Classification Decision Forest¶
Decision forest classifier is a special case of the Decision Forest model.
Details¶
Given:
\(n\) feature vectors \(X = \{x_1 = (x_{11}, \ldots, x_{1p}), \ldots, x_n = (x_{n1}, \ldots, x_{np}) \}\) of size \(p\);
their nonnegative sample weights \(w = (w_1, \ldots, w_n)\);
the vector of class labels \(y = (y_1, \ldots, y_n)\) that describes the class to which the feature vector \(x_i\) belongs, where \(y_i \in \{0, 1, \ldots, C1\}\) and \(C\) is the number of classes.
The problem is to build a decision forest classifier.
Training Stage¶
Decision forest classifier follows the algorithmic framework of decision forest training with Gini impurity metrics as impurity metrics [Breiman84]. If sample weights are provided as input, the library uses a weighted version of the algorithm.
Gini index is an impurity metric, calculated as follows:
where
\(D\) is a set of observations that reach the node;
\(p_i\) is specified in the table below:
Without sample weights 
With sample weights 

\(p_i\) is the observed fraction of observations that belong to class \(i\) in \(D\) 
\(p_i\) is the observed weighted fraction of observations that belong to class \(i\) in \(D\):
\[p_i = \frac{\sum_{d \in \{d \in D  y_d = i \}} W_d}{\sum_{d \in D} W_d}\]

Prediction Stage¶
Given decision forest classifier and vectors \(x_1, \ldots, x_r\), the problem is to calculate the labels for those vectors. To solve the problem for each given query vector \(x_i\), the algorithm finds the leaf node in a tree in the forest that gives the classification response by that tree. The forest chooses the label y taking the majority of trees in the forest voting for that label.
Outofbag Error¶
Decision forest classifier follows the algorithmic framework for calculating the decision forest outofbag (OOB) error, where aggregation of the outofbag predictions in all trees and calculation of the OOB error of the decision forest is done as follows:
For each vector \(x_i\) in the dataset \(X\), predict its label \(\hat{y_i}\) by having the majority of votes from the trees that contain \(x_i\) in their OOB set, and vote for that label.
Calculate the OOB error of the decision forest \(T\) as the average of misclassifications:
\[OOB(T) = \frac{1}{{D}^{\text{'}}}\sum _{y_i \in {D}^{\text{'}}}I\{y_i \ne \hat{y_i}\}\text{,where }{D}^{\text{'}}={\bigcup }_{b=1}^{B}\overline{D_b}.\]If OOB error value per each observation is required, then calculate the prediction error for \(x_i\): \(OOB(x_i) = I\{{y}_{i}\ne \hat{{y}_{i}}\}\)
Variable Importance¶
The library computes Mean Decrease Impurity (MDI) importance measure, also known as the Gini importance or Mean Decrease Gini, by using the Gini index as impurity metrics.
Usage of Training Alternative¶
To build a Decision Forest Classification model using methods of the Model Builder class of Decision Forest Classification, complete the following steps:
Create a Decision Forest Classification model builder using a constructor with the required number of classes and trees.
Create a decision tree and add nodes to it:
Use the
createTree
method with the required number of nodes in a tree and a label of the class for which the tree is created.Use the
addSplitNode
andaddLeafNode
methods to add split and leaf nodes to the created tree. See the note below describing the decision tree structure.After you add all nodes to the current tree, proceed to creating the next one in the same way.
Use the
getModel
method to get the trained Decision Forest Classification model after all trees have been created.
Note
Each tree consists of internal nodes (called nonleaf or split nodes) and external nodes (leaf nodes).
Each split node denotes a feature test that is a Boolean expression, for example,
f < featureValue
or f = featureValue
, where f is a feature and featureValue
is a constant.
The test type depends on the feature type: continuous, categorical, or ordinal.
For more information on the test types, see Decision Tree.
The inducted decision tree is a binary tree, meaning that each nonleaf node has exactly two branches: true and false.
Each split node contains featureIndex
, the index of the feature used for the feature test in this node, and featureValue
,
the constant for the Boolean expression in the test. Each leaf node contains a classLabel
, the predicted class for this leaf.
For more information on decision trees, see Decision Tree.
Add nodes to the created tree in accordance with the precalculated structure of the tree. Check that the leaf nodes do not have children nodes and that the splits have exactly two children.
Examples¶
Batch Processing¶
Decision forest classification follows the general workflow described in Decision Forest and Classification Usage Model.
Training¶
In addition to the parameters of a classifier (see Classification Usage Model) and decision forest parameters described in Batch Processing, the training algorithm for decision forest classification has the following parameters:
Parameter 
Default Value 
Description 



The floatingpoint type that the algorithm uses for intermediate computations. Can be 


The computation method used by the decision forest classification. For CPU:
For GPU: 

Not applicable 
The number of classes. A required parameter. 
Output¶
Decision forest classification calculates the result of regression and decision forest. For more details, refer to Batch Processing and Classification Usage Model.
Prediction¶
For the description of the input and output, refer to Classification Usage Model.
In addition to the parameters of a classifier, decision forest classification has the following parameters at the prediction stage:
Parameter 
Default Value 
Description 



The floatingpoint type that the algorithm uses for intermediate computations. Can be 


The computation method used by the decision forest classification. The only prediction method supported so far is the default dense method. 

Not applicable 
The number of classes. A required parameter. 


A flag that specifies which method is used to compute probabilities and class labels:

Examples¶
Batch Processing:
Batch Processing:
Batch Processing:
Note
There is no support for Java on GPU.
Batch Processing: