From a99e8da47830c3af0ea6b84ca03ab160e4bf227b Mon Sep 17 00:00:00 2001 From: mhjensen Date: Fri, 9 Nov 2018 05:04:05 +0100 Subject: [PATCH] update on decision trees --- .../DecisionTrees/html/DecisionTrees-bs.html | 401 +++++++++++++++++- .../html/DecisionTrees-reveal.html | 382 ++++++++++++++++- .../html/DecisionTrees-solarized.html | 387 ++++++++++++++++- doc/pub/DecisionTrees/html/DecisionTrees.html | 387 ++++++++++++++++- .../ipynb/ipynb-DecisionTrees-src.tar.gz | Bin 213 -> 213 bytes .../pdf/DecisionTrees-beamer-handouts2x3.pdf | Bin 171027 -> 273984 bytes .../pdf/DecisionTrees-beamer.pdf | Bin 153392 -> 262771 bytes .../pdf/DecisionTrees-minted.pdf | Bin 268844 -> 338128 bytes doc/pub/svm/ipynb/svm.ipynb | 180 ++++++-- doc/src/DecisionTrees/DecisionTrees.do.txt | 290 ++++++++++++- 10 files changed, 1988 insertions(+), 39 deletions(-) diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html index 4c899ab8f..37fe3d3ad 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-bs.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-bs.html @@ -44,11 +44,43 @@ Automatically generated HTML file from DocOnce source ('Nodes, leafs, roots and branches', 2, None, '___sec1'), ('How do we set it up?', 2, None, '___sec2'), ('Decision trees and Regression', 2, None, '___sec3'), - ('Maxwell-Boltzmann velocity distribution', 2, None, '___sec4')]} + ('Maxwell-Boltzmann velocity distribution', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), + ('A top-down approach, recursive binary splitting', + 2, + None, + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('A schematic procedure', 2, None, '___sec10'), + ('A classification tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Pros and cons of trees, pros', 2, None, '___sec13'), + ('Disadvantages', 2, None, '___sec14'), + ('Bagging', 2, None, '___sec15'), + ('Random forests', 2, None, '___sec16'), + ('A simple scikit-learn example', 2, None, '___sec17')]} end of tocinfo --> + + + + + + +

+ + +

Building a tree, regression

+ +

+There are mainly two steps + +

    +
  1. We split the predictor space (the set of possible values \( x_1,x_2,\dots, x_p \)) into \( J \)
  2. +
+ +distinct and non-non-overlapping regions, \( R_1,R_2,\dots,R_J \). + +
    +
  1. 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 \( R_j \).
  2. +
+ +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 predic- tive model. The goal is to find boxes \( R_1,\dots,R_J \) +that minimize the MSE, given by +$$ +\sum_{j=1}^J\sum_{i\in R_j}(y_i-\overline{y}_{R_j})^2, +$$ + +where \( \overline{y}_{R_j} \) is the mean response for the training observations +within the $j$th +box. + +

+ + +

A top-down approach, recursive binary splitting

+ +

+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 + +

+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. + +

+ + +

Making a 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 +$$ +\sum_{i:x_i\in R_j}(y_i-\overline{y}_{R_1})^2+\sum_{i:x_i\in R_2}(y_i-\overline{y}_{R_2})^2, +$$ + +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 RSS 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. + +

+ + +

Pruning the tree

+ +

+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 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 \( \alpha \). + +

+ + +

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 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. + +

+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 \( \alpha \). + +

+ + +

A schematic procedure

+ +

+

+
+

+ +

    +
  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. + +
      +
    1. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of \( \alpha \).
    2. +
    + +
  2. 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 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 \( \alpha \).
  3. +
  4. Then we average the results for each value of \( alpha \), and pick \( \alpha \) to minimize the average error.
  5. +
  6. Return the subtree from Step 2 that corresponds to the chosen value of \( \alpha \).
  7. +
+
+
+ + +

+ + +

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. + +

+ + +

Growing a classification tree

+ +

+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. + +

+ + +

Pros and cons of trees, pros

+ + + + + +

Disadvantages

+ + + +However, by aggregating many decision trees, using methods like bagging, random forests, and boosting, the predictive performance of trees can be substantially improved. + +

+ + +

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. + +

+Bootstrap aggregation, or just bagging, is a +general-purpose procedure for reducing the variance of a statistical +learning method. + +

+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. + +

+ + +

Random forests

+ +

+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. + +

+ + +

A simple scikit-learn example

+

+ + +

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']
+
+

diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html index 8e685b42d..05f0f30c5 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-reveal.html @@ -107,6 +107,22 @@ td.padding { + + + + + + + @@ -132,7 +148,7 @@ td.padding {

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

 
-

Nov 2, 2018

+

Nov 9, 2018


@@ -168,7 +184,7 @@ The main idea of decision trees is to find those descriptive features which contain the most information regarding the target feature and then split the dataset along the values of these features such that the target feature values -for the resulting sub\_datasets are as pure as possible. +for the resulting sub datasets are as pure as possible.

The descriptive feature which leaves the target feature most purely is said @@ -411,6 +427,368 @@ plt.show() +

+

Building a tree, regression

+ +

+There are mainly two steps + +

    +

  1. We split the predictor space (the set of possible values \( x_1,x_2,\dots, x_p \)) into \( J \)
  2. +
+

+ +distinct and non-non-overlapping regions, \( R_1,R_2,\dots,R_J \). + +

    +

  1. 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 \( R_j \).
  2. +
+

+ +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 predic- tive model. The goal is to find boxes \( R_1,\dots,R_J \) +that minimize the MSE, given by +

 
+$$ +\sum_{j=1}^J\sum_{i\in R_j}(y_i-\overline{y}_{R_j})^2, +$$ +

 
+ +where \( \overline{y}_{R_j} \) is the mean response for the training observations +within the $j$th +box. +

+ + +
+

A top-down approach, recursive binary splitting

+ +

+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 + +

+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. +

+ + +
+

Making a 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 +

 
+$$ +\sum_{i:x_i\in R_j}(y_i-\overline{y}_{R_1})^2+\sum_{i:x_i\in R_2}(y_i-\overline{y}_{R_2})^2, +$$ +

 
+ +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 RSS 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. +

+ + +
+

Pruning the tree

+ +

+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 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 \( \alpha \). +

+ + +
+

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 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. + +

+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 \( \alpha \). +

+ + +
+

A schematic procedure

+ +

+

+Building a Regression 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. + +
      +

    1. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of \( \alpha \).
    2. +
    +

  2. 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 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 \( \alpha \).
  3. +

  4. Then we average the results for each value of \( alpha \), and pick \( \alpha \) to minimize the average error.
  5. +

  6. Return the subtree from Step 2 that corresponds to the chosen value of \( \alpha \).
  7. +
+
+
+ + +
+

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. +

+ + +
+

Growing a classification tree

+ +

+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. +

+ + +
+

Pros and cons of trees, pros

+ + +
+ + +
+

Disadvantages

+ + +

+ +However, by aggregating many decision trees, using methods like bagging, random forests, and boosting, the predictive performance of trees can be substantially improved. +

+ + +
+

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. + +

+Bootstrap aggregation, or just bagging, is a +general-purpose procedure for reducing the variance of a statistical +learning method. + +

+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. +

+ + +
+

Random forests

+ +

+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. +

+ + +
+

A simple scikit-learn example

+

+ + +

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']
+
+
+ + diff --git a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html index 1c9cc8033..098cb9028 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees-solarized.html @@ -64,11 +64,43 @@ div { text-align: justify; text-justify: inter-word; } ('Nodes, leafs, roots and branches', 2, None, '___sec1'), ('How do we set it up?', 2, None, '___sec2'), ('Decision trees and Regression', 2, None, '___sec3'), - ('Maxwell-Boltzmann velocity distribution', 2, None, '___sec4')]} + ('Maxwell-Boltzmann velocity distribution', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), + ('A top-down approach, recursive binary splitting', + 2, + None, + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('A schematic procedure', 2, None, '___sec10'), + ('A classification tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Pros and cons of trees, pros', 2, None, '___sec13'), + ('Disadvantages', 2, None, '___sec14'), + ('Bagging', 2, None, '___sec15'), + ('Random forests', 2, None, '___sec16'), + ('A simple scikit-learn example', 2, None, '___sec17')]} end of tocinfo --> + + + + + + + @@ -90,7 +122,7 @@ end of tocinfo -->
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Nov 2, 2018

+

Nov 9, 2018












@@ -123,7 +155,7 @@ The main idea of decision trees is to find those descriptive features which contain the most information regarding the target feature and then split the dataset along the values of these features such that the target feature values -for the resulting sub\_datasets are as pure as possible. +for the resulting sub datasets are as pure as possible.

The descriptive feature which leaves the target feature most purely is said @@ -362,6 +394,355 @@ plt.show() #i.e. frequency of all velocities in range -5 to -4.9, -4.9 to -4.8, etc...

+









+ +

Building a tree, regression

+ +

+There are mainly two steps + +

    +
  1. We split the predictor space (the set of possible values \( x_1,x_2,\dots, x_p \)) into \( J \)
  2. +
+ +distinct and non-non-overlapping regions, \( R_1,R_2,\dots,R_J \). + +
    +
  1. 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 \( R_j \).
  2. +
+ +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 predic- tive model. The goal is to find boxes \( R_1,\dots,R_J \) +that minimize the MSE, given by +$$ +\sum_{j=1}^J\sum_{i\in R_j}(y_i-\overline{y}_{R_j})^2, +$$ + +where \( \overline{y}_{R_j} \) is the mean response for the training observations +within the $j$th +box. + +

+









+ +

A top-down approach, recursive binary splitting

+ +

+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 + +

+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. + +

+









+ +

Making a 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 +$$ +\sum_{i:x_i\in R_j}(y_i-\overline{y}_{R_1})^2+\sum_{i:x_i\in R_2}(y_i-\overline{y}_{R_2})^2, +$$ + +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 RSS 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. + +

+ + +

Pruning the tree

+ +

+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 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 \( \alpha \). + +

+









+ +

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 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. + +

+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 \( \alpha \). + +

+









+ +

A schematic procedure

+ +

+

+Building a Regression 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. + +
      +
    1. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of \( \alpha \).
    2. +
    + +
  2. 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 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 \( \alpha \).
  3. +
  4. Then we average the results for each value of \( alpha \), and pick \( \alpha \) to minimize the average error.
  5. +
  6. Return the subtree from Step 2 that corresponds to the chosen value of \( \alpha \).
  7. +
+
+ + +

+









+ +

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. + +

+









+ +

Growing a classification tree

+ +

+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. + +

+









+ +

Pros and cons of trees, pros

+ + + +









+ +

Disadvantages

+ + + +However, by aggregating many decision trees, using methods like bagging, random forests, and boosting, the predictive performance of trees can be substantially improved. + +

+









+ +

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. + +

+Bootstrap aggregation, or just bagging, is a +general-purpose procedure for reducing the variance of a statistical +learning method. + +

+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. + +

+









+ +

Random forests

+ +

+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. + +

+









+ +

A simple scikit-learn example

+

+ + +

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']
+
+

diff --git a/doc/pub/DecisionTrees/html/DecisionTrees.html b/doc/pub/DecisionTrees/html/DecisionTrees.html index ecadd280b..bc478fe7c 100644 --- a/doc/pub/DecisionTrees/html/DecisionTrees.html +++ b/doc/pub/DecisionTrees/html/DecisionTrees.html @@ -69,11 +69,43 @@ div { text-align: justify; text-justify: inter-word; } ('Nodes, leafs, roots and branches', 2, None, '___sec1'), ('How do we set it up?', 2, None, '___sec2'), ('Decision trees and Regression', 2, None, '___sec3'), - ('Maxwell-Boltzmann velocity distribution', 2, None, '___sec4')]} + ('Maxwell-Boltzmann velocity distribution', 2, None, '___sec4'), + ('Building a tree, regression', 2, None, '___sec5'), + ('A top-down approach, recursive binary splitting', + 2, + None, + '___sec6'), + ('Making a tree', 2, None, '___sec7'), + ('Pruning the tree', 2, None, '___sec8'), + ('Cost complexity pruning', 2, None, '___sec9'), + ('A schematic procedure', 2, None, '___sec10'), + ('A classification tree', 2, None, '___sec11'), + ('Growing a classification tree', 2, None, '___sec12'), + ('Pros and cons of trees, pros', 2, None, '___sec13'), + ('Disadvantages', 2, None, '___sec14'), + ('Bagging', 2, None, '___sec15'), + ('Random forests', 2, None, '___sec16'), + ('A simple scikit-learn example', 2, None, '___sec17')]} end of tocinfo --> + + + + + + + @@ -95,7 +127,7 @@ end of tocinfo -->

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

-

Nov 2, 2018

+

Nov 9, 2018












@@ -128,7 +160,7 @@ The main idea of decision trees is to find those descriptive features which contain the most information regarding the target feature and then split the dataset along the values of these features such that the target feature values -for the resulting sub\_datasets are as pure as possible. +for the resulting sub datasets are as pure as possible.

The descriptive feature which leaves the target feature most purely is said @@ -367,6 +399,355 @@ plt.show() #i.e. frequency of all velocities in range -5 to -4.9, -4.9 to -4.8, etc...

+









+ +

Building a tree, regression

+ +

+There are mainly two steps + +

    +
  1. We split the predictor space (the set of possible values \( x_1,x_2,\dots, x_p \)) into \( J \)
  2. +
+ +distinct and non-non-overlapping regions, \( R_1,R_2,\dots,R_J \). + +
    +
  1. 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 \( R_j \).
  2. +
+ +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 predic- tive model. The goal is to find boxes \( R_1,\dots,R_J \) +that minimize the MSE, given by +$$ +\sum_{j=1}^J\sum_{i\in R_j}(y_i-\overline{y}_{R_j})^2, +$$ + +where \( \overline{y}_{R_j} \) is the mean response for the training observations +within the $j$th +box. + +

+









+ +

A top-down approach, recursive binary splitting

+ +

+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 + +

+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. + +

+









+ +

Making a 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 +$$ +\sum_{i:x_i\in R_j}(y_i-\overline{y}_{R_1})^2+\sum_{i:x_i\in R_2}(y_i-\overline{y}_{R_2})^2, +$$ + +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 RSS 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. + +

+ + +

Pruning the tree

+ +

+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 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 \( \alpha \). + +

+









+ +

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 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. + +

+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 \( \alpha \). + +

+









+ +

A schematic procedure

+ +

+

+Building a Regression 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. + +
      +
    1. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of \( \alpha \).
    2. +
    + +
  2. 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 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 \( \alpha \).
  3. +
  4. Then we average the results for each value of \( alpha \), and pick \( \alpha \) to minimize the average error.
  5. +
  6. Return the subtree from Step 2 that corresponds to the chosen value of \( \alpha \).
  7. +
+
+ + +

+









+ +

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. + +

+









+ +

Growing a classification tree

+ +

+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. + +

+









+ +

Pros and cons of trees, pros

+ + + +









+ +

Disadvantages

+ + + +However, by aggregating many decision trees, using methods like bagging, random forests, and boosting, the predictive performance of trees can be substantially improved. + +

+









+ +

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. + +

+Bootstrap aggregation, or just bagging, is a +general-purpose procedure for reducing the variance of a statistical +learning method. + +

+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. + +

+









+ +

Random forests

+ +

+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. + +

+









+ +

A simple scikit-learn example

+

+ + +

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']
+
+

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\n", 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\n", 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\n", 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s9qOLhT9FOrYwWvIm77WFqVl7j6P7VEuhmodimWMl86mEm4R7Bpiz/+e83vo6AX7L6eaIGfi5QJXiVPhZuGeApsZSws1RAnc7W6SCFKqGFVP4ggSwcIfEENSFtl7mrm6lZGKe000SWfgxJ6U4FcUkvhYAx4tUkELVEAlfIewX7hmgqu8YZcveI7AxfnXfeyTqdLNEGn7PSMlHUUxi82Y73QRACtWc+SmArQzeYN1ExtWrQuQrWDNMZP5cp5shspCMzJ/kpnATt60FkEI1B34IYLuCV7ZSEZapdW57FIhvTSUr/q/lh3wEZ0eXJDeFm+iz5xktGXC6GdOkUM3C6wEsQ1ZCCCt5PSNBclKIZKObn2a05G3e3TCHQOttTjcHkEI1I68GsMw5FX5TMnyR0ZIBTlSGCNDkdHPEFK9mZIIUqEJcLdKxhWjtQaJr57BkzSanmzNNCtU0vBjAErrCjxKr/Y+u72NWY4srVqAWOy/mY4LkpBCZqbEr1K5qYKx1udNNuYoUqim8FsISvMKvQp1djJ/ZTKgt4viG0yLOa/mYIDkpRI4cXguQjhSqSbwUwsUWvHIWdvGp6jtG4NYF9H1suRSpLuClfEwotpxMJbkpchHuGWDOrhc50byTysrrWVLb7nSTriKF6hSvhHCxBq+chV181NiVmW8kbOGVfEwo1pxMJbkpZhLq7KKidzsXWg8TWN1Gc4u7ilSQQhXwRghL8Iqi5MJhqGKjYxOuzsZkkpNCGFextG/6MBU3kkJ1iluDWIJXCOGkkjLldBNmJDkphH+VON0Ap8XCV1xfpJYHayR8RVHp37aDifFznKjsc7opQHyzf+FOkpNC5Cexq8qp64edbkpWRd2j6tYiNTl4hSg2kY4tjI7vpH/9BDWt7a4ZjpJTqdxFclKI/EU6tjBa8ibvtYVdv6tK0RaqiXmpbiPhm56chV0cQp1dLCg7SvgjZdx43791ujnChWSYP3eSmyKdUGcXC6rOE14RJXC3u4tUKNJC1Y2Lp6RAzU62Uike1Y2VTHxQTqAS11KxcUByMleSmyKTmusqUQ3zXV+kQhEWqlKkCiGEtyQyUlWXSk4KYQI9MkQs6I1dVYquUAUpUouBbHTtTaWRMFQ73QrhFtcM80fPO9ia4iDZKdymqApVN81L9UuB6tZQk42uveti9RWgzulmCIf5JSMzkewUTimNhFHXB4BRp5uSk6LZnkrH4pPH3dCb6qd5VhJqwiyRji2MhrdybkmUynqZo1rM/F6kgmSncMZk/2VGw1vZW93lmZx1RaGqlPqiUuoNpdSYUurpGW77n5RSF5RSg0qpf1BKzc71eVxRpBZBAAthRLhngKGnv83JBduYvLOMJWs2eWKCvxvYlZ12UeEQKhySPVGFMFm4Z4BIxxbGZl0mumEONWvds/XfTFxRqALngL8A/iHbjZRSHwf+CGgHmoEPAH+WyxO44XSV6QUBZXLFLETC5OkzNK2spubWZSy67yGnm+M1lmenXeQiXghrVVWdpzRQ4bnOAFcUqlrrH2mtXwBmOv7l88Dfa60Paa0HgK8BD1rdPjNICAshzOaX7JR8FMIGo0NOtyAvXltMtRJ4Men/DwCNSqmg1vqaoFZKPQw8DNBQ38iF6EF7Wpnajtg4VE71pEbPE9Wj9Ea7HWmL+ZozfsfoazTzfamrXcDA5WtHNutqxzz13vvrs5JebNUEh9SNjFbeSO+RaE73iY7qnG9rBj1Zib5g3/NZwJXZmZivr6qnRplmWNXvr58Hc7LT7PdEstOfYo0TjKy9A11SZWt2msFrhWoVkLx0P/H3atL0KGitnwKeAlhx0yq9oLzV8gamSsy3StYb7WZx+TLb22KWTKtVkwXrJgy/RjPfl53fv5D262s3LeKejb92zdedXmmbidc/K7kIHeiipWwfB361hMUt7Tndp/dIlMXLyy1u2fuig0NeP0LVddmZTy+q138erMhOs98TyU5/GjjUzfye1zn6ydUsXj7f6eYY4rVCdRhITrXE313Zn528B6CfZAvagy+fsrElxuWz0tat28gIYYCrsrNYh/olO+MkO+1Xuf/nXFo46HQz8uK1QvUQsAr4wdT/rwL60g1dOa1YgzgXmcKrrnZBxqt5J8k2MtaSTf5t4ZrslGzMX/rsbHZt4SfZ6bxwzwBzdr3IieadVN5yPeWzvfdz54pCVSlVRrwtpUCpUqoCiGmtYyk3/UfgaaXUPxFf7fonwNN2tjUXTgWxVVevuQxXGZHpsdLNi5qJXLH7g2zynx+vZadbi1SvZ2c+zyHZ6X/hngECe3dwofUXBFa30dzS7rn5qeCSVf/EQzNCfPuU+6f+/idKqSal1LBSqglAa/1/gb8CtgOngVPAnzrT5PScDGKrrl7dfPUrV+zeldjXr3R8m2zynz/PZKdbi1SQ7Mzl68KbgjXDlNVV05zj/H83ckWPqtb6q8BXM3y7KuW23wS+aXGT8uLmIBbCTcI9A5TvfoaTTQeouXUZS+7Y4HSTPMkr2ZluUakQwh6xea4728MQVxSqfuK1MDZz+EcpbVazLBOsm8j4eoW9aueVMXjrMhZKkeprfi1SJTvf/7oQVpJC1SReDWMzh3+0dv70r5nkM/dKAlqI/Hg1F3Mh2TkzyU5nlQxfdLoJppBC1QRu2IZq7aZFTjchZ5nCq652zIHWzEwWFghhnBeKVLMXO1nNa4WfZKdzwj0DVOx9ntfbTjO30f495M0khWqB3DIvNVvYFhpimcIxX5nCK36KiLENms0O7my/uGQ1rMlGhwD39yQJ47xQpMLMvZ9eyM58N7aX7PSvUGcXgeMvEWrrZe7qVk8vpAIpVE3h9kAuNCAS93dj74PZ4Zft9bnttftBLBhwugnCZG4YYTKDGRvwS3bO/D1hrnDPAFV9xyhb9h6BjffQUNvidJMK5pbtqTzJL4GcKwkbIUQ2bhlhchvJTmGn+Y2llM+f63QzTCOFap68FMit9zRnnMOaaZgnn+Eft86TEkJYz0uZmItsuQmSncK9dOQK1PpntEqG/gvgpUDOdEVv1vBPocNk8aGx5mu+7ve5TcV6OoxfVqOKOL8VqQnZekLdkp2bPr827al+fs+QYs3OYiQ9qnlw45C/16/Ii/WUlGJ93QC6qtLpJggTeLlI9XpuQuajp/2eIcWcndmUDF9kbOQcJyr7nG6KaaRQzZPbQvm1jjOmTP4vdtl+cfnhl5oQVnBbHuZKctM8kp3OC3V2Ub73ebrbzqEaG32xkApk6N8wN/am2sVre/gly3WYSIaMhMhdMeehEZKdwmqhzi5GQ88y9tEoNXe3+6ZIBSlU8+LV3oNCeTmIZJjIPRJ7/B1d38cs/BOmxcbLQ/5282p2ZttWS7LTXar6jtGwqoZLH1xI0EdFKkihaogXeg+cvHKXye1iJpGOLYyP72Tgo2W+u+ovJn4rUiU305Ni1Hsm6qudboLppFA1yK3B7IawK+TKO99fFG543YXw8pCgUeGeAZoaSwk3l7Hovoecbo4okFuz0CinM6TQHsu62rGMq/4zcfo1m6GYsrPYSaGaI7f3pmYLu7WbFrk+fF7rOJPXUYBeH5Zy+7+LEKncnoVGeT07O777WtHlJkh2plJj/to7NZkUqgZ4tQfBS+GTTSh6kS8d+yKP3fgd5pc3ON2cvPihJ0MUL78N+c/EyuwM9wwwefoMcO3+0Qn923bM+Dix26vo/8W1t5uoDMafR/Xz57P/ij8d+y/M03XUt9+cZ4udJdlZvKRQzYHfehC86smz3+atob08cfbbfGXpX5j++HYEoR96MkRxK5Yi1Uqhzi4qercze+UwcG/G21Vdv3PGxxqedVfa26mhUQD+V9kv6Srt4dnZX+MLx24m0nEX8B/zbfq05CF2yU5hJSlUcyTh7KxQ9CIvhH6IRvNC6DkeWfj7hnpVc5nPJEEoRGZywZ6/cM/A9N9V9wHGw1t5b2WE6tVrst7v8r2rZnzs2NnKjLcLj17hxZ/+AD0JL5SfZMM9q7hycBu5FqrZcjO5AJXsdFb/th3MKhvgQmU/AZqcbo7ppFAVprFycvuTZ7/NJJMATDJhuFdVhobcQUeuEJuX/iQd4X5ywW5cpGMLFcOHqamNZ+O+pSeoWV1PoHUdwdoWgvPHCF9Ksxhq/lhOu2KMXYhmvN3/3vMdNBoAjWZbeYT/5+Nt8I3Mjzf09LeJ3vkAwZY6yU0PCHV2MR7eSv/qCWY1tvhyJxUpVGfglV6ETEWiHRK9BT/6s4Est5n5cWKNE4RPDRBsqbvq64ne1HE9DsC4Hp/uVQ3WZR5yMmLtpkWGbi/MFxrp50s7vs5j677M/MA8p5sjknglB/NhdnYm8rBk+CKV+3/OyeadVN5yPZcaGwGYSyvNLe3Tt3/tze2mPXey0Eg/Lxx7hfHJGADjkzFeOPYKj9yyibrgewyE51xzn7q5g4RXHqZ++xOETm+gpOn9XEzN5QTJTuckppCcWz3OX6p3+PbCzzrdJEtIoZoDL/QivNZxJus8IatEOrZQHu2ldt7UR2l0yPiDVMT3fRuZ+yEaDu/g8u7Y9BU9XN2bmpDoVX2tw5y5qlYW+dk2zRbve3J/B2/1HeKJ/R18ZfUXnW6OSOGFHMyHWdkZ7hmgfPczNAQi01/rXnOOwIq2qwpTuzy5v4NJnZKbepIn9new863MF4IXL99DiJepO/Nd5u2rh4pqLvfHCJ1en3YhlmSnsxYvha/NPk3XhXd9m51SqPqIncM04Z4BAnt3cHLBNqqbggw2zJ/6jiIWNLZFRll4GIDorAlOrxtmvPsEwd3PTAfjgeG3pntTE8b1OAeG3zLjpVgu131ki1mi90ejp3t9pFfVJWIx3xapCYVmZ/+2HVSc20OorZf+1Sunv15T79yhFgdCh6d7UxPGJ2McCB3Oer+G2hYuboTLodNcJp7P+uIlSnZvJtJxF5WbPmlhq68m2TmzPoZ59eJBX2enFKpZ+Hm4y6hEYQrx/doqxs9x8sbjBD7exqJCewumcrz3SJSFyzdwcXkPYV6m/J2TjG7+EN/js+jZcxluvNGRrVWsDMKDL5+y7LG9JLn3J9Hr48eeAeEPoc4uqvqOAfE8HC15m/71E9Ssvcc1cwSf2/h43vdtqG2BxOuY+s8ZNnPy9DaWdMDIbesyTgVIJtlpvb8ue53J+DRk32anFKoz8HtPQi4SZ7P3tfVSVlc9vRgm0GjNkFbiin7khr1c4Dhl/WMAlOzeafsVPchCLKtlm0vnt54BL1JlMvSaLNKxhdGSNxn7SBRgKg/nUNN6m2uKVCssuu8hTvV0cvKn22jafpjQ6Q0zdhxIdlprYOw4P6h6h5iOXxD4NTulUBVZ9W/bwXh4K6G2CIGN9vUWNNS2wJqrn+vkvA5O7t/G0s1XGGr6lemvlzQtyunqXrhTtrl0fusZEN6VmIN6pukA1U1BFn/kk+gFtU43y1bNLe1crG8i9OLLlL+zmf5t9wGfd7pZReu7gRend3VI8GN2SqGaQbEP+w/s66Zy/88prT1IdMMcAq3rHO8tWLJmE6caOznzzj6az8W3ERgeKaVs93zCPFBQsSrnRluvZPgiVFdd8/V859IJYZfE6urwysPULFvGwjs2pJQHxSN5xIuXtjJv9qfoH7v251qy03qHyo4T5er32Y/ZKYVqFsU67D+wr5vyvc9ztO00c1e3ssSBFauZJK7oExthjR85wnj34asWX+XDyiEqKYKzK2QunRBWC3V2MRp6lvdWhqlevYZgy4edbpLjEiNeJ+ngfy/+TZqO3cDo+kdMH9mS7Mysf9sO/uncr3N+fR81a51btGcHKVTFVfq37WD2uT2cX9/H3BWtjmyrMpOrfiDvaCEcfIswuyh/56Qjc1hnIvO0vK+8Jkj0Uhg9P+h0U4RNEgtILy3YRvWtQao/KEVqqsQoV6j60PTeq2YueJXsTC/SsYXR8Z1TC/j8XaSCFKpiirrcR2TLy7xXdYTBT8+iptU7H/5gy4cJtnyYM1uNr0oV9tFnz3O2/A2gxOmmCDGjydNniFbupubW+FC/SC8xynW+tpPAns2Mbv4QFQ896HSzfCvU2cWCqvOEV5RRc7fzU/LsIL8xBAP7uolseZmjra8z0T6LJWs2efLDv+j2H38HAAAgAElEQVS+h6i5dRknF2yjYvsThDq7nG6SIN4zFenYwmh4K1duLSHQepvTTRJiRqWRMIF5s5m1fLnTTXG9htoWbtz4u0Q3zOFE805GNz89fUKXMF/13BiqYb4nf0/nQ3pU01DhUNHMT00M9Sfmo7pxqN+IhXdsIBYMEKo+RPk7mwl1PuTI3qvifYG9Oxit28dkSxlL1mxyujlCzGhgXzeB0ElOLRumOH4TmCMxFeDET3fStP2c6VMBxPuMHqzjZVKoFrFQZxfj4a30r59gwdrf8M3VWWIoKlq3i/Gp01TsmAqQ7RjGYp9rNW/ldUzeIL/yhftddfG+otU3uWiX5pZ2TgGh6kOUHn+WUCczFquSnSIbGfovUpGOLYyf2Ux0wxxfTsZuqG1h0X0PMXlnGScXbCOwd4flQ1GZjvuTs6qF8IZQZxej4a3xxaQ+GGFySnNLO4GN96BujTIaepZIx5ast5fsFNm4plBVSs1TSm1RSr2nlDqllEo7RqiU+qpSalwpNZz05wN2t9fr1NgVFt66gIALT1MJjfTz+Z88yqWR/qv+no9F9z1EdVOQYM2wya0UhgwNOd0C35LsLFxiHnXyxbsXi1Qzs7NQDbUtVH5wFU03y0iKmUojYVR18Qz7g7uG/h8HokAjcAvwY6XUAa31oTS3fVZrfb+trfMRdbkv/pdad37Yn9zfwVt9h3hifwfA9N/zPWkjceRryfBFQHYCcMpEfbXTTfAryc4CJE6cOjl14pSX51GbnZ2FSvzMq7Erjjy/8AdXFKpKqTnAp4BWrfUwsEsptRV4APgjRxuXAy/Nrwn3DDBn18tEFvZwobKEAE1ON+kqiXPfNTr+X62n/57v+cWqsZHXG3dzw95eBvgUdW3LLGi5EPaT7DRHbSDCoMe3obIiO81w4roh6movoju2yLaBBQp1dhE4t4e9y/qYhbtGQq3kikIVuAmIaa2PJn3tALA2w+03KKX6gfPAd7TWT6S7kVLqYeBhgIb6Ri5ED87YEBUbh0pQ0dznxoQHmjN8vZTeaPc1X4/qUe763AIGLs++5nt1tWN0fPe1nJ/biNjoBCWBEOH7rqO05gbKZ9cwdgF6L0QteT6joqOa7+x4honJ+Lnv0Ynx6e9NTE7yjR3f44sf+F3Dj1vCXcy5ZRXnl40xa+gCl0NDlM21oncv/ecASPs5yEVUj+Z9X7eY/Oj1lFTOY/xsBWMmfdaio5reI/Z+bvVkJdolPytJbMjOBss+g27IzljjBCNr7yBaWWL7Z8oMiZ+F77xrfnYWrpnS+c1c+vXLTIyMUj52kMHBIGUVqb9fJTtnMtl/mYkVQwx+5HZKqqoomajI6/PqRHYWyi2FahUwmPK1K0C6auIHwFNAH3A78LxS6rLW+vupN9RaPzV1W1bctEovKG+dsSFqyNytqRaXX9t71xvtThu0AAOXZ6e9jxlCO7uoLftnzv3qdY7PvwqN9POlHV/nsXVfnr7SP/D2BV699DNiOn7uu046TTumY7x6qZNH192fZ8/AfC5e7mHk4F5mv/QedbPMP8Eq23F/+f6b9ka7Lfs82CXysy0EVvXQ97Hlps2H7j0SZfHyclMeK1fRwSE3nkxleXauvOlD2onPoB3ZGe4ZiO+53NZL2aKVLPbAvNTU7Ow9EqWiaZhXf2lVdpqhgbOvv0T9uzGuDG6gvn3FVd+V7Mwu3DNAw+FOTq04yaL2hwp6LCeys1BuKVSH4Zrt6mqAa1ZgaK3fSfrfPUqpvwE+DVwTtl5n9rBYaSQM1VBZ7/xwf/JcqsT8qY4zzzKpJzPeZ1JPFjTfKvl86pP7zT/Bym3TPERRkOxMkWtuhjq7qOjdTqitF7V6peMX77lKl51P7u+wNDvNMGv5ctS+X6T9nmRnblTDfKeb4Ai3rPo/CpQppZK7W1YB6RYDpNKAsqRVDsu2ZUfrPc2s3bQo98fqGWD2uT2cut751e+pc6kSq1IPD3UzPhnLeL/xyRgHQocLfv4lazZRc+syyha+weRpCUjhaZKdKWbKzdZ7mrnrs9dT1XeM8MrDVK9e45kiNVN2HggdtiU7hYNGi3fnFFf0qGqt31NK/Qj4c6XUF4ivXN0IrE69rVJqI/AvwGXgNuD3gT+2sbmukesec6HOLsbPbGaoLcKsFSsd344q+eo/+Ur/8VV/bduQxKzlyynvPUL1L98E5OQU4U2SnfkZGJrF/MZSwnXVBFs+7HRzcpYuOx+c9zDPbXzc4ZblRldXUHou7HQzPKuYTqNK5pYeVYDfAyqBi8SHoh7RWh9SSt2llEruBvxt4Bjxoa1/BP5Sa/1d21ubJFg3YejrdkoMb03eWUZg4z2O9xwkegQSV//jk7GregbsdOK6+BWqnEktPE6yMw864q0tkzJlZ3/UO/l1uvoSgdBJyVxhSM49qkqpfwY+Bnxaa/180tcVsBn4PPHgy2tLFK11P/Cbab6+k/iCgcT/fy6fx7dSPvNrsk0eN1vTymoONsx3vCcV0s+lSu4ZsEtDbQunGk9zofUX1MuZ1JZSY1dcu2evHSQ7M3M6OxN7LHtBpuzsOPMsqz70+w61KncNtS1EVpzmRO9OmiRzhQFGhv4fBd4CvqaUekFrnUiF/0k8aJ/KN2iLkZ2Tx/WIe+a2pJtLNT1/yuYFqc0t7VysbyLEywQPbc/pTGoh8iDZaaJiXXiTKTsPDx1xqEXGNbe0cwoIVR+SzDVAdR9AV1U63QzH5Fyoaq0PKKWeIR6sDwBPK6X+GPgD4tuePGJNE4tXpp6DfLhlbku2uVRO7O3WUNvC2WVHWDwCPZnXIniGWzZQF++T7LSXmbnpJpmy02t7Yja3tHM2PEIT1RxN3VjNQW7NzlBnF+PhrRxdPVFUm/wnMzpH9SvAKPCnSqkvAv8N+CnwgNZZ9sYQeXmt4wwHXz7l6jmwfuCWIt4M2VY8e52TZ5eHRvr5wmt/UchzS3baJJGb2bJzXtUYVFel/Z4oTm7LznDPAJGOLYyGnmXyzjJq1rbnvcbEqew063kNrfrXWvcqpf6a+NF8fwvsAf611vqqSzql1JeBfw0sA8aA14Eva61nPhrKZ9JfpTUbukqTnjBrVdY38cb1nQT2nCTSYf5BAPl4/3Nz9YktTl/dOyl5/0g75zMnnnvfpW7+7s0O/ugu43tRSnYak6l3q652ATu/fyHnx0n3s5LY5P/1wGnmNs58CIwwXywYsGxKmp+yc35jKeHmKIs/8kl0bW3ej+NUdqbb8zcf+az6DyX9/Xe01iNpbrMO+F/Et0j5KBADXlVKOXUshmOcvkorjchWIDNpqG2hZm07k3eW0fOBV4l0bDF9VeraTYum93BM/pNpL1ynPzduk7p/ZKaVzlb0HCQ/99bugnaokOzMUabPeaZTqXIV6uxi5M3HCLX1Mnd1q+O7oIiZSXaCXpB/kepUdmba8zcfhnpUlVKbiC8AuAAsAP4DaeZXaa0/nnK/B4gf63cn8FK+jRX5UdUB4qOOIpOG2ha4rwX1+ktUXTzP8OkzYPDEqmxznPwYnrlQl/tMeZzU/SMzrXQ26wo+23Pn06sq2em8cM8AVX3HaFizkEs3fNBT+6f6nWSndZzKzkz7pecj5x5VpdRvAE8DB4EPAd3AF5RSuRymWz31XLJ5mnC9muvyW10pgZqeDhQ2FzDd/pGvhDqvuUI38wo+23Mb7VWV7HSP+Y2lMOSeXVBEnGRnejpypaAt1JzKTrP3S8+pUFVKrQGeA84AH9dah4A/Id4j+5c5PMTfAPuBn+fVSiFs5KbtvIxy28K78K7DxKK9nKjMv2c12967mW6X7vtmPvffvZnbY0t2utNEfbXTTRAu47bsNINT2Znr8+ZqxqF/pdQtwDbiw08f01qfB9BaP6eUegPYqJS6a2pz6XT3/yawBliTtH+gEK4U3wHAu4uw3bRYINKxhdHxnfSvnqCmtT3vAyfS7R8Z01efXZ7pCv6RWzYxP5D/9M6M+/72zXxuumSnENm5aQ2Fm7LTLE5lZ9b90vOQtVBVSt0I/F9AE+8NOJ5yky8DrwDfAO5Ic/9vET+2b73W+t28Wuhxdp5AJcwRoo/q028Czm1E7fXPTaizi7K6fUy2lFFz97qCTkVL7B/5tT3f4QfdP+Gzy36DB+c9zOLl5dO3yXYFX8h8q+S9K6ODYfT8YE73k+wsTKbPf13tmAOtEVZQ1YH4Yb4m83p2JqjuA4yWFDbjx6nszLZfej6yFqpa62PEJ/5n+v6rgEr3PaXU3wC/RTxovXN0hsnSXaX1RrtZXJ7L9DT/C43086UdX+exdV8m6bRHx1TWN3H25j4iEztZ0jGXkdvWETS4qCodo+GZ+Nx4+bNSFZhg8oOrCJpwdG/qHKr7bvkMi2mc/r7ZV/CFkuwsTKberd5oN/Gdu0QiO/9g0Zeu+lnwm2LMzsRo1NGp0ahCeC070zG06j9XSqnHiZ/A8pvAgFIqEdjDWuthK55TeJOTe2Om01DbAmtaOFv2Ej3vvMrS3b2EeSCnYjVboPpxWCkXZs0FnGnlqtlX8E6R7BS5SmRnB+lXcXuJZOf7Ih1biFbuZvIjhY9GgT+y05JCFfi9qf92pnz9z4CvWvScwmNmutJz0sI7NgAvUXuxjIs53qfYAtUumVauPjpyf0HzT11KslPMKDk7/fCzINl5tdqbGhi7e3nBRapfstOSQlVrnXZIy+/celawW+W6v5soblbNP3Ujyc6rSXamZ+YelcJd1NgV0x7LL9mZz8lUIgPZCy53ue7v5rhR725V5SQzV/PmsnLVakYWUgnjbM3O6mpKQ979uU7NzpgubI9K4UK1AVMexg3ZaQarhv6FyMoLV3rxrarec7oZGbm9F0pXV5jyOOnmUPUeiV61clWIYuGF7HQzt+emmfySnVKoCkd46UqvZPgiUPjKf7NJD74Qxlzqm2A0ep5I9AQX66sLngPoBC+s0nYzN+fm6OanCVUdYaJyFgGanG6Oa0ihKhzhlSs9XZXfcapCCHcJttRByyehAyK7dzKoO2EtnitWU7PTjbkpjAn3DBDYu4OTzTupvOV6Aq23ee5zaSWZoypEFuGyPir3/5xwjxy1nqv+bTuYNbCP09WXnG6KENeo3PRJKoL3cVPPDYwc3Ot0c4Rg8vQZopW7qbl1GUvWbJIiNYUUqil0sJ5oeDCv+/rxrOBi1tzSzpVbSzjRvJOK7U9IsZqDUGcXo+Gt9N1xklkrWiRwRU7szk618DoqJt03nUcUr8C82cxavtzpZriSDP2byG8TsQUsWbOJU42dhKoP0bh3B2HMOanKj0KdXQSOv8TAR83ZqFoUD7uzc7KqwdbnEyKTcM8A1aff5NSaYWqcboxLSaHqQcW0atENmlvaOXP4NMGaYUacbkwSN55pvXBZFZc+WCNFqnCl97OzGbgFpqZ7BueP8dqb251smrCJm3Iz1NlFRe92LrQeZtaKlZKbGUih6kFGVi1OVAbRQ2/jplkeiTOqH1v3Zc+cjhGbN5uxkXN53deqCwu3XZSURsJgzompQlgiY3Zemm1zS/LjxezMRA+NMFGZfW9iK7LTLbmZKFLDKw8T2HiPFKlZuKd6EUUjcUb1E/s7nG5KzlRjI8eXnqRi+xOEOrsM3dfN26GYTVWbs1G1m0QHzTu8QIhCeDE7C+H37Fy8FGYtWypF6gykR9Ui2a4Ev/d0twMtcofkM6pfOPYKj9yyyRM9A80t7VysbyLEy5Qef5ZIxzEqN33S6WYJm8ipVPaR7EzPq9kpsosfLCOykR5Vi/j9SjBf6c6o9oqG2haqV6+h6WaZ8p6qf9sO3ov8X/ZWd1FZLxtVi/xJdqbn5ewUVwt1djF+ZjP7A4clL3MghaqwTeoZ1eOT3jujeqJeJmEmC/cMMLr5aUrHtzHRPouate22DWOFRvr5/E8e9dTnR7jXxcs9TjchIz9kp4jnZaRjC+WD32XyzjLH5qZ6LTulUE2jkL1U7eDV/VqznVHtNWrsitNNcFwoepHfH/wdRqpPcPmzS2zfqLrY5uuJwmXKyPkVV4iETtvcmtz5KTuLXVXVeU7dPYf/WvYOJeXOTCnyWnbKHNUsrNwGqpDHzue5y8Ij4PB8bd+cUV1rbE6Rm7ZDMdOTZ7/N27F9PDF3jPu5x9bn7o/KfD03syo7N31+LQOXr12hn+vjprtNuGeAhn1P8S5z8m6X1bJmp48/9r7MztEhOi69wVuX3+GJ/R18ZfUXbX16L2anFKpZWDlXys55WCpQDYya/rhGpZ5R7VUnKvuoHx+kf9sO5t27bsbbu2U7FDOFohfZcvGHaDTP1xzmN6J302zj83ecefaa+XpWBL6s+M+PVfmWrkg143EHL0+g9xziFPGFk26TLTt7j0RtbIm9/JSd4Z4B5ux6kZ1LuvjnwSOOFYp2ZaeZZOjfIl4dnhfZNdS2EGi9jdCnI4yGtzK6+Wmnm+SIv37nG+jJcQAmlWLbFfuGTUMj/bxy8We2zdeTFf/2sjs7gy11jNywgfp9i7my5yCnejoteR5RvEKdXVRsf4ITzTt54QNDaBRg//QNu7PTLNKjapFsV4K9Nl8AD56PoOsucfFyj+zXZoKG2hZY08JJOjixfydLOuYyclvxHK165Gev8XLl84yXxK/KY3rC1p6BJ/d3MEn6+Xpu7xkQM8uWna33WNNvX99+M+GmRdy060XO1O5zbc+q8J5wzwBVfcfoa+tl9NYWOt/ceU2hKNmZnRSqPlfffjPDHcco2X2MQd0Ja5Fi1SRL1mzibNlL9HX/M8HdvYROr6e+/Wanm3UNM+cLRjq28PS8bzOZMp3PzrA7EDpMTPtgrrNwlWBLHf3dS7j13CAHVjjdGuE0M3MzWDNM3w3z2XalN+OiOMnOzGToPwMdrHe6Caap3PRJKoL3cd32RgZf63T1NixmsHPrjYV3bKB69RrCKw9T0bvd8KlVdjBjvmBiW5Vo5W7emT9ALOWq3M6we27j47z8r17k4EMv81vLPoFC8VvLPuGbOdDCOROVQYb6Ik43wzF2ZWdZeGRq7YR7mTXPWnUfmD5+2+kFxV7NTtf0qCql5gF/D/wacAn4stb6mskbSikF/A/gC1Nf+jvgj7TW2uw2BeeOE74y69qvmzBXyu7VjPPuXUf/Nmga2sllS57BPZK33sj1KrWQM7SDLR9mNHyWxSPQE5v59l4VrBkmsrSBv/vYn7uiV97qk3q8spDKldlpUb7V1Y5lXPVvhpKmRbx3upGRn+7kZF8fgdbbXPFZt4vR7CwkN4tB/7YdjIa30r16glmNLTy3xh0FoddOOXNNoQo8DkSBRuAW4MdKqQNa60Mpt3sY+E1gFaCBV4ATwJNmN+iVx49QHrTmFCI/rWZ0k3x/APMpbpPFj8GbpDTijeLGqJLhi/G/GNyay0rpTuoxe/jMIwupXJedVuVbx3dfY3H5MkseG+LD/7Q8yNLN0N/7NoPh4pkulU92FpqbfpVY4T9a8jbRDXOocdkFjx3ZaSZXDP0rpeYAnwK+orUe1lrvArYCD6S5+eeBx7TWZ7TWZ4HHgAdta6xwtXyOGUwN6HyGvSrrm3jj+uOMhrfSv22H4fu72cC+bsr3Ps/rjbs5UdnnisBN7AXotdWrZpPstEbFQw9SEbyPpqH5TjfFNkaz04zc9KNwz8D0Cv/ohjm2H4QyEy9mp1t6VG8CYlrro0lfOwCsTXPblVPfS77dynQPqpR6mHgvAg31jVyIHjTUKFU5joqav69pVI/SG+02/XFnEru9iuFZdxE7W8nYBfftvRcd1QXtCdgf7WfL0VcY1+//AG7peYX7qj7DvPLMK/K/8+4zTEzGA3picpJv7PgeX/zA7xp89mZKbtzEyMIRosMTDJ3bw2RVLWUVhX1+zPmsZF4pPdNjx64MUdLwHuO//RHmVN5F6ewaV+zb+MzJZ6f/zRLy/7dLT09Wol34c5LChuxscCSv0rEzO2N31DKs7iR2do4r8zKh0NyE/LKzkNyMzrqdQzfOYmxiglGL/j0L/6wYz83YYISSwBUGPnMb5VXuyctkdmSn2dxSqFYBqWeWXgHSzbaumvpe8u2qlFIqda6V1vop4CmAFTet0gvKWw01Sg2FAEwf/u+Ndls6fJVJ/y92UF39CgOfu91VV3gJvUeiLF5envf9n97zHFpNxgc1p2gm2Tr8w4zDGqGRfl795c+mV0LGdIxXL3Xy6Lr785izUw7UcKqnk5Gf7qPp2A2Mrn+koG2rzPisZJsvmO2xRzc/TX/J24ysnqDmtnYaahfO+FxmzFnL5TGOHui+ZvVqTMc4Pt5d0GcoITE/1QND/5Zn58qbPqSdyKt07MzO0IEuxs9sY3JFhNkOncmei0JzE4xnZ6G5efb1X7DyWD1HB2+lvt2af89CPytGczPSsYWB8Z1EV0So2XgPDbWLDD2fX7LTCm4pVIeB1GqwBhjK4bY1wLAVCwJ0sB4VDpn9sI6ZqHTvL93QSD+PHvzvfKfpj/P+Ic1nRWW2M7TznbPT3NLOKSBUfYj67U8QOr3B0W2rjM4XHNjXTeX+n3OieSeVt1xvaH6VGXPWcnmMx1f9teWh6oEiFVyanX5Q334zoc6HmLvvJUK8zKnVp125t2p/tJ8/+cljBRU4RrPTitx0m1xzMzEf9eRUXgZa1+V1UeOn7DSbWwrVo0CZUqpFa53YO2kVkLoYgKmvrQJ+OcPthIc8ub+DQ0O5n32c7soxny02rNoupLmlnYv1TYRu2Ev5S5sZ3fwhKh56sKDHtEq4ZwCAydNnKI2EmX1uD0fbTjN3dZuhX8xmrCT12mpUF5DstFDiIID67U9wemgfJ/v6WLJmk9PNukrHmWcLXqlvNDud3mbJLUKdXQSOv8SJG48T+LixvLzqcSQ7s3JFoaq1fk8p9SPgz5VSXyC+cnUjsDrNzf8R+AOl1E+ID1T8Z+BvbWusMJ2Tq02t3D8u9QSrpZshcsu/oq7NHcOoMHW0X+92Kpb2xdOgGk6tH2builbDoWvGSlI3rEb1yrZUINlph2BLHWEeYemuF+nvfZuTdLhm26rEkZh2Z2ehuRkLBtAj6Tr9vSPU2cX4mc2E2iIEDF7Up/JLdlrFFav+p/weUAlcBL4PPKK1PqSUukspNZx0u/8NvAR0AQeBH099TXiU31ebLlmzicDH2zizZh/le5+nf9sOBvZ1E+4ZmO7NtEviOcM9A9NBG155mMFfXcHA525n4HO3U7O23XDoJv5NCllJasZjmMUjw/4Jkp0WC7bUTe8EUPdahJGDe51uEnD1kZh+zE43CvcMMLr5acbPbGbyzjICG+8pqEj1W3ZawTWFqta6X2v9m1rrOVrrpsSG1VrrnVrrqqTbaa31H2qt5039+UOZY2VMacg9V7L5/IDlswVVuue16/QqiE8FqFnbzvn1fajyV5jf8wIN+56iYvsTtp1mFenYQvnuZ2g4/H0a9j1F+eB3p4M22PJhGmpbpv8YERrp5zNb/z0TOnUl6YShf5ts895EZpKd9tHLVnHdrFWU9Y853ZTp7Ixpf2enm6RuPbXovocK6lmX7MyNawpVt9LBeqLh1EW13qUDc2a+kY2M/oCZdeWYPPxll4baFmrWtjP4iet499/M4d1/M4dQWy/jZzYzuvlp1OU+S543cfzpyQXbuLLmDKfXDfPuv5nD5c8uKThoIf5eXor0E5tMXUk6YWjOmhvmvXlp2F84IzwYr/2dPoq6mLLTDfq37Yh3LLT1Evh4mylzlf2UnVZyxRxVUbycWG3q5KTzhtoW1rY/TPjStcdAzntxmH/e+NhVX5u854NEfrYlr+dSY/GdiCrGz3FyarL/IpNXLSfeS4DZpeV0fOKbbPrxHzA2EWV2aTlPfuxrOT+WW86b9tiwv7BRsKWO0Okb0W+8ycjAy5xddoSFd2xwpC1+yE6jJ/mt3bQo45ZRZp+GFursoqrvGBDP0tGSt+lfP0HNWnO2KvNjdlpFClXhqOQfsFz2AzTjytHpSefpilSA/rEqLmw8ftXXJmYtJvyRn+f1PLF57z9PoLGwyf6ZpL6Xf/jaX/l2Qr8QMLUTQM8iync/w5mh+PkJThSriezMdR9Vt2Wnqg6k30Qti3RFarav5yvSsYXRkjcZ+0h8s/54lpp7FGqxZ6eR0SspVIvM2KEqhtjFMAOu3BNwJoVeOWYa/nLLVh6pw0m9R6Isuv0hh1qTXbr38viV09Pfd9t7OxMZ9he5iu8E8ABL9i7m5Bvb0BcvUX73GlfsBJCJm7Kzsr6JvdWdBMLv0L8N5t27rqC2mSXcM0Bg7w5OLthGdVOQRfdZk71+y06jjGatzFEtIvXtNxO98wHq9y3myp6DnNzl7BwjJybl+33SuZ3SvZepjC4KsEO2z50M+4tcBVvqqNz0SZZcuJeS3TFGXnzZtnmrXs/OxHz96IY59AWeYXTz07bvgJIqMQe1r+Wf49OkLCpSwZvZafZnzkjWSo9qDuILqkIFHaV69dya988QtmJuTTaJPQFv2vUildcP03e5x7FegEL288v3uDm/Tzq3U7r3MpXRRQF2SPe5k95U93JLdmZSuemTDHfeaOsJVsmf4QfnPWzovm7JzsQ+06caOznx0500bT9HmMKOnDYisdtKYp7saHirqXNQs/Fidpq1d3k+WSuFqk3smluTi2BLHaO7bH/aq6SblB8/ijw3+f7Q+H3SuZ0yvZehkX5+/bmH8loUYMZ51zM9fqbFINKb6k5uys5M7DzBKvUzfN8tn2ExjTnf323Z6cSR06Obn2a85G3ql1RCNejqCgZXmzsHNRuvZafZi+iMZq0M/QtHFLKfn9c3rQ7OT78HY6ave00h/7ZWb32Trm3SmyrMEGypY3T9Iyw9dRflL73HyV0dlkwFSP0Md5x5Nuf7ujU7m1vaCWy8h4GPXp7eri/U2XXNn7rAaNr71wVGr7ltbDAy/ff+bTum/4xufnp6H9TEISeX713FkjyYQfMAABnDSURBVDWbHJ9j7NbsNGP/Xch/5Ep6VIXtMk3Kz7VnwOlV+4V67c3tTjdhmtlX4YUsuLB627BMbfudG+8huOgG055HFK9gSx20PEjFth3w0lYGw51EVpg3FSDdZ/iVUCePjtyf08+Km7OzobYF7mvh5LwOzoT30Xzu6iJfB+bQ+Ucvzfg4auQ9ACKqndqyzvgXp3pNAU4vu0RgReG7oBRLdpq9ADmfkSvpURW2yzQpP5eeAb8fFWc3s6/CC1lwYdZVu9G2/Z/D+e1TK0Qm8+5dx6xFD3Hd9kZGfrqPUz2dpjxuIT9fXsnOJWs2UbO2fbq3M/FnaHVzTn8Sx0HH5s256v6X713F5XtX5XVEdDrFkp1mLaKLDobznl4lPao5MmNBlYjLNCn/8NCRGe9rxqbVIs6Kq/B8F1zYsW1YxrZdOWHK4wuRLDFvdemuFznx052c7OsjUOAcyHSf4ZjObUGTl7Iz7XtUa+wxxi5ELRvKL6bsNGMRXaHTq6RQtUmwbiLjiRrFJtNE8t4j0Rnv68VV+1YvEMqXFcOA+S64sOOXaGrbEuEpi6jczcvZmZgKsHQz9Pe+zWC4E9ZmKMRykO7ny84N/+0m2WmsLQlmZqdZi+gKyVkpVG2SvI1Kb7SbxeXLHGyNd3lx1b5Z23qYyW0HHzj1S1SKVPfzQ3ZWPBSftzp3+x7OY+681VxJdppDstMYMxarSqEqhIWsXiCUL7cNA9r9S1RW+udOx9zfc+kF8+5dR7hnFddtf4LTvdZuYeUHkp258cIFSKEdArKYqkjp2XPh8ojTzTCFE6e05MrqBUL5cvtVuB2kN1XYza4trHIl2WmcZGfuCllAlUx6VA2QBVXu5MbhIXDfEFEyL1yFW0V6U4WTrN7CygjJTuOKOTuNMDNnpUdVeJpbN7AGc8/GFuaS3lRjouFBp5vgO/PuXUdF8D6u297IlT0HTdvCKleSncJqZuWsFKrC09w6PAQyRORGZg1FFZUyGXizyrx71zG6/hFuOngHIz/dZ+tUAMlOYRWzc1YSSHiWm4eHwJtDRG7dDsYMMuRfmGh4UKY9WcDsLaxyIdlpLj/nplFW5Kz0qArPkuEh81l5XrSTZM/UwuhgvdNN8L2Khx6cngow+FqnpVMBJDvN5dfcNMqqnJVCNQ8yX8sdZHjIXG6es2YGKVKF2827dx3R2z7FddsbGX+nx7JpAJKd5vF7bhplRc7K0L9BOliPCoecbobAe8NDVjFr2MmK01bcQIb8zSPD/9ara1tG/9nVNJ97hQGLnkOyM86M7PRrbhplZc5Kj6oQFrBzf0Izhp0yzVnzeu+ADPmbR4b/7TNRGf+8jh854nBL7Oel7PRrbhpldc5KoVqk1NgVqA043QzfyiUAzQhks4ad/DhnTYpU4VUlTYsYPdHI4BvdnNm62enm2MpL2enH3DTKjpyVQlWIAqWGZq4BaEZPqFlbzPh1zpoUqeaKH3oic/StFmypI3rnAyy5cC8lu2Oc2brZ0ROsrJCu2PRadvo1N42yOmelUBWiQKmhmUsAmnE1b+aw03MbH+fgQy9f8yeXuWxuPIZR9ksVXhdsqaNy0yeZteghSnbHGHnxZdsPBbBSumLTa9npt9w0yq6clUI1D9Kr4LxcfsjtCILU0OwOv5tTAJpxNe+WYSe3bc0ii6esJ/lnn/r2m5m16CHq9y025QQrN2RnumIz1+LRL9npttw0ys6clUJVeFIuP+R2BEFqaP7ha381YwCadTVvdNjJil8+btuaRealWk8WVdmvvv1mRtc/wh19d6L7+gp6LDdkZ7piM5fi0S/Z6bbcNMrunJVCVXhOLj/kdgRButB898rpGQPQrKt5o8NOVvzycdMxjFKk2kt6Vb3HDdmZqdh8s6+raLLTTblplBM5K4Wq8JyZfshDI/18Zuu/Z8LiIEgXmmUlpfzWsk9kDUAnJuDn+gvKSK+Bm7ZmkSLVXtKr6gxVOZey/rG87++G7MxUbP5K480zFo9+yE435aZRTuWsFKrCU3L5If/WG//ApUg/MYuDIN/QLGQCfr5yuYI32mvghnleIEWqELlwS3YWUmz6ITvdkpv5ciJn5WSqItS/bQezx89xojJCgCanm2NIth/yr6z+IqGRfrYd337N/aw4McQrp7tk+gX1yC2bpk9jSe01SP5eJm7YmkWKVGfJSVX2utQ3QaxmiLOvv8TCOzYYuq9bstMruQnWZKcbcjMfTu6kIoVqkQl1djEe3kr/+glqWttpqG1xukmGzPRD/uT+DiaZvOZ+XggCq8z0Cyr1Nrn+YnL6F44Uqc6S46TtFWypI8w6grt7OTN0gFgwQHNLe873l+w0zorsdDo38+H0dn+uKFSVUvOAvwd+DbgEfFlrnbYfXCn1VeC/AskTdT6ktX7X6nYmi29RFfJUb0Kos4vR0LOoO8uouXud54pUyP5DnriyTTa7tJyffnpz3uc4+8FMv6By6TWYSb5nZud7Pz3V1mIuUt2Sm9Krap94sfoAS3fVEPlxD6c+0UkJd+V0X8lO4/yYnUY5XaSCSwpV4HEgCjQCtwA/Vkod0FofynD7Z7XW99vWOh9pvCHA0Ac/SNCDRepMcrn6LUYzXcGb8b4lz9Ey8l7nc794T2ql4+EJMDzq6J6tjuem9KraL9hSx8DwvyJ4fhCz9l2Q7EzPb9lplFv2pHZ8MZVSag7wKeArWuthrfUuYCvwgLMtE17j1bk/Tiv0fct3O5t87jc93F/m/DW2k0Wq5KYwk2RnfryUnUa5aWqV82kPNwExrfXRpK8dANZmuc8GpVQ/cB74jtb6iXQ3Uko9DDwM0FDfyIXoQZOaPPX4leOoaKnh+0X1KL3RblPbkovYqgki6g4mRioZORK1/flnEh3V9BbQrm8t+1bG7xXyuE5KfU/6o/18/ej/5Ms3Pcq88jpTnqPQ9+077z7DxGS8V2FicpJv7PgeX/zA75p6v+mh/rJqAGIRzYWDzv6bTk5Wokodi1DLchMMZmc1qJEzqDLjWWiUU9npNrGlowwvaiM2AujCchMkO/PlhexMlcvv2XjeVsY7BC44/+/vhkK1Cq4ZwbgCVGe4/Q+Ap4A+4HbgeaXUZa3191NvqLV+auq2rLhplV5Q3mpaowHUUH5zVHuj3SwuX2ZqW3IROtBFbVknA5+73ZXzU3uPRFm8vNzpZhhm5Vyh3iNRKpqGpx9/6/7nODT0DluHf+iKIbnQSD+v/vJnxHS8kIzpGK9e6uTRdfdnfS+M3C/dlf2Fg1EWtDr3WRkeDVM+19GeBstyE4xnZ75ZaJRT2ek2A4e6CZ5/jRMbSyiZuMuTuQnWZueBty/wzXcfm37sp/cUX3amM9PvWTf1pCZYPvSvlNqhlNIZ/uwChoHUhKsBhtI9ntb6Ha31Oa31hNZ6D/A3wKetfRVCZGbHcYNv9R3iW29sdt2xe/nuCZjr/dwYmnYM+XsxN+WkKmGUldnZcebZ6cd245GlVmdnPtyYt2BDoaq1Xqe1Vhn+rAGOAmVKqeQuvlVApgUB1zwFoMxutxC5sDoA+6PvP/62d3/GxOQE4J4NovOdozXT/aKDYVeGZqJItbo31Wu5KSdVCaOszM7QSD+vXPzZ9GN/641/cN2RpVZlZ74Sq/vdlLcJjg/9a63fU0r9CPhzpdQXiK9e3QisTnd7pdRG4F+Ay8BtwO8Df2xTcz2tNBLOPDDoc1YNMeWz/6gRHWeenX78iaSr6Hy2QbFCvnsCZrufGwtUsK9IzYXkZvEK9wwwZ//P2d/6DnMxdzpbOl7MzuQ9YSf0JNuOb5/+fz9nZz7cmrfJHF/1P+X3gErgIvB94JHEFitKqbuUUsNJt/1t4BjxIa5/BP5Sa/1dm9vrWbq6wukmOMKKISarz2xO9AqkXj0nuKVnwExuDU03FalJXJWb8b2lZfjfSqHOLsp3P8OJ5p3MXd1qaMP/fHktOxOPPT2HczJ2zUEGfszOfLg1b1O5olDVWvdrrX9Taz1Ha92UvGm11nqn1roq6f8/p7UOaq2rtNbLtdbfdqbV3hLuGWD2uT2crr7kdFNsZ9UQk9VnNmc6KSbBT9vHJIb63Tr0BK4rUiU3i0y4Z4CqvmOEVx4m8PE2W4pUL2ZnusdO5afszJdXilRwwdC/l3nldKpQZxeB4y8Rautl1oqVrlzxbyWrhpgyzRV6s8+cbdAOhA5P9wokWz7vA548hi+d5A2l3RqYLljh7ylyUpV15jeWEq6rZpENRSp4MzvTPTb4KzcL5aUiFaRQ9b1QZxcVvdsJtfUS2HhP0RWpZhxxl0lq6H1tz3f4QfdP+JVGc+aNPbfxcc9u2ZULL4SlFKnGyElV/uHV7Ew8tp+zsxBePH7aFUP/wlpNK6uZtWxp0RWpYP3wfIIbtz9xKy8M84Pjx6MK4SjJTv/xQudAOlKoCl+z62jAdENkbhQa6efzP3nUkV8Gbt1yKh2XLp7yBFlUZR0duUJs3mxbnkuy82pOZmehruoccMHx00Z5r8XCMD0yRCwYcLoZjrBjTpKVQ2RmS17Ba9fpLF6Yh5pMilQhJDtTOZGdZvBK50A20qMqRIHsGiIrlN1DbKk9qF4ISilSzSO9qmImkp3W8kORClKo+l5pRObZWc2uIbJC2TXE5sUCFaRINZOcVGWucM8Ac3a9yOuNu51uiqkkO63jlyIVZOi/KKjqADDqdDN8ywtbntgxxOa1If5ksrpfuFVi55YLrYdt2+TfLpKd5vNKgWpksar0qPpYqLOL2ef2sLe6y+mmCIdZOcTm1R5UiIelFKnWkEVV5qjqO0bF0j6qV6/xVZHqFV6ZngD+LFJBelR9K9TZxfiZzYTaIsxasVICrsiZPcTm5d7TBBnqF15RPn8uE/XVTjejKHlleoLXilQjuSuFqg+Fewao6N3O2JoyAncX3yb/4lpmDbH5oUAFKVKFd6ixK043oai5fXqCVwpUyD93pVD1qdp5ZQw2zJciVRTML8VpghSp9vHKMdOuV1uc2wuK7IqhSAUpVP1rdIhYcI7TrRAelVycgjeCMBdSpAovCfcMUDF+jhOVEQI0Od0c4RJeKlCh8NyVQlUIAfi3OAUpUJ0WDQ9Kr6pBoc4uAsdf4vz6PmY1tsjomACKr0gFKVR9SXUfcLoJwiP8XJwmSJHqLB2sR4VDTjfDU0KdXYyGnuW9tjA1a2WdgfDmFCyzslcKVZ8JdXYxHt5K9+oJauplpb+4WjEUpsmkSBVeteA6zeDqNQSlSC16XutFBXOzVwpVnwj3DBDYu4Px8Z1M3llGzd3r5CpcXFOYgrfCLl9SoLqPDP8bJ1tSFTcvFqhgfv5Koeoj8xtLCTeXsei+h5xuinBIsRamyaRIdR8Z/jemNBIGqVGLmhSp75NCVQgPk8L0fVKgCj/R1RVON0E4QArUa0mh6iM6coXYvNlON0NYRIrSzJwqUvsnjR0FKMRM+rftYNbAPk4vu4RMlCgeXlwslWB1/kqhWgAlG1kLi0xfVU9WEh0cmv661wLMak72okqRaoxs/j+zSMcWRsd3MrhhDjWt7bLOoEh4tRcV7MlgKVR9Ys6uFzlfexCodLopwqB0PaUQDy19IerJ8LLa5GSM4dF4Ae9kkTqnQv5thDlCnV0sKDtK36/PYcmaTU43R9jAywUq2NdRIIWqxyVW+59s3knlLdcTaL3N6SaJDLIVpCJ38XCsdGwuqhSpwirVjZWoRjlR0O+8PMyfYOdolhSqHpYoUqOVu6m5dRkL79jgdJMEUpBaJTkYVWnU9ueXAtUcsk1VetWn3+TiqitAndNNERaRAjU/Uqh63PzGUkYWNDC2fLnTTSk6mQpS8G4IuVEiGPn/27u7GLuqMg7jz9uOpZ0WqHxYUGhLAjZAsTQSL0SRGE0DiTTRO9RYgwExJEZuRNJEUC4wQmJijEmTarFBE8JHUDRqbCARlURQakWF2qAtH5VxbFpap7S1y4t9BseZ085MO7PX2ns/v2Qy5+w5M3mzss87/7P2xyLfFf2G1JnhbaomGt6+h4VPPsqLy37JguVvZ/lFLtTSNm0IqJDvmgCDasOlkb25S+gEZ0nrV0JABUOqZs/w9j3M+9Vmdq/8M4PvXc0yQ2rrNP081FE5L1w1qLbB4sHcFbSKt4HKq5SACoZUzb7FgyPsW3EB7zCktooBdeYYVBtszv7XcpfQeIbSchhQ1VVHznSyoS3acpgfygipYFBtrOHte1j47G94auVTnLbgbJYv9tP4ZAylZSopoIIhdbZ5P9XK0JZtDO74ETtW7yK4NHc5OkltCqhQTkgFg+oJy3lBwGiDe/HCHZzueU3HZDAtW6kBFQypml0j33+Eg3Oe4cDqYQbXXuON/RvMgDr7DKonIeeMwLwVBxj8kCF1LINpM5QWUMFZVNVnePseli6Zy/CyQwxeZUhtqrYFVCgzpIJBtZFO3fkM895zOgvOXpq7lOzGh9O2NIy2KTGcjjKkqm6jd2sxpDZPmwMqlNefwaDaOENbtjF4+BVePHeErp5+bzhtjpIboAFVOQz+9gleXbCVI2e43HWTtDGgQrmzqGMZVBtkaMs2Dr/0XYZWjzC4sluHjNraJNqo5HAKnotagi5eUPXmctfnPMapS890ueuGaOv/ntL79FhzchcQEbdExNMR8UZEbJrC678QEbsjYl9EfCciTqmhzOyGtmxj/q7HOXrlQGdOvj+0b/jNL6iaRJsaRdvsPzj8f5/OS2x+Y2dRmx5S7Z3NMRpSD77195x2xQrOu+7TnejhTdbm/z0l9OmxEwaTKWFG9RXgLmANcNxjIRGxBrgN+GDv9x4B7uxtq02uK/7PvwD2ve2sVjc4D+s3S1M+lbd0FrVxvbPLquWuF3HY5a6L1tYZVKj69dGjVasoYbW/qcoeVFNKDwNExBXAeZO8/FPAxpTSc73f+SpwPxmaba5DVm2+MXQ6eqT63rLm0DZNCaej2noualN7p1SiNgdU+F/fjrkDRYTU6fTj7EF1mi4FHh3zfCuwJCLOTClNiOgRcSNwY+/p/ndfc+7zNdQ4FWcB/zyh37wb4J6ZrKUkJz4u7eWY9FfSuCzLXcAU2DvbyzHpz3Hpr6RxmVLvbFpQXQTsHfN89PGpwIRmm1LaAGyooa5piYinU0pX5K6jNI7LRI5Jf47LtNk7W8ox6c9x6a+J4zKrF1NFxBMRkY7x9eQJ/Mn9wNhj7qOPXz/5aiWpDPZOSarM6oxqSunqGf6TzwGrgAd6z1cB/+h36EqSmsreKUmVEm5PNRAR84G5wNyImB8RxwrQ3wNuiIhLImIxsB7YVFOpM6m4Q2qFcFwmckz66/y42DvV45j057j017hxiZRS3gIi7gC+PG7znSmlOyJiKfAn4JKU0s7e628Fvkh1O5aHgM+mlN6osWRJys7eKakLsgdVSZIkqZ/sh/4lSZKkfgyqkiRJKpJBNZPprtPdZhFxRkQ8EhEHIuLvEXF97ppyc/+YKCJOiYiNvX3k9Yh4NiKuyV2X6uV7o2Lf7M/9Y6Km986m3fC/Taa8TncHfAs4BCwBLgd+HBFbR5d77Cj3j4kGgF3AB4CdwLXAAxFxWUrpbzkLU618b1Tsm/25f0zU6N7pxVSZRcRdwHkppXW5a8khIhYCe4CVKaUXets2Ay+nlDq/DnnX94/JRMQfqK50fyh3LapXl98b9s3JdXn/mIom9U4P/Su3dwJHRpttz1aqtcmlY4qIJVT7T9dnkNQ99k2dsKb1ToOqclsE7Bu3bS/VGuRSXxHxFuB+4L6U0l9y1yPVzL6pE9LE3mlQnQWzsE53m41fg5zec9cgV18RMQfYTHV+3i2Zy9EMsndOmX1T09bU3unFVLNgFtbpbrMXgIGIuCiltL23bRUNOSShekVEABupLiC5NqV0OHNJmkH2zimzb2pamtw7nVHNZJrrdLdWSukA8DDwlYhYGBFXAmupPvV1lvvHMX0buBj4SEppJHcxqp/vDfvm8bh/HFNje6dBNZ/1wAhwG/CJ3uP1WSvK53NUtxF5DfgBcLO3WHH/GC8ilgE3Ud2KZ3dE7O99fTxzaaqX742KfbM/949xmt47vT2VJEmSiuSMqiRJkopkUJUkSVKRDKqSJEkqkkFVkiRJRTKoSpIkqUgGVUmSJBXJoCpJkqQiGVQlSZJUJIOqOikifh4RKSI+Nm57RMSm3s/uzlWfJJXGvqkcXJlKnRQRq4DfAc8Dl6WU/tPbfi9wK7AhpXRTxhIlqSj2TeXgjKo6KaW0FdgMXAx8EiAibqdqtg8AN+erTpLKY99UDs6oqrMi4nzgBWA3cC/wTeBnwHUppUM5a5OkEtk3VTdnVNVZKaVdwDeA5VTN9tfAR8c324i4KiJ+GBEv987BWld7sZJUAPum6mZQVdcNjXl8Q0rp331eswj4I/B5YKSWqiSpXPZN1cagqs6KiOuBe6gOYUHVUCdIKf0kpXR7SulB4Ghd9UlSaeybqptBVZ0UEdcCm6g+8b+L6irWz0TEipx1SVKp7JvKwaCqzomI9wEPAi8Ba1JKQ8B6YAD4Ws7aJKlE9k3lYlBVp0TE5cBjwF7gwymlVwF6h6eeBtZGxPszlihJRbFvKieDqjojIi4EfgokqhmBHeNe8qXe96/XWpgkFcq+qdwGchcg1SWl9FfgnOP8/BdA1FeRJJXNvqncDKrSJCJiEXBh7+kcYGnvUNi/Uko781UmSWWyb2qmuDKVNImIuBp4vM+P7ksprau3Gkkqn31TM8WgKkmSpCJ5MZUkSZKKZFCVJElSkQyqkiRJKpJBVZIkSUUyqEqSJKlIBlVJkiQVyaAqSZKkIhlUJUmSVKT/Agw0/Vj2MM7+AAAAAElFTkSuQmCC\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Phi(-1.0, -2) = [0.74081822]\n", + "Phi(-1.0, 1) = [0.30119421]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from __future__ import division, print_function, unicode_literals\n", "\n", @@ -1674,9 +1758,7 @@ { "cell_type": "code", "execution_count": 4, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import numpy\n", @@ -1805,25 +1887,51 @@ }, { "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " pcost dcost gap pres dres\n", + " 0: 1.0780e+02 -7.6366e+02 9e+02 0e+00 4e+01\n", + " 1: 9.3245e+01 9.7637e+00 8e+01 1e-16 3e+00\n", + " 2: 6.7311e+01 3.2553e+01 3e+01 1e-16 1e+00\n", + " 3: 2.6071e+01 1.5068e+01 1e+01 1e-16 7e-01\n", + " 4: 3.7092e+01 2.3152e+01 1e+01 2e-16 4e-01\n", + " 5: 2.5352e+01 1.8652e+01 7e+00 2e-16 3e-16\n", + " 6: 2.0062e+01 1.9974e+01 9e-02 5e-17 1e-16\n", + " 7: 2.0001e+01 2.0000e+01 9e-04 8e-17 4e-16\n", + " 8: 2.0000e+01 2.0000e+01 9e-06 9e-17 2e-16\n", + "Optimal solution found.\n" + ] + }, + { + "data": { + "text/plain": [ + "20.00000617311241" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# Import the necessary packages\n", "import numpy\n", "from cvxopt import matrix\n", "from cvxopt import solvers\n", - "P = matrix(numpy.diag([1,0]), tc=’d’)\n", - "q = matrix(numpy.array([3,4]), tc=’d’)\n", - "G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)\n", - "h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’)\n", + "P = matrix(numpy.diag([1,0]), tc='d')\n", + "q = matrix(numpy.array([3,4]), tc='d')\n", + "G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc='d')\n", + "h = matrix(numpy.array([0,0,-15,100,80]), tc='d')\n", "# Construct the QP, invoke solver\n", "sol = solvers.qp(P,q,G,h)\n", "# Extract optimal value and solution\n", - "sol[’x’] \n", - "sol[’primal objective’]" + "sol['x'] \n", + "sol['primal objective']" ] }, { @@ -1865,7 +1973,25 @@ ] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.0" + } + }, "nbformat": 4, "nbformat_minor": 2 } diff --git a/doc/src/DecisionTrees/DecisionTrees.do.txt b/doc/src/DecisionTrees/DecisionTrees.do.txt index ee7b7686b..2691dbe60 100644 --- a/doc/src/DecisionTrees/DecisionTrees.do.txt +++ b/doc/src/DecisionTrees/DecisionTrees.do.txt @@ -26,7 +26,7 @@ The main idea of decision trees is to find those descriptive features which contain the most _information_ regarding the target feature and then split the dataset along the values of these features such that the target feature values -for the resulting sub\_datasets are as pure as possible. +for the resulting sub datasets are as pure as possible. The descriptive feature which leaves the target feature most purely is said to be the most informative one. This process of finding the _most @@ -65,6 +65,7 @@ Then we are essentially done! + !split ===== Decision trees and Regression ===== !bc pycod @@ -262,6 +263,293 @@ plt.show() !ec +!split +===== Building a tree, regression ===== + +There are mainly two steps +o 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, $R_1,R_2,\dots,R_J$. +o 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 $R_j$. + +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 predic- tive model. The goal is to find boxes $R_1,\dots,R_J$ +that minimize the MSE, given by +!bt +\[ +\sum_{j=1}^J\sum_{i\in R_j}(y_i-\overline{y}_{R_j})^2, +\] +!et +where $\overline{y}_{R_j}$ is the mean response for the training observations +within the $j$th +box. + +!split +===== A top-down approach, recursive binary splitting ===== + +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 + +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. + +!split +===== Making a 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 $R_2$ +!bt +\[ +\left\{X\vert x_j < s\right\}, +\] +!et +and +!bt +\[ +\left\{X\vert x_j \geq s\right\}, +\] +!et +so that we obtain the lowest MSE, that is +!bt +\[ +\sum_{i:x_i\in R_j}(y_i-\overline{y}_{R_1})^2+\sum_{i:x_i\in R_2}(y_i-\overline{y}_{R_2})^2, +\] +!et +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 RSS 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. + +!split +===== Pruning the tree ===== + +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 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 $\alpha$. + +!split +===== Cost complexity pruning ===== +For each value of $\alpha$ there corresponds a subtree $T \in T_0$ such that +!bt +\[ +\sum_{m=1}^{\overline{T}}\sum_{i:x_i\in R_m}(y_i-\overline{y}_{R_m})^2+\alpha\overline{T}, +\] +!et +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 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. + + +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 $\alpha$. + + +!split +===== A schematic procedure ===== + +!bblock Building a Regression Tree +o 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. +o Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of $\alpha$. +o 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 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 $\alpha$. +o Then we average the results for each value of $alpha$, and pick $\alpha$ to minimize the average error. +o Return the subtree from Step 2 that corresponds to the chosen value of $\alpha$. +!eblock + + +!split +===== 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. + +!split +===== Growing a classification tree ===== + +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. +!split +===== 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) +* 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) +!split +===== Disadvantages ===== + +* 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. + +!split +===== 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. + +_Bootstrap aggregation_, or just _bagging_, is a +general-purpose procedure for reducing the variance of a statistical +learning method. + + +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. + + +!split +===== Random forests ===== + +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 +!bt +\[ +m\approx \sqrt{p}. +\] +!et +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. + +!split +===== A simple scikit-learn example ===== +!bc pycod +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'] +!ec