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# predictorImportance

Estimates of predictor importance

## 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 Definitions.

## Input Arguments

 `ens` A classification ensemble 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.

```load fisheriris ```

Grow an ensemble of 100 classification trees using AdaBoostM2.

```ens = fitensemble(meas,species,'AdaBoostM2',100,'Tree'); ```

Estimate the predictor importance for all predictor variables.

```imp = predictorImportance(ens) ```
```imp = 0.0004 0.0016 0.1187 0.0403 ```

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.

```load fisheriris ```

Grow an ensemble of 100 classification trees using AdaBoostM2. Specify to identify surrogate splits.

```t = templateTree('Surrogate','on'); ens = fitensemble(meas,species,'AdaBoostM2',100,t); ```

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

```[imp,ma] = predictorImportance(ens) ```
```imp = 0.0674 0.0417 0.1582 0.1537 ma = 1.0000 0 0 0 0.0115 1.0000 0.0022 0.0054 0.2963 0.1893 1.0000 0.5695 0.0615 0.0317 0.1833 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.