predictorImportance
Estimates of predictor importance for regression tree
Syntax
imp = predictorImportance(tree)
Description
computes estimates of predictor importance for imp
= predictorImportance(tree
)tree
by summing
changes in the mean squared error due to splits on every predictor and dividing the sum
by the number of branch nodes.
Output Arguments

A row vector with the same number of elements as the number of predictors
(columns) in 
Examples
Estimate Predictor Importance
Estimate the predictor importance for all predictor variables in the data.
Load the carsmall
data set.
load carsmall
Grow a regression tree for MPG
using Acceleration
, Cylinders
, Displacement
, Horsepower
, Model_Year
, and Weight
as predictors.
X = [Acceleration Cylinders Displacement Horsepower Model_Year Weight]; tree = fitrtree(X,MPG);
Estimate the predictor importance for all predictor variables.
imp = predictorImportance(tree)
imp = 1×6
0.0647 0.1068 0.1155 0.1411 0.3348 2.6565
Weight
, the last predictor, has the most impact on mileage. The predictor with the minimal impact on making predictions is the first variable, which is Acceleration
.
Predictor Importance and Surrogate Splits
Estimate the predictor importance for all variables in the data and where the regression tree contains surrogate splits.
Load the carsmall
data set.
load carsmall
Grow a regression tree for MPG
using Acceleration
, Cylinders
, Displacement
, Horsepower
, Model_Year
, and Weight
as predictors. Specify to identify surrogate splits.
X = [Acceleration Cylinders Displacement Horsepower Model_Year Weight]; tree = fitrtree(X,MPG,'Surrogate','on');
Estimate the predictor importance for all predictor variables.
imp = predictorImportance(tree)
imp = 1×6
1.0449 2.4560 2.5570 2.5788 2.0832 2.8938
Comparing imp
to the results in Estimate Predictor Importance, Weight
still has the most impact on mileage, but Cylinders
is the fourth most important predictor.
Unbiased Predictor Importance Estimates
Load the carsmall
data set. Consider a model that predicts the mean fuel economy of a car given its acceleration, number of cylinders, engine displacement, horsepower, manufacturer, model year, and weight. Consider Cylinders
, Mfg
, and Model_Year
as categorical variables.
load carsmall Cylinders = categorical(Cylinders); Mfg = categorical(cellstr(Mfg)); Model_Year = categorical(Model_Year); X = table(Acceleration,Cylinders,Displacement,Horsepower,Mfg,... Model_Year,Weight,MPG);
Display the number of categories represented in the categorical variables.
numCylinders = numel(categories(Cylinders))
numCylinders = 3
numMfg = numel(categories(Mfg))
numMfg = 28
numModelYear = numel(categories(Model_Year))
numModelYear = 3
Because there are 3 categories only in Cylinders
and Model_Year
, the standard CART, predictorsplitting algorithm prefers splitting a continuous predictor over these two variables.
Train a regression tree using the entire data set. To grow unbiased trees, specify usage of the curvature test for splitting predictors. Because there are missing values in the data, specify usage of surrogate splits.
Mdl = fitrtree(X,'MPG','PredictorSelection','curvature','Surrogate','on');
Estimate predictor importance values by summing changes in the risk due to splits on every predictor and dividing the sum by the number of branch nodes. Compare the estimates using a bar graph.
imp = predictorImportance(Mdl); figure; bar(imp); title('Predictor Importance Estimates'); ylabel('Estimates'); xlabel('Predictors'); h = gca; h.XTickLabel = Mdl.PredictorNames; h.XTickLabelRotation = 45; h.TickLabelInterpreter = 'none';
In this case, Displacement
is the most important predictor, followed by Horsepower
.
More About
Predictor Importance
predictorImportance
computes importance measures of the predictors in a tree by
summing changes in the node risk due to splits on every predictor, and then dividing the sum
by the total number of branch nodes. The change in the node risk is the difference between
the risk for the parent node and the total risk for the two children. For example, if a tree
splits a parent node (for example, node 1) into two child nodes (for example, nodes 2 and
3), then predictorImportance
increases the importance of the split predictor by
(R_{1} – R_{2} – R_{3})/N_{branch},
where R_{i} is node risk of node i, and N_{branch} is the total number of branch nodes. A node risk is defined as a node error weighted by the node probability:
R_{i} = P_{i}E_{i},
where P_{i} is the node probability of node i, and E_{i} is the mean squared error of node i.
The estimates of predictor importance depend on whether you use surrogate splits for training.
If you use surrogate splits,
predictorImportance
sums the changes in the node risk over all splits at each branch node, including surrogate splits. If you do not use surrogate splits, then the function takes the sum over the best splits found at each branch node.Estimates of predictor importance do not depend on the order of predictors if you use surrogate splits, but do depend on the order if you do not use surrogate splits.
If you use surrogate splits,
predictorImportance
computes estimates before the tree is reduced by pruning (or merging leaves). If you do not use surrogate splits,predictorImportance
computes estimates after the tree is reduced by pruning. Therefore, pruning affects the predictor importance for a tree grown without surrogate splits, and does not affect the predictor importance for a tree grown with surrogate splits.
Extended Capabilities
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
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