RegressionBaggedEnsemble

Regression ensemble grown by resampling

Description

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.

Creation

Description

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).

For a description of bagged classification ensembles, see Bootstrap Aggregation (Bagging) and Random Forest.

Properties

BinEdges — Bin edges for numeric predictors

cell array of p numeric vectors

This property is read-only.

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';
end
for j = idxNumeric 
    x = X(:,j);
    % Convert x to array if x is a table.
    if istable(x) 
        x = table2array(x);
    end
    % Group x into bins by using the discretize function.
    xbinned = discretize(x,[-inf; edges{j}; inf]); 
    Xbinned(:,j) = xbinned;
end

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.

CategoricalPredictors — Indices of categorical predictors

vector of positive integers | []

This property is read-only.

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 ([]).

Data Types: single | double

CombineWeights — How the ensemble combines weak learner weights

'WeightedAverage' | 'WeightedSum'

This property is read-only.

How the ensemble combines weak learner weights, returned as either 'WeightedAverage' or 'WeightedSum'.

Data Types: char

ExpandedPredictorNames — Expanded predictor names

cell array of character vectors

This property is read-only.

Expanded predictor names, returned 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.

Data Types: cell

FitInfo — Fit information

numeric array

Fit information, returned as a numeric array. The FitInfoDescription property describes the content of this array.

Data Types: double

FitInfoDescription — Description of information in FitInfo

character vector | cell array of character vectors

Description of the information in FitInfo, returned as a character vector or cell array of character vectors.

Data Types: char | cell

FResample — Fraction of training data resampled during object construction

numeric scalar between 0 and 1

Fraction of training data resampled during object construction, returned as a numeric scalar between 0 and 1. fitrensemble resamples the training data at random for every weak learner when constructing the ensemble.

Data Types: double

HyperparameterOptimizationResults — Description of cross-validation optimization of hyperparameters

BayesianOptimization object | table of hyperparameters and associated values

This property is read-only.

Description of the cross-validation optimization of hyperparameters, returned 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)

LearnerNames — Names of weak learners in ensemble

cell array of character vectors

This property is read-only.

Names of weak learners in ensemble, returned as a cell array of character vectors. The name of each learner appears just once. For example, if you have an ensemble of 100 trees, LearnerNames is {'Tree'}.

Data Types: cell

Method — Method that creates ensemble

character vector

Method that fitrensemble uses to create the ensemble, returned as a character vector.

Data Types: char

ModelParameters — Parameters used in training ensemble

EnsembleParams object

Parameters used in training the ensemble, returned as an EnsembleParams object. The properties of ModelParameters include the type of ensemble, either 'classification' or 'regression', the Method used to create the ensemble, and other parameters, depending on the ensemble.

NumObservations — Number of observations in the training data

positive integer

This property is read-only.

Number of observations in the training data, returned as a positive integer. NumObservations can be less than the number of rows of input data when there are missing values in the input data or response data.

Data Types: double

NumTrained — Number of trained weak learners

positive integer

This property is read-only.

Number of trained weak learners in the ensemble, returned as a positive integer.

Data Types: double

PredictorNames — Predictor names

cell array of character vectors

This property is read-only.

Predictor names, specified as a cell array of character vectors. The order of the entries in PredictorNames is the same as in the training data.

Data Types: cell

ReasonForTermination — Reason that fitrensemble stopped adding weak learners to the ensemble

character vector

This property is read-only.

Reason that fitrensemble stopped adding weak learners to the ensemble, returned as a character vector.

Data Types: char

Regularization — Result of using regularize on ensemble

structure

Result of using the regularize method on the ensemble, returned as a structure. Use Regularization with shrink to lower resubstitution error and shrink the ensemble.

Data Types: struct

Replace — Indication that ensemble was trained with replacement

true | false

Indication that the ensemble was trained with replacement, returned as true or false.

Data Types: logical

ResponseName — Name of the response variable

character vector

This property is read-only.

Name of the response variable, returned as a character vector.

Data Types: char

ResponseTransform — Function for transforming raw response values

"none" (default) | function handle | function name

Function for transforming raw response values, specified as a function handle or function name. The default is "none", which means @(y)y, or no transformation. The function should accept a vector (the original response values) and return a vector of the same size (the transformed response values).

Example: Suppose you create a function handle that applies an exponential transformation to an input vector by using myfunction = @(y)exp(y). Then, you can specify the response transformation as ResponseTransform=myfunction.

Data Types: char | string | function_handle

Trained — Trained regression models

cell vector

Trained regression models, returned as a cell vector. The entries of the cell vector contain the corresponding compact regression models.

If Method is 'LogitBoost' or 'GentleBoost', then the ensemble stores trained learner j in the CompactRegressionLearner property of the object stored in Trained{j}. That is, to access trained learner j, use ens.Trained{j}.CompactRegressionLearner.

Data Types: cell

TrainedWeights — Trained weak learner weights

numeric vector

This property is read-only.

Trained weights for the weak learners in the ensemble, returned as a numeric vector. TrainedWeights has T elements, where T is the number of weak learners in learners. The ensemble computes predicted response by aggregating weighted predictions from its learners.

Data Types: double

UseObsForLearner — Indicator that observation was used to train learner

N-by-NumTrained real matrix

Indicator that observation was used to train learner, returned as a logical matrix of size N-by-NumTrained, where N is the number of rows of training data 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.

Data Types: logical

W — Scaled weights in tree

numeric vector

This property is read-only.

Scaled weights in tree, returned as a numeric vector. W has length n, the number of rows in the training data.

Data Types: double

X — Predictor values

real matrix | table

This property is read-only.

Predictor values, returned as a real matrix or table. Each column of X represents one variable (predictor), and each row represents one observation.

Data Types: double | table

Y — Class labels

categorical array | cell array of character vectors | character array | logical vector | numeric vector

This property is read-only.

Class labels corresponding to the observations in X, returned as a categorical array, cell array of character vectors, character array, logical vector, or a numeric vector. Each row of Y represents the classification of the corresponding row of X.

Data Types: single | double | logical | char | string | cell | categorical

Object Functions

compact	Reduce size of regression ensemble model
crossval	Cross-validate machine learning model
cvshrink	Cross-validate pruning and regularization of regression ensemble
gather	Gather properties of Statistics and Machine Learning Toolbox object from GPU
lime	Local interpretable model-agnostic explanations (LIME)
loss	Regression error for regression ensemble model
oobLoss	Out-of-bag error for bagged regression ensemble model
oobPermutedPredictorImportance	Out-of-bag predictor importance estimates for random forest of regression trees by permutation
oobPredict	Predict out-of-bag responses of bagged regression ensemble
partialDependence	Compute partial dependence
plotPartialDependence	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
predict	Predict responses using regression ensemble model
predictorImportance	Estimates of predictor importance for regression ensemble of decision trees
regularize	Find optimal weights for learners in regression ensemble
resubLoss	Resubstitution loss for regression ensemble model
resubPredict	Predict response of regression ensemble by resubstitution
resume	Resume training of regression ensemble model
shapley	Shapley values
shrink	Prune regression ensemble

Examples

Train Bagged Ensemble of Regression Trees

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 = 
  RegressionBaggedEnsemble
             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.

view(Mdl.Trained{1},'Mode','graph')

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

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

L = resubLoss(Mdl)

L = 
12.4048

Tips

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

view(ens.Trained{t})

Alternative Functionality

Bootstrap Aggregation Methods

For classification or regression, you can choose two approaches for bagging:

• Classification: create a bagged ensemble using fitcensemble or TreeBagger.

• Regression: create a bagged ensemble using fitrensemble or TreeBagger.

For help choosing between these approaches, see Ensemble Algorithms and Suggestions for Choosing an Appropriate Ensemble Algorithm.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The predict function supports code generation.

• To integrate the prediction of an ensemble into Simulink^®, you can use the RegressionEnsemble Predict block in the Statistics and Machine Learning Toolbox™ library or a MATLAB^® Function block with the predict function.

• When you train an ensemble by using fitrensemble, the following restrictions apply.

  • The value of the ResponseTransform name-value argument cannot be an anonymous function.

  • Code generation limitations for regression trees also apply to ensembles of regression trees. You cannot use surrogate splits; that is, the value of the Surrogate name-value argument must be 'off'.

• For fixed-point code generation, the following additional restrictions apply.

  • When you train an ensemble by using fitrensemble, the value of the ResponseTransform name-value argument must be 'none' (default).

  • Categorical predictors (logical, categorical, char, string, or cell) are not supported. You cannot use the CategoricalPredictors name-value argument. To include categorical predictors in a model, preprocess them by using dummyvar before fitting the model.

For more information, see Introduction to Code Generation.

Version History

Introduced in R2011a