Contents

# Details

Given
n
feature vectors
X
= {
x
1
= (
x
11
,…,
x
1
p
), ...,
x
n
= (
x
n
1
,…,
x
np
) } of
n
p
-dimensional feature vectors, a vector of class labels
y
= (
y
1
, … ,
y
n
), where
y
i
{0, 1, ... ,
C
- 1} describes the class to which the feature vector
x
i
belongs 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, that are calculated as follows:
where
is the fraction of observations in the subset
D
that belong to the
i
-th class.

## Prediction Stage

Given decision forest classifier and vectors
x
1
, ... ,
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.

## Out-of-bag Error

Decision forest classifier follows the algorithmic framework for calculating the decision forest out-of-bag (OOB) error, where aggregation of the out-of-bag 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
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:
• If OOB error value per each observation is required, then calculate the prediction error for
x
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.

## Training Alternative

If you already have a set of precomputed values for nodes in each tree, you can use the Model Builder class to get a trained Intel DAAL Decision Forest Classification model based on the external model you have.
The following schema illustrates the use of the Model Builder class for Decision Forest Classification:
For general information on using the Model Builder class, see Training and Prediction. For details on using the Model Builder class for Decision Forest Classification, see Usage of training alternative.

#### Product and Performance Information

1

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Notice revision #20110804