# predictorImportance

Estimates of predictor importance for classification ensemble of decision trees

## Syntax

imp = predictorImportance(ens)
[imp,ma] = predictorImportance(ens)

## Description

imp = predictorImportance(ens) computes estimates of predictor importance for ens by summing these estimates over all weak learners in the ensemble. imp has one element for each input predictor in the data used to train this ensemble. A high value indicates that this predictor is important for ens.

[imp,ma] = predictorImportance(ens) returns a P-by-P matrix with predictive measures of association for P predictors, when the learners in ens contain surrogate splits. See More About.

## Input Arguments

 ens A classification ensemble of decision trees, created by fitcensemble, or by the compact method.

## Output Arguments

 imp A row vector with the same number of elements as the number of predictors (columns) in ens.X. The entries are the estimates of predictor importance, with 0 representing the smallest possible importance. ma A P-by-P matrix of predictive measures of association for P predictors. Element ma(I,J) is the predictive measure of association averaged over surrogate splits on predictor J for which predictor I is the optimal split predictor. predictorImportance averages this predictive measure of association over all trees in the ensemble.

## Examples

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Estimate the predictor importance for all variables in the Fisher iris data.

Train a classification ensemble using AdaBoostM2. Specify tree stumps as the weak learners.

t = templateTree('MaxNumSplits',1);

Estimate the predictor importance for all predictor variables.

imp = predictorImportance(ens)
imp = 1×4

0.0004    0.0016    0.1266    0.0324

The first two predictors are not very important in the ensemble.

Estimate the predictor importance for all variables in the Fisher iris data for an ensemble where the trees contain surrogate splits.

Grow an ensemble of 100 classification trees using AdaBoostM2. Specify tree stumps as the weak learners, and also identify surrogate splits.

t = templateTree('MaxNumSplits',1,'Surrogate','on');

Estimate the predictor importance and predictive measures of association for all predictor variables.

[imp,ma] = predictorImportance(ens)
imp = 1×4

0.0674    0.0417    0.1582    0.1537

ma = 4×4

1.0000         0         0         0
0.0115    1.0000    0.0022    0.0054
0.3186    0.2137    1.0000    0.6391
0.0392    0.0073    0.1137    1.0000

The first two predictors show much more importance than the analysis in Estimate Predictor Importance.

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## Algorithms

Element ma(i,j) is the predictive measure of association averaged over surrogate splits on predictor j for which predictor i is the optimal split predictor. This average is computed by summing positive values of the predictive measure of association over optimal splits on predictor i and surrogate splits on predictor j and dividing by the total number of optimal splits on predictor i, including splits for which the predictive measure of association between predictors i and j is negative.