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Package: classreg.learning.regr
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.


Create a bagged regression ensemble object using fitrensemble. Set the name-value pair argument 'Method' of fitrensemble to 'Bag' to use bootstrap aggregation (bagging, for example, random forest).



Bin edges for numeric predictors, specified as a cell array of p numeric vectors, where p is the number of predictors. Each vector includes the bin edges for a numeric predictor. The element in the cell array for a categorical predictor is empty because the software does not bin categorical predictors.

The software bins numeric predictors only if you specify the 'NumBins' name-value argument as a positive integer scalar when training a model with tree learners. The BinEdges property is empty if the 'NumBins' value is empty (default).

You can reproduce the binned predictor data Xbinned by using the BinEdges property of the trained model mdl.

X = mdl.X; % Predictor data
Xbinned = zeros(size(X));
edges = mdl.BinEdges;
% Find indices of binned predictors.
idxNumeric = find(~cellfun(@isempty,edges));
if iscolumn(idxNumeric)
    idxNumeric = idxNumeric';
for j = idxNumeric 
    x = X(:,j);
    % Convert x to array if x is a table.
    if istable(x) 
        x = table2array(x);
    % Group x into bins by using the discretize function.
    xbinned = discretize(x,[-inf; edges{j}; inf]); 
    Xbinned(:,j) = xbinned;
Xbinned contains the bin indices, ranging from 1 to the number of bins, for numeric predictors. Xbinned values are 0 for categorical predictors. If X contains NaNs, then the corresponding Xbinned values are NaNs.


Categorical predictor indices, specified as a vector of positive integers. CategoricalPredictors contains index values indicating that the corresponding predictors are categorical. The index values are between 1 and p, where p is the number of predictors used to train the model. If none of the predictors are categorical, then this property is empty ([]).


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 fitrensemble 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 fitrensemble 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 fitrensemble 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 or table 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.

Object Functions

compactReduce size of regression ensemble model
crossvalCross-validate regression ensemble model
cvshrinkCross-validate shrinking (pruning) ensemble
gatherGather properties of Statistics and Machine Learning Toolbox object from GPU
limeLocal interpretable model-agnostic explanations (LIME)
lossRegression error for regression ensemble model
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
partialDependenceCompute partial dependence
plotPartialDependenceCreate partial dependence plot (PDP) and individual conditional expectation (ICE) plots
predictPredict responses using ensemble of regression models
predictorImportanceEstimates of predictor importance for regression ensemble of decision trees
regularizeFind optimal weights for learners in regression ensemble model
removeLearnersRemove members of compact regression ensemble
resubLossResubstitution loss for regression ensemble model
resubPredictPredict response of regression ensemble by resubstitution
resumeResume training of regression ensemble model
shapleyShapley values
shrinkPrune regression ensemble

Copy Semantics

Value. To learn how value classes affect copy operations, see Copying Objects.


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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.

Mdl = fitrensemble(X,Y,'Method','bag')
Mdl = 
             ResponseName: 'Y'
    CategoricalPredictors: []
        ResponseTransform: 'none'
          NumObservations: 94
               NumTrained: 100
                   Method: 'Bag'
             LearnerNames: {'Tree'}
     ReasonForTermination: 'Terminated normally after completing the requested number of training cycles.'
                  FitInfo: []
       FitInfoDescription: 'None'
           Regularization: []
                FResample: 1
                  Replace: 1
         UseObsForLearner: [94x100 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.


Figure Regression tree viewer contains an axes object and other objects of type uimenu, uicontrol. The axes object contains 24 objects of type line, text. One or more of the lines displays its values using only markers

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

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

L = resubLoss(Mdl)
L = 12.4048


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


Extended Capabilities

Version History

Introduced in R2011a