(self):
-		self.labelCodes = []
-		self.labelCodesCount = []
-		for l in self.labels:
-			if l not in self.labelCodes:
-				self.labelCodes.append(l)
-				self.labelCodesCount.append(0)
-			self.labelCodesCount[self.labelCodes.index(l)] += 1
+# Simple class of Decision Tree
+# Aimed for who want to learn Decision Tree, so it is not optimized
+class DecisionTree(object):
+	def __init__(self, sample, attributes, labels):
+		self.sample = sample
+		self.attributes = attributes
+		self.labels = labels
+		self.labelCodes = None
+		self.labelCodesCount = None
+		self.initLabelCodes()
+		# print(self.labelCodes)
+		self.root = None
+		self.entropy = self.getEntropy([x for x in range(len(self.labels))])
 
-
    
-	def getLabelCodeId(self, sampleId):
-		return self.labelCodes.index(self.labels[sampleId])
+	def initLabelCodes(self):
+		self.labelCodes = []
+		self.labelCodesCount = []
+		for l in self.labels:
+			if l not in self.labelCodes:
+				self.labelCodes.append(l)
+				self.labelCodesCount.append(0)
+			self.labelCodesCount[self.labelCodes.index(l)] += 1
 
-
    
-	def getAttributeValues(self, sampleIds, attributeId):
+	def getLabelCodeId(self, sampleId):
+		return self.labelCodes.index(self.labels[sampleId])
+
+	def getAttributeValues(self, sampleIds, attributeId):
 		vals = []
-		for sid in sampleIds:
-			val = self.sample[sid][attributeId]
-			if val not in vals:
+		for sid in sampleIds:
+			val = self.sample[sid][attributeId]
+			if val not in vals:
 				vals.append(val)
-		# print(vals)
-		return vals
+		# print(vals)
+		return vals
 
-
    
-	def getEntropy(self, sampleIds):
-		entropy = 0
-		labelCount = [0] * len(self.labelCodes)
-		for sid in sampleIds:
-			labelCount[self.getLabelCodeId(sid)] += 1
-		# print("-ge", labelCount)
-		for lv in labelCount:
-			# print(lv)
-			if lv != 0:
-				entropy += -lv/len(sampleIds) * math.log(lv/len(sampleIds), 2)
-			else:
-				entropy += 0
-		return entropy
+	def getEntropy(self, sampleIds):
+		entropy = 0
+		labelCount = [0] * len(self.labelCodes)
+		for sid in sampleIds:
+			labelCount[self.getLabelCodeId(sid)] += 1
+		# print("-ge", labelCount)
+		for lv in labelCount:
+			# print(lv)
+			if lv != 0:
+				entropy += -lv/len(sampleIds) * math.log(lv/len(sampleIds), 2)
+			else:
+				entropy += 0
+		return entropy
 
-
    
-	def getDominantLabel(self, sampleIds):
-		labelCodesCount = [0] * len(self.labelCodes)
-		for sid in sampleIds:
-			labelCodesCount[self.labelCodes.index(self.labels[sid])] += 1
-		return self.labelCodes[labelCodesCount.index(max(labelCodesCount))]
+	def getDominantLabel(self, sampleIds):
+		labelCodesCount = [0] * len(self.labelCodes)
+		for sid in sampleIds:
+			labelCodesCount[self.labelCodes.index(self.labels[sid])] += 1
+		return self.labelCodes[labelCodesCount.index(max(labelCodesCount))]
 
-
    
-	def getInformationGain(self, sampleIds, attributeId):
-		gain = self.getEntropy(sampleIds)
+	def getInformationGain(self, sampleIds, attributeId):
+		gain = self.getEntropy(sampleIds)
 		attributeVals = []
 		attributeValsCount = []
 		attributeValsIds = []
-		for sid in sampleIds:
-			val = self.sample[sid][attributeId]
-			if val not in attributeVals:
+		for sid in sampleIds:
+			val = self.sample[sid][attributeId]
+			if val not in attributeVals:
 				attributeVals.append(val)
-				attributeValsCount.append(0)
+				attributeValsCount.append(0)
 				attributeValsIds.append([])
 			vid = attributeVals.index(val)
-			attributeValsCount[vid] += 1
+			attributeValsCount[vid] += 1
 			attributeValsIds[vid].append(sid)
-		# print("-gig", self.attributes[attributeId])
-		for vc, vids in zip(attributeValsCount, attributeValsIds):
-			# print("-gig", vids)
-			gain -= vc/len(sampleIds) * self.getEntropy(vids)
-		return gain
+		# print("-gig", self.attributes[attributeId])
+		for vc, vids in zip(attributeValsCount, attributeValsIds):
+			# print("-gig", vids)
+			gain -= vc/len(sampleIds) * self.getEntropy(vids)
+		return gain
 
-
    
-	def getAttributeMaxInformationGain(self, sampleIds, attributeIds):
-		attributesEntropy = [0] * len(attributeIds)
-		for i, attId in zip(range(len(attributeIds)), attributeIds):
-			attributesEntropy[i] = self.getInformationGain(sampleIds, attId)
-		maxId = attributeIds[attributesEntropy.index(max(attributesEntropy))]
-		return self.attributes[maxId], maxId
+	def getAttributeMaxInformationGain(self, sampleIds, attributeIds):
+		attributesEntropy = [0] * len(attributeIds)
+		for i, attId in zip(range(len(attributeIds)), attributeIds):
+			attributesEntropy[i] = self.getInformationGain(sampleIds, attId)
+		maxId = attributeIds[attributesEntropy.index(max(attributesEntropy))]
+		return self.attributes[maxId], maxId
 
-
    
-	def isSingleLabeled(self, sampleIds):
-		label = self.labels[sampleIds[0]]
-		for sid in sampleIds:
-			if self.labels[sid] != label:
-				return False
-		return True
+	def isSingleLabeled(self, sampleIds):
+		label = self.labels[sampleIds[0]]
+		for sid in sampleIds:
+			if self.labels[sid] != label:
+				return False
+		return True
 
-
    
-	def getLabel(self, sampleId):
-		return self.labels[sampleId]
+	def getLabel(self, sampleId):
+		return self.labels[sampleId]
 
-
    
-	def id3(self):
-		sampleIds = [x for x in range(len(self.sample))]
-		attributeIds = [x for x in range(len(self.attributes))]
-		self.root = self.id3Recv(sampleIds, attributeIds, self.root)
+	def id3(self):
+		sampleIds = [x for x in range(len(self.sample))]
+		attributeIds = [x for x in range(len(self.attributes))]
+		self.root = self.id3Recv(sampleIds, attributeIds, self.root)
 
-
    
-	def id3Recv(self, sampleIds, attributeIds, root):
-		root = Node() # Initialize current root
-		if self.isSingleLabeled(sampleIds):
-			root.value = self.labels[sampleIds[0]]
-			return root
-		# print(attributeIds)
-		if len(attributeIds) == 0:
-			root.value = self.getDominantLabel(sampleIds)
-			return root
-		bestAttrName, bestAttrId = self.getAttributeMaxInformationGain(
+	def id3Recv(self, sampleIds, attributeIds, root):
+		root = Node() # Initialize current root
+		if self.isSingleLabeled(sampleIds):
+			root.value = self.labels[sampleIds[0]]
+			return root
+		# print(attributeIds)
+		if len(attributeIds) == 0:
+			root.value = self.getDominantLabel(sampleIds)
+			return root
+		bestAttrName, bestAttrId = self.getAttributeMaxInformationGain(
 			sampleIds, attributeIds)
-		# print(bestAttrName)
+		# print(bestAttrName)
 		root.value = bestAttrName
-		root.childs = []  # Create list of children
-		for value in self.getAttributeValues(sampleIds, bestAttrId):
-			# print(value)
+		root.childs = []  # Create list of children
+		for value in self.getAttributeValues(sampleIds, bestAttrId):
+			# print(value)
 			child = Node()
 			child.value = value
-			root.childs.append(child)  # Append new child node to current
-									   # root
+			root.childs.append(child)  # Append new child node to current
+									   # root
 			childSampleIds = []
-			for sid in sampleIds:
-				if self.sample[sid][bestAttrId] == value:
+			for sid in sampleIds:
+				if self.sample[sid][bestAttrId] == value:
 					childSampleIds.append(sid)
-			if len(childSampleIds) == 0:
-				child.next = self.getDominantLabel(sampleIds)
-			else:
-				# print(bestAttrName, bestAttrId)
-				# print(attributeIds)
-				if len(attributeIds) > 0 and bestAttrId in attributeIds:
+			if len(childSampleIds) == 0:
+				child.next = self.getDominantLabel(sampleIds)
+			else:
+				# print(bestAttrName, bestAttrId)
+				# print(attributeIds)
+				if len(attributeIds) > 0 and bestAttrId in attributeIds:
 					toRemove = attributeIds.index(bestAttrId)
 					attributeIds.pop(toRemove)
-				child.next = self.id3Recv(
+				child.next = self.id3Recv(
 					childSampleIds, attributeIds, child.next)
-		return root
+		return root
 
-
    
-	def printTree(self):
-		if self.root:
+	def printTree(self):
+		if self.root:
 			roots = deque()
-			roots.append(self.root)
-			while len(roots) > 0:
+			roots.append(self.root)
+			while len(roots) > 0:
 				root = roots.popleft()
-				print(root.value)
-				if root.childs:
-					for child in root.childs:
-						print('({})'.format(child.value))
+				print(root.value)
+				if root.childs:
+					for child in root.childs:
+						print('({})'.format(child.value))
 						roots.append(child.next)
-				elif root.next:
-					print(root.next)
+				elif root.next:
+					print(root.next)
 
-
    
-def test():
-	f = open('DataFiles/rideclass.csv')
-	attributes = f.readline().split(',')
-	attributes = attributes[1:len(attributes)-1]
-	print(attributes)
+
+def test():
+	f = open('DataFiles/rideclass.csv')
+	attributes = f.readline().split(',')
+	attributes = attributes[1:len(attributes)-1]
+	print(attributes)
 	sample = f.readlines()
 	f.close()
-	for i in range(len(sample)):
-		sample[i] = re.sub('\d+,', '', sample[i])
-		sample[i] = sample[i].strip().split(',')
+	for i in range(len(sample)):
+		sample[i] = re.sub('\d+,', '', sample[i])
+		sample[i] = sample[i].strip().split(',')
 	labels = []
-	for s in sample:
+	for s in sample:
 		labels.append(s.pop())
-	# print(sample)
-	# print(labels)
+	# print(sample)
+	# print(labels)
 	decisionTree = DecisionTree(sample, attributes, labels)
-	print("System entropy {}".format(decisionTree.entropy))
+	print("System entropy {}".format(decisionTree.entropy))
 	decisionTree.id3()
 	decisionTree.printTree()
 
-
    
-if __name__ == '__main__':
+
+if __name__ == '__main__':
 	test()
+
    
 
    
 
 
 
    
-
    Cancer Data again now with Decision Trees and other Methods 
    
+
    Cancer Data again now with Decision Trees and other Methods 
    
 
    
 
 
@@ -1181,7 +1158,7 @@ deep_tree_clf.fit(X_train_scaled, y_train)
 
 
 
    
-
    Another example, the moons again 
    
+
    Another example, the moons again 
    
 
    
 
 
@@ -1254,7 +1231,7 @@ plt.show()
 
 
 
    
-
    Playing around with regions 
    
+
    Playing around with regions 
    
 
    
 
 
@@ -1283,7 +1260,7 @@ plt.show()
 
 
 
    
-
    Regression trees 
    
+
    Regression trees 
    
 
    
 
 
@@ -1306,7 +1283,7 @@ tree_reg.fit(X, y)
 
 
 
    
-
    Final regressor code 
    
+
    Final regressor code 
    
 
    
 
 
@@ -1385,7 +1362,7 @@ plt.show()
 
 
 
    
-
    Pros and cons of trees, pros 
    
+
    Pros and cons of trees, pros 
    
 
 
      
 
    •  White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)
      • 
@@ -1400,7 +1377,7 @@ plt.show()
 
 
 
      
-
      Disadvantages 
      
+
      Disadvantages 
      
 
 
        
 
      •  Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches
        • 
@@ -1418,7 +1395,7 @@ However, by aggregating many decision trees, using methods like bagging, random
 
 
 
        
-
        Bagging 
        
+
        Bagging 
        
 
 
        
 The plain decision trees suffer from high
@@ -1437,7 +1414,7 @@ learning method.
 
 
 
        
-
        More bagging 
        
+
        More bagging 
        
 
 
        
 Bagging typically results in improved accuracy
@@ -1466,7 +1443,7 @@ predictor, averaged over all \( B \) trees.
 
 
 
        
-
        Simple example, head or tail 
        
+
        Simple example, head or tail 
        
 
        
 
 
@@ -1487,7 +1464,7 @@ plt.show()
 
 
 
        
-
        Bagging Example 
        
+
        Bagging Example 
        
 
        
 
 
@@ -1539,7 +1516,7 @@ voting_clf.fit(X_train, y_train)
 
 
 
        
-
        Random forests 
        
+
        Random forests 
        
 
 
        
 Random forests provide an improvement over bagged trees by way of a
@@ -1585,7 +1562,7 @@ this setting.
 
 
 
        
-
        A simple scikit-learn example 
        
+
        A simple scikit-learn example 
        
 
        
 
 
@@ -1604,7 +1581,7 @@ accuracy = cross_validate(Random_Forest_model,X,Y,cv=Please, not the moons again! 
+
        Please, not the moons again! 
        
 
        
 
 
@@ -1663,7 +1640,7 @@ voting_clf.fit(X_train, y_train)
 
 
 
        
-
        Bagging examples 
        
+
        Bagging examples 
        
 
 
        
 
@@ -1725,7 +1702,7 @@ plt.show()
 
 
 
        
-
        Then random forests 
        
+
        Then random forests 
        
 
        
 
 
diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html
index b75715681..94d27f261 100644
--- a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html
+++ b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html
@@ -67,52 +67,47 @@ div { text-align: justify; text-justify: inter-word; }
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -195,21 +190,10 @@ given some assumptions, make predictions about the target feature value
 
 
        A typical Decision Tree with its pertinent Jargon, Classification Problem 
        
 
-
        
-In the figure here we present a decision tree obtained from a classification problem
-
 
        
 









        
 
-
        A typical Decision Tree with its pertinent Jargon, Regeression Problem 
        
-
-
        
-In the figure we present a decision tree obtained from a simple regression  problem
-
-
        
-









        
-
-
        General Features 
        
+
        General Features 
        
 
 
        
 The overarching approach to decision trees is a top-down approach.
@@ -227,7 +211,7 @@ node.
 
        
 









        
 
-
        How do we set it up? 
        
+
        How do we set it up? 
        
 
 
        
 In simplified terms, the process of training a decision tree and
@@ -245,7 +229,7 @@ Then we are essentially done!
 
        
 









        
 
-
        Decision trees and Regression  
        
+
        Decision trees and Regression  
        
 
        
 
 
@@ -341,7 +325,7 @@ plt.show()
 
        
 









        
 
-
        Building a tree, regression 
        
+
        Building a tree, regression 
        
 
 
        
 There are mainly two steps
@@ -369,7 +353,7 @@ within box \( j \).
 
        
 









        
 
-
        A top-down approach, recursive binary splitting 
        
+
        A top-down approach, recursive binary splitting 
        
 
 
        
 Unfortunately, it is computationally infeasible to consider every
@@ -388,7 +372,7 @@ better tree in some future step.
 
        
 









        
 
-
        Making a tree 
        
+
        Making a tree 
        
 
 
        
 In order to implement the recursive binary splitting we start by selecting
@@ -439,7 +423,7 @@ region contains more than five observations.
 
        
 
 
-
        Pruning the tree 
        
+
        Pruning the tree 
        
 
 
        
 The above procedure is rather straightforward, but leads often to
@@ -458,7 +442,7 @@ parameter \( \alpha \).
 
        
 









        
 
-
        Cost complexity pruning 
        
+
        Cost complexity pruning 
        
 For each value of \( \alpha \)  there corresponds a subtree \( T \in T_0 \) such that
 $$
 \sum_{m=1}^{\overline{T}}\sum_{i:x_i\in R_m}(y_i-\overline{y}_{R_m})^2+\alpha\overline{T},
@@ -489,7 +473,7 @@ subtree corresponding to \( \alpha \).
 
        
 









        
 
-
        Schematic Regression Procedure 
        
+
        Schematic Regression Procedure 
        
 
 
        
 
        
@@ -515,7 +499,7 @@ subtree corresponding to \( \alpha \).
 
        
 









        
 
-
        A Classification Tree 
        
+
        A Classification Tree 
        
 
 
        
 A classification tree is very similar to a regression tree, except
@@ -534,7 +518,7 @@ fall into that region.
 
        
 









        
 
-
        Growing a classification tree 
        
+
        Growing a classification tree 
        
 
 
        
 The task of growing a
@@ -558,7 +542,7 @@ than is the classification error rate.
 
        
 









        
 
-
        Classification tree, how to split nodes 
        
+
        Classification tree, how to split nodes 
        
 
 
        
 If our targets are the outcome of a classification process that takes
@@ -608,7 +592,7 @@ $$
 
        
 









        
 
-
        Visualizing the Tree, Classification 
        
+
        Visualizing the Tree, Classification 
        
 
        
 
 
@@ -649,7 +633,7 @@ os.system(cmd)
 
        
 









        
 
-
        Visualizing the Tree, The Moons  
        
+
        Visualizing the Tree, The Moons  
        
 
        
 
 
@@ -681,7 +665,7 @@ os.system(cmd)
 
        
 









        
 
-
        Computing the Gini index 
        
+
        Computing the Gini index 
        
 
 
        
 The example we will look at is a classical one in many Machine
@@ -721,7 +705,7 @@ The table here summarizes the various attributes and
 
        
 









        
 
-
        Simple Python Code to read in Data 
        
+
        Simple Python Code to read in Data 
        
 
 
        
 
@@ -783,7 +767,7 @@ display(y)
 
        
 









        
 
-
        Computing the Gini Factor  
        
+
        Computing the Gini Factor  
        
 
 
        
 The above functions (gini, entropy and misclassification error) are
@@ -861,7 +845,7 @@ split = get_split(dataset)
 
        
 









        
 
-
        Entropy and the ID3 algorithm 
        
+
        Entropy and the ID3 algorithm 
        
 
 
        
 ID3, learns decision trees by constructing
@@ -897,216 +881,203 @@ attributes at each step while growing the tree.
 
        
 









        
 
-
        Implementing the ID3 Algorithm 
        
+
        Implementing the ID3 Algorithm 
        
 
 
        
-import re
-import math
-from collections import deque
 
-
        
-
-
-
-
-
+
+
        import re
+import math
+from collections import deque
 
-
        
-class Node(object):
-	def __init__(self):
-		self.value = None
-		self.next = None
-		self.childs = None
+# x is examples in training set
+# y is set of targets
+# label is target attributes
+# Node is a class which has properties values, childs, and next
+# root is top node in the decision tree
 
-
        
-
-
-class DecisionTree(object):
-	def __init__(self, sample, attributes, labels):
-		self.sample = sample
-		self.attributes = attributes
-		self.labels = labels
-		self.labelCodes = None
-		self.labelCodesCount = None
-		self.initLabelCodes()
-		# print(self.labelCodes)
-		self.root = None
-		self.entropy = self.getEntropy([x for x in range(len(self.labels))])
+class Node(object):
+	def __init__(self):
+		self.value = None
+		self.next = None
+		self.childs = None
 
-
        
-	def initLabelCodes(self):
-		self.labelCodes = []
-		self.labelCodesCount = []
-		for l in self.labels:
-			if l not in self.labelCodes:
-				self.labelCodes.append(l)
-				self.labelCodesCount.append(0)
-			self.labelCodesCount[self.labelCodes.index(l)] += 1
+# Simple class of Decision Tree
+# Aimed for who want to learn Decision Tree, so it is not optimized
+class DecisionTree(object):
+	def __init__(self, sample, attributes, labels):
+		self.sample = sample
+		self.attributes = attributes
+		self.labels = labels
+		self.labelCodes = None
+		self.labelCodesCount = None
+		self.initLabelCodes()
+		# print(self.labelCodes)
+		self.root = None
+		self.entropy = self.getEntropy([x for x in range(len(self.labels))])
 
-
        
-	def getLabelCodeId(self, sampleId):
-		return self.labelCodes.index(self.labels[sampleId])
+	def initLabelCodes(self):
+		self.labelCodes = []
+		self.labelCodesCount = []
+		for l in self.labels:
+			if l not in self.labelCodes:
+				self.labelCodes.append(l)
+				self.labelCodesCount.append(0)
+			self.labelCodesCount[self.labelCodes.index(l)] += 1
 
-
        
-	def getAttributeValues(self, sampleIds, attributeId):
+	def getLabelCodeId(self, sampleId):
+		return self.labelCodes.index(self.labels[sampleId])
+
+	def getAttributeValues(self, sampleIds, attributeId):
 		vals = []
-		for sid in sampleIds:
-			val = self.sample[sid][attributeId]
-			if val not in vals:
+		for sid in sampleIds:
+			val = self.sample[sid][attributeId]
+			if val not in vals:
 				vals.append(val)
-		# print(vals)
-		return vals
+		# print(vals)
+		return vals
 
-
        
-	def getEntropy(self, sampleIds):
-		entropy = 0
-		labelCount = [0] * len(self.labelCodes)
-		for sid in sampleIds:
-			labelCount[self.getLabelCodeId(sid)] += 1
-		# print("-ge", labelCount)
-		for lv in labelCount:
-			# print(lv)
-			if lv != 0:
-				entropy += -lv/len(sampleIds) * math.log(lv/len(sampleIds), 2)
-			else:
-				entropy += 0
-		return entropy
+	def getEntropy(self, sampleIds):
+		entropy = 0
+		labelCount = [0] * len(self.labelCodes)
+		for sid in sampleIds:
+			labelCount[self.getLabelCodeId(sid)] += 1
+		# print("-ge", labelCount)
+		for lv in labelCount:
+			# print(lv)
+			if lv != 0:
+				entropy += -lv/len(sampleIds) * math.log(lv/len(sampleIds), 2)
+			else:
+				entropy += 0
+		return entropy
 
-
        
-	def getDominantLabel(self, sampleIds):
-		labelCodesCount = [0] * len(self.labelCodes)
-		for sid in sampleIds:
-			labelCodesCount[self.labelCodes.index(self.labels[sid])] += 1
-		return self.labelCodes[labelCodesCount.index(max(labelCodesCount))]
+	def getDominantLabel(self, sampleIds):
+		labelCodesCount = [0] * len(self.labelCodes)
+		for sid in sampleIds:
+			labelCodesCount[self.labelCodes.index(self.labels[sid])] += 1
+		return self.labelCodes[labelCodesCount.index(max(labelCodesCount))]
 
-
        
-	def getInformationGain(self, sampleIds, attributeId):
-		gain = self.getEntropy(sampleIds)
+	def getInformationGain(self, sampleIds, attributeId):
+		gain = self.getEntropy(sampleIds)
 		attributeVals = []
 		attributeValsCount = []
 		attributeValsIds = []
-		for sid in sampleIds:
-			val = self.sample[sid][attributeId]
-			if val not in attributeVals:
+		for sid in sampleIds:
+			val = self.sample[sid][attributeId]
+			if val not in attributeVals:
 				attributeVals.append(val)
-				attributeValsCount.append(0)
+				attributeValsCount.append(0)
 				attributeValsIds.append([])
 			vid = attributeVals.index(val)
-			attributeValsCount[vid] += 1
+			attributeValsCount[vid] += 1
 			attributeValsIds[vid].append(sid)
-		# print("-gig", self.attributes[attributeId])
-		for vc, vids in zip(attributeValsCount, attributeValsIds):
-			# print("-gig", vids)
-			gain -= vc/len(sampleIds) * self.getEntropy(vids)
-		return gain
+		# print("-gig", self.attributes[attributeId])
+		for vc, vids in zip(attributeValsCount, attributeValsIds):
+			# print("-gig", vids)
+			gain -= vc/len(sampleIds) * self.getEntropy(vids)
+		return gain
 
-
        
-	def getAttributeMaxInformationGain(self, sampleIds, attributeIds):
-		attributesEntropy = [0] * len(attributeIds)
-		for i, attId in zip(range(len(attributeIds)), attributeIds):
-			attributesEntropy[i] = self.getInformationGain(sampleIds, attId)
-		maxId = attributeIds[attributesEntropy.index(max(attributesEntropy))]
-		return self.attributes[maxId], maxId
+	def getAttributeMaxInformationGain(self, sampleIds, attributeIds):
+		attributesEntropy = [0] * len(attributeIds)
+		for i, attId in zip(range(len(attributeIds)), attributeIds):
+			attributesEntropy[i] = self.getInformationGain(sampleIds, attId)
+		maxId = attributeIds[attributesEntropy.index(max(attributesEntropy))]
+		return self.attributes[maxId], maxId
 
-
        
-	def isSingleLabeled(self, sampleIds):
-		label = self.labels[sampleIds[0]]
-		for sid in sampleIds:
-			if self.labels[sid] != label:
-				return False
-		return True
+	def isSingleLabeled(self, sampleIds):
+		label = self.labels[sampleIds[0]]
+		for sid in sampleIds:
+			if self.labels[sid] != label:
+				return False
+		return True
 
-
        
-	def getLabel(self, sampleId):
-		return self.labels[sampleId]
+	def getLabel(self, sampleId):
+		return self.labels[sampleId]
 
-
        
-	def id3(self):
-		sampleIds = [x for x in range(len(self.sample))]
-		attributeIds = [x for x in range(len(self.attributes))]
-		self.root = self.id3Recv(sampleIds, attributeIds, self.root)
+	def id3(self):
+		sampleIds = [x for x in range(len(self.sample))]
+		attributeIds = [x for x in range(len(self.attributes))]
+		self.root = self.id3Recv(sampleIds, attributeIds, self.root)
 
-
        
-	def id3Recv(self, sampleIds, attributeIds, root):
-		root = Node() # Initialize current root
-		if self.isSingleLabeled(sampleIds):
-			root.value = self.labels[sampleIds[0]]
-			return root
-		# print(attributeIds)
-		if len(attributeIds) == 0:
-			root.value = self.getDominantLabel(sampleIds)
-			return root
-		bestAttrName, bestAttrId = self.getAttributeMaxInformationGain(
+	def id3Recv(self, sampleIds, attributeIds, root):
+		root = Node() # Initialize current root
+		if self.isSingleLabeled(sampleIds):
+			root.value = self.labels[sampleIds[0]]
+			return root
+		# print(attributeIds)
+		if len(attributeIds) == 0:
+			root.value = self.getDominantLabel(sampleIds)
+			return root
+		bestAttrName, bestAttrId = self.getAttributeMaxInformationGain(
 			sampleIds, attributeIds)
-		# print(bestAttrName)
+		# print(bestAttrName)
 		root.value = bestAttrName
-		root.childs = []  # Create list of children
-		for value in self.getAttributeValues(sampleIds, bestAttrId):
-			# print(value)
+		root.childs = []  # Create list of children
+		for value in self.getAttributeValues(sampleIds, bestAttrId):
+			# print(value)
 			child = Node()
 			child.value = value
-			root.childs.append(child)  # Append new child node to current
-									   # root
+			root.childs.append(child)  # Append new child node to current
+									   # root
 			childSampleIds = []
-			for sid in sampleIds:
-				if self.sample[sid][bestAttrId] == value:
+			for sid in sampleIds:
+				if self.sample[sid][bestAttrId] == value:
 					childSampleIds.append(sid)
-			if len(childSampleIds) == 0:
-				child.next = self.getDominantLabel(sampleIds)
-			else:
-				# print(bestAttrName, bestAttrId)
-				# print(attributeIds)
-				if len(attributeIds) > 0 and bestAttrId in attributeIds:
+			if len(childSampleIds) == 0:
+				child.next = self.getDominantLabel(sampleIds)
+			else:
+				# print(bestAttrName, bestAttrId)
+				# print(attributeIds)
+				if len(attributeIds) > 0 and bestAttrId in attributeIds:
 					toRemove = attributeIds.index(bestAttrId)
 					attributeIds.pop(toRemove)
-				child.next = self.id3Recv(
+				child.next = self.id3Recv(
 					childSampleIds, attributeIds, child.next)
-		return root
+		return root
 
-
        
-	def printTree(self):
-		if self.root:
+	def printTree(self):
+		if self.root:
 			roots = deque()
-			roots.append(self.root)
-			while len(roots) > 0:
+			roots.append(self.root)
+			while len(roots) > 0:
 				root = roots.popleft()
-				print(root.value)
-				if root.childs:
-					for child in root.childs:
-						print('({})'.format(child.value))
+				print(root.value)
+				if root.childs:
+					for child in root.childs:
+						print('({})'.format(child.value))
 						roots.append(child.next)
-				elif root.next:
-					print(root.next)
+				elif root.next:
+					print(root.next)
 
-
        
-def test():
-	f = open('DataFiles/rideclass.csv')
-	attributes = f.readline().split(',')
-	attributes = attributes[1:len(attributes)-1]
-	print(attributes)
+
+def test():
+	f = open('DataFiles/rideclass.csv')
+	attributes = f.readline().split(',')
+	attributes = attributes[1:len(attributes)-1]
+	print(attributes)
 	sample = f.readlines()
 	f.close()
-	for i in range(len(sample)):
-		sample[i] = re.sub('\d+,', '', sample[i])
-		sample[i] = sample[i].strip().split(',')
+	for i in range(len(sample)):
+		sample[i] = re.sub('\d+,', '', sample[i])
+		sample[i] = sample[i].strip().split(',')
 	labels = []
-	for s in sample:
+	for s in sample:
 		labels.append(s.pop())
-	# print(sample)
-	# print(labels)
+	# print(sample)
+	# print(labels)
 	decisionTree = DecisionTree(sample, attributes, labels)
-	print("System entropy {}".format(decisionTree.entropy))
+	print("System entropy {}".format(decisionTree.entropy))
 	decisionTree.id3()
 	decisionTree.printTree()
 
-
        
-if __name__ == '__main__':
-	test()
 
+if __name__ == '__main__':
+	test()
+
        
 
        
 









        
 
-
        Cancer Data again now with Decision Trees and other Methods 
        
+
        Cancer Data again now with Decision Trees and other Methods 
        
 
        
 
 
@@ -1155,7 +1126,7 @@ deep_tree_clf.fit(X_train_scaled, y_train)
 
        
 









        
 
-
        Another example, the moons again 
        
+
        Another example, the moons again 
        
 
        
 
 
@@ -1227,7 +1198,7 @@ plt.show()
 
        
 









        
 
-
        Playing around with regions 
        
+
        Playing around with regions 
        
 
        
 
 
@@ -1255,7 +1226,7 @@ plt.show()
 
        
 









        
 
-
        Regression trees 
        
+
        Regression trees 
        
 
        
 
 
@@ -1277,7 +1248,7 @@ tree_reg.fit(X, y)
 
        
 









        
 
-
        Final regressor code 
        
+
        Final regressor code 
        
 
        
 
 
@@ -1355,7 +1326,7 @@ plt.show()
 
        
 









        
 
-
        Pros and cons of trees, pros 
        
+
        Pros and cons of trees, pros 
        
 
 
          
 
        •  White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)
          • 
@@ -1369,7 +1340,7 @@ plt.show()
 
 









          
 
-
          Disadvantages 
          
+
          Disadvantages 
          
 
 
            
 
          •  Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches
            • 
@@ -1386,7 +1357,7 @@ However, by aggregating many decision trees, using methods like bagging, random
 
            
 









            
 
-
            Bagging 
            
+
            Bagging 
            
 
 
            
 The plain decision trees suffer from high
@@ -1405,7 +1376,7 @@ learning method.
 
            
 









            
 
-
            More bagging 
            
+
            More bagging 
            
 
 
            
 Bagging typically results in improved accuracy
@@ -1434,7 +1405,7 @@ predictor, averaged over all \( B \) trees.
 
            
 









            
 
-
            Simple example, head or tail 
            
+
            Simple example, head or tail 
            
 
            
 
 
@@ -1454,7 +1425,7 @@ plt.show()
 
            
 









            
 
-
            Bagging Example 
            
+
            Bagging Example 
            
 
            
 
 
@@ -1505,7 +1476,7 @@ voting_clf.fit(X_train, y_train)
 
            
 









            
 
-
            Random forests 
            
+
            Random forests 
            
 
 
            
 Random forests provide an improvement over bagged trees by way of a
@@ -1549,7 +1520,7 @@ this setting.
 
            
 









            
 
-
            A simple scikit-learn example 
            
+
            A simple scikit-learn example 
            
 
            
 
 
@@ -1567,7 +1538,7 @@ accuracy = cross_validate(Random_Forest_model,X,Y,cv=Please, not the moons again! 
+
            Please, not the moons again! 
            
 
            
 
 
@@ -1625,7 +1596,7 @@ voting_clf.fit(X_train, y_train)
 
            
 









            
 
-
            Bagging examples 
            
+
            Bagging examples 
            
 
 
            
 
@@ -1686,7 +1657,7 @@ plt.show()
 
            
 









            
 
-
            Then random forests 
            
+
            Then random forests 
            
 
            
 
 
diff --git a/doc/pub/DecisionTrees/html/DecisionTrees.html b/doc/pub/DecisionTrees/html/DecisionTrees.html
index 5885a1674..d41c8cb6d 100644
--- a/doc/pub/DecisionTrees/html/DecisionTrees.html
+++ b/doc/pub/DecisionTrees/html/DecisionTrees.html
@@ -72,52 +72,47 @@ div { text-align: justify; text-justify: inter-word; }
                2,
                None,
                '___sec1'),
-              ('A typical Decision Tree with its pertinent Jargon, Regeression '
-               'Problem',
-               2,
-               None,
-               '___sec2'),
-              ('General Features', 2, None, '___sec3'),
-              ('How do we set it up?', 2, None, '___sec4'),
-              ('Decision trees and Regression', 2, None, '___sec5'),
-              ('Building a tree, regression', 2, None, '___sec6'),
+              ('General Features', 2, None, '___sec2'),
+              ('How do we set it up?', 2, None, '___sec3'),
+              ('Decision trees and Regression', 2, None, '___sec4'),
+              ('Building a tree, regression', 2, None, '___sec5'),
               ('A top-down approach, recursive binary splitting',
                2,
                None,
-               '___sec7'),
-              ('Making a tree', 2, None, '___sec8'),
-              ('Pruning the tree', 2, None, '___sec9'),
-              ('Cost complexity pruning', 2, None, '___sec10'),
-              ('Schematic Regression Procedure', 2, None, '___sec11'),
-              ('A Classification Tree', 2, None, '___sec12'),
-              ('Growing a classification tree', 2, None, '___sec13'),
-              ('Classification tree, how to split nodes', 2, None, '___sec14'),
-              ('Visualizing the Tree, Classification', 2, None, '___sec15'),
-              ('Visualizing the Tree, The Moons', 2, None, '___sec16'),
-              ('Computing the Gini index', 2, None, '___sec17'),
-              ('Simple Python Code to read in Data', 2, None, '___sec18'),
-              ('Computing the Gini Factor', 2, None, '___sec19'),
-              ('Entropy and the ID3 algorithm', 2, None, '___sec20'),
-              ('Implementing the ID3 Algorithm', 2, None, '___sec21'),
+               '___sec6'),
+              ('Making a tree', 2, None, '___sec7'),
+              ('Pruning the tree', 2, None, '___sec8'),
+              ('Cost complexity pruning', 2, None, '___sec9'),
+              ('Schematic Regression Procedure', 2, None, '___sec10'),
+              ('A Classification Tree', 2, None, '___sec11'),
+              ('Growing a classification tree', 2, None, '___sec12'),
+              ('Classification tree, how to split nodes', 2, None, '___sec13'),
+              ('Visualizing the Tree, Classification', 2, None, '___sec14'),
+              ('Visualizing the Tree, The Moons', 2, None, '___sec15'),
+              ('Computing the Gini index', 2, None, '___sec16'),
+              ('Simple Python Code to read in Data', 2, None, '___sec17'),
+              ('Computing the Gini Factor', 2, None, '___sec18'),
+              ('Entropy and the ID3 algorithm', 2, None, '___sec19'),
+              ('Implementing the ID3 Algorithm', 2, None, '___sec20'),
               ('Cancer Data again now with Decision Trees and other Methods',
                2,
                None,
-               '___sec22'),
-              ('Another example, the moons again', 2, None, '___sec23'),
-              ('Playing around with regions', 2, None, '___sec24'),
-              ('Regression trees', 2, None, '___sec25'),
-              ('Final regressor code', 2, None, '___sec26'),
-              ('Pros and cons of trees, pros', 2, None, '___sec27'),
-              ('Disadvantages', 2, None, '___sec28'),
-              ('Bagging', 2, None, '___sec29'),
-              ('More bagging', 2, None, '___sec30'),
-              ('Simple example, head or tail', 2, None, '___sec31'),
-              ('Bagging Example', 2, None, '___sec32'),
-              ('Random forests', 2, None, '___sec33'),
-              ('A simple scikit-learn example', 2, None, '___sec34'),
-              ('Please, not the moons again!', 2, None, '___sec35'),
-              ('Bagging examples', 2, None, '___sec36'),
-              ('Then random forests', 2, None, '___sec37')]}
+               '___sec21'),
+              ('Another example, the moons again', 2, None, '___sec22'),
+              ('Playing around with regions', 2, None, '___sec23'),
+              ('Regression trees', 2, None, '___sec24'),
+              ('Final regressor code', 2, None, '___sec25'),
+              ('Pros and cons of trees, pros', 2, None, '___sec26'),
+              ('Disadvantages', 2, None, '___sec27'),
+              ('Bagging', 2, None, '___sec28'),
+              ('More bagging', 2, None, '___sec29'),
+              ('Simple example, head or tail', 2, None, '___sec30'),
+              ('Bagging Example', 2, None, '___sec31'),
+              ('Random forests', 2, None, '___sec32'),
+              ('A simple scikit-learn example', 2, None, '___sec33'),
+              ('Please, not the moons again!', 2, None, '___sec34'),
+              ('Bagging examples', 2, None, '___sec35'),
+              ('Then random forests', 2, None, '___sec36')]}
 end of tocinfo -->
 
 
@@ -200,21 +195,10 @@ given some assumptions, make predictions about the target feature value
 
 
            A typical Decision Tree with its pertinent Jargon, Classification Problem 
            
 
-
            
-In the figure here we present a decision tree obtained from a classification problem
-
 
            
 









            
 
-
            A typical Decision Tree with its pertinent Jargon, Regeression Problem 
            
-
-
            
-In the figure we present a decision tree obtained from a simple regression  problem
-
-
            
-









            
-
-
            General Features 
            
+
            General Features 
            
 
 
            
 The overarching approach to decision trees is a top-down approach.
@@ -232,7 +216,7 @@ node.
 
            
 









            
 
-
            How do we set it up? 
            
+
            How do we set it up? 
            
 
 
            
 In simplified terms, the process of training a decision tree and
@@ -250,7 +234,7 @@ Then we are essentially done!
 
            
 









            
 
-
            Decision trees and Regression  
            
+
            Decision trees and Regression  
            
 
            
 
 
@@ -346,7 +330,7 @@ plt.show()
 
            
 









            
 
-
            Building a tree, regression 
            
+
            Building a tree, regression 
            
 
 
            
 There are mainly two steps
@@ -374,7 +358,7 @@ within box \( j \).
 
            
 









            
 
-
            A top-down approach, recursive binary splitting 
            
+
            A top-down approach, recursive binary splitting 
            
 
 
            
 Unfortunately, it is computationally infeasible to consider every
@@ -393,7 +377,7 @@ better tree in some future step.
 
            
 









            
 
-
            Making a tree 
            
+
            Making a tree 
            
 
 
            
 In order to implement the recursive binary splitting we start by selecting
@@ -444,7 +428,7 @@ region contains more than five observations.
 
            
 
 
-
            Pruning the tree 
            
+
            Pruning the tree 
            
 
 
            
 The above procedure is rather straightforward, but leads often to
@@ -463,7 +447,7 @@ parameter \( \alpha \).
 
            
 









            
 
-
            Cost complexity pruning 
            
+
            Cost complexity pruning 
            
 For each value of \( \alpha \)  there corresponds a subtree \( T \in T_0 \) such that
 $$
 \sum_{m=1}^{\overline{T}}\sum_{i:x_i\in R_m}(y_i-\overline{y}_{R_m})^2+\alpha\overline{T},
@@ -494,7 +478,7 @@ subtree corresponding to \( \alpha \).
 
            
 









            
 
-
            Schematic Regression Procedure 
            
+
            Schematic Regression Procedure 
            
 
 
            
 
            
@@ -520,7 +504,7 @@ subtree corresponding to \( \alpha \).
 
            
 









            
 
-
            A Classification Tree 
            
+
            A Classification Tree 
            
 
 
            
 A classification tree is very similar to a regression tree, except
@@ -539,7 +523,7 @@ fall into that region.
 
            
 









            
 
-
            Growing a classification tree 
            
+
            Growing a classification tree 
            
 
 
            
 The task of growing a
@@ -563,7 +547,7 @@ than is the classification error rate.
 
            
 









            
 
-
            Classification tree, how to split nodes 
            
+
            Classification tree, how to split nodes 
            
 
 
            
 If our targets are the outcome of a classification process that takes
@@ -613,7 +597,7 @@ $$
 
            
 









            
 
-
            Visualizing the Tree, Classification 
            
+
            Visualizing the Tree, Classification 
            
 
            
 
 
@@ -654,7 +638,7 @@ os.system(cmd)
 
            
 









            
 
-
            Visualizing the Tree, The Moons  
            
+
            Visualizing the Tree, The Moons  
            
 
            
 
 
@@ -686,7 +670,7 @@ os.system(cmd)
 
            
 









            
 
-
            Computing the Gini index 
            
+
            Computing the Gini index 
            
 
 
            
 The example we will look at is a classical one in many Machine
@@ -726,7 +710,7 @@ The table here summarizes the various attributes and
 
            
 









            
 
-
            Simple Python Code to read in Data 
            
+
            Simple Python Code to read in Data 
            
 
 
            
 
@@ -788,7 +772,7 @@ display(y)
 
            
 









            
 
-
            Computing the Gini Factor  
            
+
            Computing the Gini Factor  
            
 
 
            
 The above functions (gini, entropy and misclassification error) are
@@ -866,7 +850,7 @@ split = get_split(dataset)
 
            
 









            
 
-
            Entropy and the ID3 algorithm 
            
+
            Entropy and the ID3 algorithm 
            
 
 
            
 ID3, learns decision trees by constructing
@@ -902,216 +886,203 @@ attributes at each step while growing the tree.
 
            
 









            
 
-
            Implementing the ID3 Algorithm 
            
+
            Implementing the ID3 Algorithm 
            
 
 
            
-import re
-import math
-from collections import deque
 
-
            
-
-
-
-
-
+
+
            import re
+import math
+from collections import deque
 
-
            
-class Node(object):
-	def __init__(self):
-		self.value = None
-		self.next = None
-		self.childs = None
+# x is examples in training set
+# y is set of targets
+# label is target attributes
+# Node is a class which has properties values, childs, and next
+# root is top node in the decision tree
 
-
            
-
-
-class DecisionTree(object):
-	def __init__(self, sample, attributes, labels):
-		self.sample = sample
-		self.attributes = attributes
-		self.labels = labels
-		self.labelCodes = None
-		self.labelCodesCount = None
-		self.initLabelCodes()
-		# print(self.labelCodes)
-		self.root = None
-		self.entropy = self.getEntropy([x for x in range(len(self.labels))])
+class Node(object):
+	def __init__(self):
+		self.value = None
+		self.next = None
+		self.childs = None
 
-
            
-	def initLabelCodes(self):
-		self.labelCodes = []
-		self.labelCodesCount = []
-		for l in self.labels:
-			if l not in self.labelCodes:
-				self.labelCodes.append(l)
-				self.labelCodesCount.append(0)
-			self.labelCodesCount[self.labelCodes.index(l)] += 1
+# Simple class of Decision Tree
+# Aimed for who want to learn Decision Tree, so it is not optimized
+class DecisionTree(object):
+	def __init__(self, sample, attributes, labels):
+		self.sample = sample
+		self.attributes = attributes
+		self.labels = labels
+		self.labelCodes = None
+		self.labelCodesCount = None
+		self.initLabelCodes()
+		# print(self.labelCodes)
+		self.root = None
+		self.entropy = self.getEntropy([x for x in range(len(self.labels))])
 
-
            
-	def getLabelCodeId(self, sampleId):
-		return self.labelCodes.index(self.labels[sampleId])
+	def initLabelCodes(self):
+		self.labelCodes = []
+		self.labelCodesCount = []
+		for l in self.labels:
+			if l not in self.labelCodes:
+				self.labelCodes.append(l)
+				self.labelCodesCount.append(0)
+			self.labelCodesCount[self.labelCodes.index(l)] += 1
 
-
            
-	def getAttributeValues(self, sampleIds, attributeId):
-		vals = []
-		for sid in sampleIds:
-			val = self.sample[sid][attributeId]
-			if val not in vals:
-				vals.append(val)
-		# print(vals)
-		return vals
+	def getLabelCodeId(self, sampleId):
+		return self.labelCodes.index(self.labels[sampleId])
 
-
            
-	def getEntropy(self, sampleIds):
-		entropy = 0
-		labelCount = [0] * len(self.labelCodes)
-		for sid in sampleIds:
-			labelCount[self.getLabelCodeId(sid)] += 1
-		# print("-ge", labelCount)
-		for lv in labelCount:
-			# print(lv)
-			if lv != 0:
-				entropy += -lv/len(sampleIds) * math.log(lv/len(sampleIds), 2)
-			else:
-				entropy += 0
-		return entropy
+	def getAttributeValues(self, sampleIds, attributeId):
+		vals = []
+		for sid in sampleIds:
+			val = self.sample[sid][attributeId]
+			if val not in vals:
+				vals.append(val)
+		# print(vals)
+		return vals
 
-
            
-	def getDominantLabel(self, sampleIds):
-		labelCodesCount = [0] * len(self.labelCodes)
-		for sid in sampleIds:
-			labelCodesCount[self.labelCodes.index(self.labels[sid])] += 1
-		return self.labelCodes[labelCodesCount.index(max(labelCodesCount))]
+	def getEntropy(self, sampleIds):
+		entropy = 0
+		labelCount = [0] * len(self.labelCodes)
+		for sid in sampleIds:
+			labelCount[self.getLabelCodeId(sid)] += 1
+		# print("-ge", labelCount)
+		for lv in labelCount:
+			# print(lv)
+			if lv != 0:
+				entropy += -lv/len(sampleIds) * math.log(lv/len(sampleIds), 2)
+			else:
+				entropy += 0
+		return entropy
 
-
            
-	def getInformationGain(self, sampleIds, attributeId):
-		gain = self.getEntropy(sampleIds)
-		attributeVals = []
-		attributeValsCount = []
-		attributeValsIds = []
-		for sid in sampleIds:
-			val = self.sample[sid][attributeId]
-			if val not in attributeVals:
-				attributeVals.append(val)
-				attributeValsCount.append(0)
-				attributeValsIds.append([])
-			vid = attributeVals.index(val)
-			attributeValsCount[vid] += 1
-			attributeValsIds[vid].append(sid)
-		# print("-gig", self.attributes[attributeId])
-		for vc, vids in zip(attributeValsCount, attributeValsIds):
-			# print("-gig", vids)
-			gain -= vc/len(sampleIds) * self.getEntropy(vids)
-		return gain
+	def getDominantLabel(self, sampleIds):
+		labelCodesCount = [0] * len(self.labelCodes)
+		for sid in sampleIds:
+			labelCodesCount[self.labelCodes.index(self.labels[sid])] += 1
+		return self.labelCodes[labelCodesCount.index(max(labelCodesCount))]
 
-
            
-	def getAttributeMaxInformationGain(self, sampleIds, attributeIds):
-		attributesEntropy = [0] * len(attributeIds)
-		for i, attId in zip(range(len(attributeIds)), attributeIds):
-			attributesEntropy[i] = self.getInformationGain(sampleIds, attId)
-		maxId = attributeIds[attributesEntropy.index(max(attributesEntropy))]
-		return self.attributes[maxId], maxId
+	def getInformationGain(self, sampleIds, attributeId):
+		gain = self.getEntropy(sampleIds)
+		attributeVals = []
+		attributeValsCount = []
+		attributeValsIds = []
+		for sid in sampleIds:
+			val = self.sample[sid][attributeId]
+			if val not in attributeVals:
+				attributeVals.append(val)
+				attributeValsCount.append(0)
+				attributeValsIds.append([])
+			vid = attributeVals.index(val)
+			attributeValsCount[vid] += 1
+			attributeValsIds[vid].append(sid)
+		# print("-gig", self.attributes[attributeId])
+		for vc, vids in zip(attributeValsCount, attributeValsIds):
+			# print("-gig", vids)
+			gain -= vc/len(sampleIds) * self.getEntropy(vids)
+		return gain
 
-
            
-	def isSingleLabeled(self, sampleIds):
-		label = self.labels[sampleIds[0]]
-		for sid in sampleIds:
-			if self.labels[sid] != label:
-				return False
-		return True
+	def getAttributeMaxInformationGain(self, sampleIds, attributeIds):
+		attributesEntropy = [0] * len(attributeIds)
+		for i, attId in zip(range(len(attributeIds)), attributeIds):
+			attributesEntropy[i] = self.getInformationGain(sampleIds, attId)
+		maxId = attributeIds[attributesEntropy.index(max(attributesEntropy))]
+		return self.attributes[maxId], maxId
 
-
            
-	def getLabel(self, sampleId):
-		return self.labels[sampleId]
+	def isSingleLabeled(self, sampleIds):
+		label = self.labels[sampleIds[0]]
+		for sid in sampleIds:
+			if self.labels[sid] != label:
+				return False
+		return True
 
-
            
-	def id3(self):
-		sampleIds = [x for x in range(len(self.sample))]
-		attributeIds = [x for x in range(len(self.attributes))]
-		self.root = self.id3Recv(sampleIds, attributeIds, self.root)
+	def getLabel(self, sampleId):
+		return self.labels[sampleId]
 
-
            
-	def id3Recv(self, sampleIds, attributeIds, root):
-		root = Node() # Initialize current root
-		if self.isSingleLabeled(sampleIds):
-			root.value = self.labels[sampleIds[0]]
-			return root
-		# print(attributeIds)
-		if len(attributeIds) == 0:
-			root.value = self.getDominantLabel(sampleIds)
-			return root
-		bestAttrName, bestAttrId = self.getAttributeMaxInformationGain(
+	def id3(self):
+		sampleIds = [x for x in range(len(self.sample))]
+		attributeIds = [x for x in range(len(self.attributes))]
+		self.root = self.id3Recv(sampleIds, attributeIds, self.root)
+
+	def id3Recv(self, sampleIds, attributeIds, root):
+		root = Node() # Initialize current root
+		if self.isSingleLabeled(sampleIds):
+			root.value = self.labels[sampleIds[0]]
+			return root
+		# print(attributeIds)
+		if len(attributeIds) == 0:
+			root.value = self.getDominantLabel(sampleIds)
+			return root
+		bestAttrName, bestAttrId = self.getAttributeMaxInformationGain(
 			sampleIds, attributeIds)
-		# print(bestAttrName)
-		root.value = bestAttrName
-		root.childs = []  # Create list of children
-		for value in self.getAttributeValues(sampleIds, bestAttrId):
-			# print(value)
-			child = Node()
-			child.value = value
-			root.childs.append(child)  # Append new child node to current
-									   # root
-			childSampleIds = []
-			for sid in sampleIds:
-				if self.sample[sid][bestAttrId] == value:
-					childSampleIds.append(sid)
-			if len(childSampleIds) == 0:
-				child.next = self.getDominantLabel(sampleIds)
-			else:
-				# print(bestAttrName, bestAttrId)
-				# print(attributeIds)
-				if len(attributeIds) > 0 and bestAttrId in attributeIds:
-					toRemove = attributeIds.index(bestAttrId)
-					attributeIds.pop(toRemove)
-				child.next = self.id3Recv(
-					childSampleIds, attributeIds, child.next)
-		return root
+		# print(bestAttrName)
+		root.value = bestAttrName
+		root.childs = []  # Create list of children
+		for value in self.getAttributeValues(sampleIds, bestAttrId):
+			# print(value)
+			child = Node()
+			child.value = value
+			root.childs.append(child)  # Append new child node to current
+									   # root
+			childSampleIds = []
+			for sid in sampleIds:
+				if self.sample[sid][bestAttrId] == value:
+					childSampleIds.append(sid)
+			if len(childSampleIds) == 0:
+				child.next = self.getDominantLabel(sampleIds)
+			else:
+				# print(bestAttrName, bestAttrId)
+				# print(attributeIds)
+				if len(attributeIds) > 0 and bestAttrId in attributeIds:
+					toRemove = attributeIds.index(bestAttrId)
+					attributeIds.pop(toRemove)
+				child.next = self.id3Recv(
+					childSampleIds, attributeIds, child.next)
+		return root
 
-
            
-	def printTree(self):
-		if self.root:
-			roots = deque()
-			roots.append(self.root)
-			while len(roots) > 0:
-				root = roots.popleft()
-				print(root.value)
-				if root.childs:
-					for child in root.childs:
-						print('({})'.format(child.value))
-						roots.append(child.next)
-				elif root.next:
-					print(root.next)
+	def printTree(self):
+		if self.root:
+			roots = deque()
+			roots.append(self.root)
+			while len(roots) > 0:
+				root = roots.popleft()
+				print(root.value)
+				if root.childs:
+					for child in root.childs:
+						print('({})'.format(child.value))
+						roots.append(child.next)
+				elif root.next:
+					print(root.next)
 
-
            
-def test():
-	f = open('DataFiles/rideclass.csv')
-	attributes = f.readline().split(',')
-	attributes = attributes[1:len(attributes)-1]
-	print(attributes)
-	sample = f.readlines()
-	f.close()
-	for i in range(len(sample)):
-		sample[i] = re.sub('\d+,', '', sample[i])
-		sample[i] = sample[i].strip().split(',')
-	labels = []
-	for s in sample:
-		labels.append(s.pop())
-	# print(sample)
-	# print(labels)
-	decisionTree = DecisionTree(sample, attributes, labels)
-	print("System entropy {}".format(decisionTree.entropy))
-	decisionTree.id3()
-	decisionTree.printTree()
 
-
            
-if __name__ == '__main__':
+def test():
+	f = open('DataFiles/rideclass.csv')
+	attributes = f.readline().split(',')
+	attributes = attributes[1:len(attributes)-1]
+	print(attributes)
+	sample = f.readlines()
+	f.close()
+	for i in range(len(sample)):
+		sample[i] = re.sub('\d+,', '', sample[i])
+		sample[i] = sample[i].strip().split(',')
+	labels = []
+	for s in sample:
+		labels.append(s.pop())
+	# print(sample)
+	# print(labels)
+	decisionTree = DecisionTree(sample, attributes, labels)
+	print("System entropy {}".format(decisionTree.entropy))
+	decisionTree.id3()
+	decisionTree.printTree()
+
+
+if __name__ == '__main__':
 	test()
-
+
            
 
            
 









            
 
-
            Cancer Data again now with Decision Trees and other Methods 
            
+
            Cancer Data again now with Decision Trees and other Methods 
            
 
            
 
 
@@ -1160,7 +1131,7 @@ deep_tree_clf.fit(X_train_scaled, y_train)
 
            
 









            
 
-
            Another example, the moons again 
            
+
            Another example, the moons again 
            
 
            
 
 
@@ -1232,7 +1203,7 @@ plt.show()
 
            
 









            
 
-
            Playing around with regions 
            
+
            Playing around with regions 
            
 
            
 
 
@@ -1260,7 +1231,7 @@ plt.show()
 
            
 









            
 
-
            Regression trees 
            
+
            Regression trees 
            
 
            
 
 
@@ -1282,7 +1253,7 @@ tree_reg.fit(X, y)
 
            
 









            
 
-
            Final regressor code 
            
+
            Final regressor code 
            
 
            
 
 
@@ -1360,7 +1331,7 @@ plt.show()
 
            
 









            
 
-
            Pros and cons of trees, pros 
            
+
            Pros and cons of trees, pros 
            
 
 
              
 
            •  White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)
              • 
@@ -1374,7 +1345,7 @@ plt.show()
 
 









              
 
-
              Disadvantages 
              
+
              Disadvantages 
              
 
 
                
 
              •  Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches
                • 
@@ -1391,7 +1362,7 @@ However, by aggregating many decision trees, using methods like bagging, random
 
                
 









                
 
-
                Bagging 
                
+
                Bagging 
                
 
 
                
 The plain decision trees suffer from high
@@ -1410,7 +1381,7 @@ learning method.
 
                
 









                
 
-
                More bagging 
                
+
                More bagging 
                
 
 
                
 Bagging typically results in improved accuracy
@@ -1439,7 +1410,7 @@ predictor, averaged over all \( B \) trees.
 
                
 









                
 
-
                Simple example, head or tail 
                
+
                Simple example, head or tail 
                
 
                
 
 
@@ -1459,7 +1430,7 @@ plt.show()
 
                
 









                
 
-
                Bagging Example 
                
+
                Bagging Example 
                
 
                
 
 
@@ -1510,7 +1481,7 @@ voting_clf.fit(X_train, y_train)
 
                
 









                
 
-
                Random forests 
                
+
                Random forests 
                
 
 
                
 Random forests provide an improvement over bagged trees by way of a
@@ -1554,7 +1525,7 @@ this setting.
 
                
 









                
 
-
                A simple scikit-learn example 
                
+
                A simple scikit-learn example 
                
 
                
 
 
@@ -1572,7 +1543,7 @@ accuracy = cross_validate(Random_Forest_mode
 
                
 









                
 
-
                Please, not the moons again! 
                
+
                Please, not the moons again! 
                
 
                
 
 
@@ -1630,7 +1601,7 @@ voting_clf.fit(X_train, y_train)
 
                
 









                
 
-
                Bagging examples 
                
+
                Bagging examples 
                
 
 
                
 
@@ -1691,7 +1662,7 @@ plt.show()
 
                
 









                
 
-
                Then random forests 
                
+
                Then random forests 
                
 
                
 
 
diff --git a/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb b/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb
index e06ed31ed..41458d8a9 100644
--- a/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb
+++ b/doc/pub/DecisionTrees/ipynb/DecisionTrees.ipynb
@@ -47,12 +47,8 @@
     "\n",
     "## A typical Decision Tree with its pertinent Jargon, Classification Problem\n",
     "\n",
-    "In the figure here we present a decision tree obtained from a classification problem\n",
     "\n",
     "\n",
-    "## A typical Decision Tree with its pertinent Jargon, Regeression Problem\n",
-    "\n",
-    "In the figure we present a decision tree obtained from a simple regression  problem\n",
     "\n",
     "\n",
     "## General Features\n",
@@ -818,17 +814,26 @@
     "The ID3 algorithm uses this information gain measure to select among the candidate\n",
     "attributes at each step while growing the tree.\n",
     "\n",
-    "## Implementing the ID3 Algorithm\n",
-    "\n",
+    "## Implementing the ID3 Algorithm"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
     "import re\n",
     "import math\n",
     "from collections import deque\n",
     "\n",
-    "\n",
-    "\n",
-    "\n",
-    "\n",
-    "\n",
+    "# x is examples in training set\n",
+    "# y is set of targets\n",
+    "# label is target attributes\n",
+    "# Node is a class which has properties values, childs, and next\n",
+    "# root is top node in the decision tree\n",
     "\n",
     "class Node(object):\n",
     "\tdef __init__(self):\n",
@@ -836,8 +841,8 @@
     "\t\tself.next = None\n",
     "\t\tself.childs = None\n",
     "\n",
-    "\n",
-    "\n",
+    "# Simple class of Decision Tree\n",
+    "# Aimed for who want to learn Decision Tree, so it is not optimized\n",
     "class DecisionTree(object):\n",
     "\tdef __init__(self, sample, attributes, labels):\n",
     "\t\tself.sample = sample\n",
@@ -1006,15 +1011,19 @@
     "\n",
     "\n",
     "if __name__ == '__main__':\n",
-    "\ttest()\n",
-    "\n",
-    "\n",
+    "\ttest()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "## Cancer Data again now with Decision Trees and other Methods"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
@@ -1072,7 +1081,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
@@ -1153,7 +1162,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
@@ -1190,7 +1199,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
@@ -1206,7 +1215,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
@@ -1227,7 +1236,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
    "metadata": {
     "collapsed": false
    },
@@ -1275,7 +1284,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
@@ -1393,7 +1402,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "metadata": {
     "collapsed": false
    },
@@ -1422,7 +1431,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 15,
    "metadata": {
     "collapsed": false
    },
@@ -1528,7 +1537,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
    "metadata": {
     "collapsed": false
    },
@@ -1555,7 +1564,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
    "metadata": {
     "collapsed": false
    },
@@ -1583,7 +1592,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 18,
    "metadata": {
     "collapsed": false
    },
@@ -1599,7 +1608,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 19,
    "metadata": {
     "collapsed": false
    },
@@ -1617,7 +1626,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 20,
    "metadata": {
     "collapsed": false
    },
@@ -1640,7 +1649,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 21,
    "metadata": {
     "collapsed": false
    },
@@ -1658,7 +1667,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 22,
    "metadata": {
     "collapsed": false
    },
@@ -1670,7 +1679,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 23,
    "metadata": {
     "collapsed": false
    },
@@ -1684,7 +1693,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 24,
    "metadata": {
     "collapsed": false
    },
@@ -1727,7 +1736,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 25,
    "metadata": {
     "collapsed": false
    },
@@ -1740,7 +1749,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 26,
    "metadata": {
     "collapsed": false
    },
diff --git a/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz b/doc/pub/DecisionTrees/ipynb/ipynb-DecisionTrees-src.tar.gz
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diff --git a/doc/src/DecisionTrees/DecisionTrees.do.txt b/doc/src/DecisionTrees/DecisionTrees.do.txt
index abcc176f6..b1286f7b2 100644
--- a/doc/src/DecisionTrees/DecisionTrees.do.txt
+++ b/doc/src/DecisionTrees/DecisionTrees.do.txt
@@ -35,13 +35,8 @@ given some assumptions, make predictions about the target feature value
 !split
 ===== A typical Decision Tree with its pertinent Jargon, Classification Problem =====
 
-In the figure here we present a decision tree obtained from a classification problem
 
 
-!split
-===== A typical Decision Tree with its pertinent Jargon, Regeression Problem =====
-
-In the figure we present a decision tree obtained from a simple regression  problem
 
 
 !split
@@ -665,12 +660,13 @@ attributes at each step while growing the tree.
 !split
 =====  Implementing the ID3 Algorithm =====
 
+!bc pycod
 import re
 import math
 from collections import deque
 
 # x is examples in training set
-# y is set of attributes
+# y is set of targets
 # label is target attributes
 # Node is a class which has properties values, childs, and next
 # root is top node in the decision tree
@@ -852,7 +848,7 @@ def test():
 
 if __name__ == '__main__':
 	test()
-
+!ec
 
 !split
 =====  Cancer Data again now with Decision Trees and other Methods =====