Main Content

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


expand all

Create Regression Ensemble

fitrensembleFit ensemble of learners for regression
compactCreate compact regression ensemble
fitensembleFit ensemble of learners for classification and regression

Modify Regression Ensemble

regularizeFind weights to minimize resubstitution error plus penalty term
removeLearnersRemove members of compact regression ensemble
resumeResume training ensemble
shrinkPrune ensemble

Cross-Validate Regression Ensemble

cvshrinkCross-validate shrinking (pruning) 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
resubLossRegression error by resubstitution

Classify Observations

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

Gather Properties of Regression Ensemble

gatherGather properties of Statistics and Machine Learning Toolbox object from GPU
TreeBaggerCreate bag of decision trees
fitrensembleFit ensemble of learners for regression
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 ensemble
limeLocal interpretable model-agnostic explanations (LIME)
partialDependenceCompute partial dependence
plotPartialDependenceCreate partial dependence plot (PDP) and individual conditional expectation (ICE) plots
predictorImportanceEstimates of predictor importance for regression ensemble
shapleyShapley values


expand all

RegressionEnsembleEnsemble regression
CompactRegressionEnsembleCompact regression ensemble class
RegressionPartitionedEnsembleCross-validated regression ensemble
TreeBaggerBag of decision trees
CompactTreeBaggerCompact ensemble of decision trees grown by bootstrap aggregation
RegressionBaggedEnsembleRegression ensemble grown by resampling