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RegressionBaggedEnsemble class

Superclasses: RegressionEnsemble

Regression ensemble grown by resampling


RegressionBaggedEnsemble combines a set of trained weak learner models and data on which these learners were trained. It can predict ensemble response for new data by aggregating predictions from its weak learners.


ens = fitensemble(tbl,ResponseVarName,'bag',nlearn,learners,'type','regression') creates a bagged regression ensemble. For more information on the syntax, see the fitensemble function reference page.

ens = fitensemble(tbl,formula,'bag',nlearn,learners,'type','regression') creates a bagged regression ensemble. For more information on the syntax, see the fitensemble function reference page.

ens = fitensemble(tbl,Y,'bag',nlearn,learners,'type','regression') creates a bagged regression ensemble. For more information on the syntax, see the fitensemble function reference page.

ens = fitensemble(X,Y,'bag',nlearn,learners,'type','regression') creates a bagged regression ensemble. For more information on the syntax, see the fitensemble function reference page.



List of categorical predictors. CategoricalPredictors is a numeric vector with indices from 1 to p, where p is the number of columns of X.


A character vector describing how the ensemble combines learner predictions.


Expanded predictor names, stored as a cell array of character vectors.

If the model uses encoding for categorical variables, then ExpandedPredictorNames includes the names that describe the expanded variables. Otherwise, ExpandedPredictorNames is the same as PredictorNames.


A numeric array of fit information. The FitInfoDescription property describes the content of this array.


Character vector describing the meaning of the FitInfo array.


A numeric scalar between 0 and 1. FResample is the fraction of training data fitensemble resampled at random for every weak learner when constructing the ensemble.


Description of the cross-validation optimization of hyperparameters, stored as a BayesianOptimization object or a table of hyperparameters and associated values. Nonempty when the OptimizeHyperparameters name-value pair is nonempty at creation. Value depends on the setting of the HyperparameterOptimizationOptions name-value pair at creation:

  • 'bayesopt' (default) — Object of class BayesianOptimization

  • 'gridsearch' or 'randomsearch' — Table of hyperparameters used, observed objective function values (cross-validation loss), and rank of observations from lowest (best) to highest (worst)


Cell array of character vectors with names of the weak learners in the ensemble. The name of each learner appears just once. For example, if you have an ensemble of 100 trees, LearnerNames is {'Tree'}.


A character vector with the name of the algorithm fitensemble used for training the ensemble.


Parameters used in training ens.


Numeric scalar containing the number of observations in the training data.


Number of trained learners in the ensemble, a positive scalar.


A cell array of names for the predictor variables, in the order in which they appear in X.


A character vector describing the reason fitensemble stopped adding weak learners to the ensemble.


A structure containing the result of the regularize method. Use Regularization with shrink to lower resubstitution error and shrink the ensemble.


Boolean flag indicating if training data for weak learners in this ensemble were sampled with replacement. Replace is true for sampling with replacement, false otherwise.


A character vector with the name of the response variable Y.


Function handle for transforming scores, or character vector representing a built-in transformation function. 'none' means no transformation; equivalently, 'none' means @(x)x.

Add or change a ResponseTransform function using dot notation:

ens.ResponseTransform = @function


The trained learners, a cell array of compact regression models.


A numeric vector of weights the ensemble assigns to its learners. The ensemble computes predicted response by aggregating weighted predictions from its learners.


A logical matrix of size N-by-NumTrained, where N is the number of rows (observations) in the training data X, and NumTrained is the number of trained weak learners. UseObsForLearner(I,J) is true if observation I was used for training learner J, and is false otherwise.


The scaled weights, a vector with length n, the number of rows in X. The sum of the elements of W is 1.


The matrix of predictor values that trained the ensemble. Each column of X represents one variable, and each row represents one observation.


The numeric column vector with the same number of rows as X that trained the ensemble. Each entry in Y is the response to the data in the corresponding row of X.


oobLossOut-of-bag regression error
oobPermutedPredictorImportancePredictor importance estimates by permutation of out-of-bag predictor observations for random forest of regression trees
oobPredictPredict out-of-bag response of ensemble

Inherited Methods

compactCreate compact regression ensemble
crossvalCross validate ensemble
cvshrinkCross validate shrinking (pruning) ensemble
regularizeFind weights to minimize resubstitution error plus penalty term
resubLossRegression error by resubstitution
resubPredictPredict response of ensemble by resubstitution
resumeResume training ensemble
shrinkPrune ensemble
lossRegression error
predictPredict responses using ensemble of regression models
predictorImportanceEstimates of predictor importance
removeLearnersRemove members of compact regression ensemble

Copy Semantics

Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB® documentation.


expand all

Load the carsmall data set. Consider a model that explains a car's fuel economy (MPG) using its weight (Weight) and number of cylinders (Cylinders).

load carsmall
X = [Weight Cylinders];
Y = MPG;

Train a bagged ensemble of 100 regression trees using all measurements.

rng(1) % For reproducibility
Mdl = fitensemble(X,Y,'bag',100,'Tree','Type','regression')
Mdl = 

             ResponseName: 'Y'
    CategoricalPredictors: []
        ResponseTransform: 'none'
          NumObservations: 94
               NumTrained: 100
                   Method: 'Bag'
             LearnerNames: {'Tree'}
     ReasonForTermination: 'Terminated normally after completing the reque...'
                  FitInfo: []
       FitInfoDescription: 'None'
           Regularization: []
                FResample: 1
                  Replace: 1
         UseObsForLearner: [94×100 logical]

Mdl is a RegressionBaggedEnsemble model object.

Mdl.Trained is the property that stores a 100-by-1 cell vector of the trained, compact regression trees (CompactRegressionTree model objects) that compose the ensemble.

Plot a graph of the first trained regression tree.


By default, fitensemble grows deep trees for bags of trees.

Estimate the in-sample mean-squared error (MSE).

L = resubLoss(Mdl)
L =



For a bagged ensemble of regression trees, the Trained property of ens stores a cell vector of ens.NumTrained CompactRegressionTree model objects. For a textual or graphical display of tree t in the cell vector, enter


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