# predictorImportance

Estimates of predictor importance for regression ensemble

## 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.

## Input Arguments

 ens A regression ensemble, created by fitrensemble, 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 predictor variables in the data.

Grow an ensemble of 100 regression trees for MPG using Acceleration, Cylinders, Displacement, Horsepower, Model_Year, and Weight as predictors. Specify tree stumps as the weak learners.

X = [Acceleration Cylinders Displacement Horsepower Model_Year Weight];
t = templateTree('MaxNumSplits',1);
ens = fitrensemble(X,MPG,'Method','LSBoost','Learners',t);

Estimate the predictor importance for all predictor variables.

imp = predictorImportance(ens)
imp = 1×6

0.0150         0    0.0066    0.1111    0.0437    0.5181

Weight, the last predictor, has the most impact on mileage. The second predictor has importance 0, which means that the number of cylinders has no impact on predictions made with ens.

Estimate the predictor importance for all variables in the data and where the regression tree ensemble contains surrogate splits.

Grow an ensemble of 100 regression trees for MPG using Acceleration, Cylinders, Displacement, Horsepower, Model_Year, and Weight as predictors. Specify tree stumps as the weak learners, and also identify surrogate splits.

X = [Acceleration Cylinders Displacement Horsepower Model_Year Weight];
t = templateTree('MaxNumSplits',1,'Surrogate','on');
ens = fitrensemble(X,MPG,'Method','LSBoost','Learners',t);

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

[imp,ma] = predictorImportance(ens)
imp = 1×6

0.2141    0.3798    0.4369    0.6498    0.3728    0.5700

ma = 6×6

1.0000    0.0098    0.0102    0.0098    0.0033    0.0067
0    1.0000         0         0         0         0
0.0056    0.0084    1.0000    0.0078    0.0022    0.0084
0.3537    0.4769    0.5834    1.0000    0.1612    0.5827
0.0061    0.0070    0.0063    0.0064    1.0000    0.0056
0.0154    0.0296    0.0533    0.0447    0.0070    1.0000

Comparing imp to the results in Estimate Predictor Importance, Horsepower has the greatest impact on mileage, with Weight having the second greatest impact.

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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.