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Regression Tree Ensembles

Random forests, boosted and bagged regression trees

A regression tree ensemble is a predictive model composed of a weighted combination of multiple regression trees. In general, combining multiple regression trees increases predictive performance. To boost regression trees using LSBoost, use fitrensemble. To bag regression trees or to grow a random forest [12], use fitrensemble or TreeBagger. To implement quantile regression using a bag of regression trees, use TreeBagger.

For classification ensembles, such as boosted or bagged classification trees, random subspace ensembles, or error-correcting output codes (ECOC) models for multiclass classification, see Classification Ensembles.


Regression LearnerTrain regression models to predict data using supervised machine learning


RegressionEnsemble PredictPredict responses using ensemble of decision trees for regression (Since R2021a)


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Create Regression Ensemble

fitrensembleFit ensemble of learners for regression
compactReduce size of regression ensemble model
fitensembleFit ensemble of learners for classification and regression

Modify Regression Ensemble

regularizeFind optimal weights for learners in regression ensemble
removeLearnersRemove members of compact regression ensemble
resumeResume training of regression ensemble model
shrinkPrune regression ensemble

Cross-Validate Regression Ensemble

cvshrinkCross-validate pruning and regularization of regression ensemble
kfoldLossLoss for cross-validated partitioned regression model
kfoldPredictPredict responses for observations in cross-validated regression model
kfoldfunCross-validate function for regression

Measure Performance

lossRegression error for regression ensemble model
resubLossResubstitution loss for regression ensemble model

Classify Observations

predictPredict responses using regression ensemble model
resubPredictPredict response of regression ensemble by resubstitution

Gather Properties of Regression Ensemble

gatherGather properties of Statistics and Machine Learning Toolbox object from GPU (Since R2020b)
fitrensembleFit ensemble of learners for regression
TreeBaggerEnsemble of bagged decision trees
predictPredict responses using ensemble of bagged decision trees
oobPredictEnsemble predictions for out-of-bag observations
quantilePredictPredict response quantile using bag of regression trees
oobQuantilePredictQuantile predictions for out-of-bag observations from bag of regression trees
crossvalCross-validate machine learning model
limeLocal interpretable model-agnostic explanations (LIME) (Since R2020b)
partialDependenceCompute partial dependence (Since R2020b)
permutationImportancePredictor importance by permutation (Since R2024a)
plotPartialDependenceCreate partial dependence plot (PDP) and individual conditional expectation (ICE) plots
predictorImportanceEstimates of predictor importance for regression ensemble of decision trees
shapleyShapley values (Since R2021a)


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RegressionEnsembleEnsemble regression
CompactRegressionEnsembleCompact regression ensemble
RegressionPartitionedEnsembleCross-validated regression ensemble
TreeBaggerEnsemble of bagged decision trees
CompactTreeBaggerCompact ensemble of bagged decision trees
RegressionBaggedEnsembleRegression ensemble grown by resampling