RegressionEnsemble

Ensemble regression

Description

RegressionEnsemble 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

Create a regression ensemble object using fitrensemble.

Properties

Ensemble Properties

CombineWeights — Method used to combine weak learner weights

Read-only: 'WeightedAverage' | 'WeightedSum'

This property is read-only.

Method used to combine weak learner weights, returned as either 'WeightedAverage' or 'WeightedSum'.

Data Types: char

FitInfo — Fit information

Read-only: numeric array

This property is read-only.

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

Read-only: character vector | cell array of character vectors

This property is read-only.

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

Data Types: char | cell

LearnerNames — Names of weak learners in ensemble

Read-only: cell array of character vectors

This property is read-only.

Names of weak learners in the 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 used to create ensemble

Read-only: character vector

This property is read-only.

Method used by fitrensemble to create the ensemble, returned as a character vector.

Data Types: char

ModelParameters — Parameters used in training ensemble

Read-only: EnsembleParams object

This property is read-only.

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.

NumTrained — Number of trained weak learners

Read-only: positive integer

This property is read-only.

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

Data Types: double

ReasonForTermination — Reason function stopped adding weak learners

Read-only: character vector

This property is read-only.

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

Data Types: char

Regularization — Result of using regularize

Read-only: structure

This property is read-only.

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

Data Types: struct

Trained — Trained weak learners

Read-only: cell vector

This property is read-only.

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

Data Types: cell

TrainedWeights — Trained weak learner weights

Read-only: numeric vector

This property is read-only.

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

Data Types: double

Predictor Properties

BinEdges — Bin edges for numeric predictors

Read-only: 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 the numeric predictors. Xbinned values are 0 for categorical predictors. If X contains NaNs, then the corresponding Xbinned values are NaNs.

Data Types: cell

CategoricalPredictors — Categorical predictor indices

Read-only: 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

ExpandedPredictorNames — Expanded predictor names

Read-only: 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

PredictorNames — Predictor names

Read-only: 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

X — Predictor values

Read-only: 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

Response Properties

ResponseName — Name of response variable

Read-only: 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

Y — Class labels

Read-only: 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 numeric vector. Each row of Y represents the classification of the corresponding row of X.

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

Other Data Properties

HyperparameterOptimizationResults — Description of cross-validation optimization of hyperparameters

Read-only: BayesianOptimization object | table

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. This property is nonempty if the OptimizeHyperparameters name-value argument is nonempty when you create the model. The value of HyperparameterOptimizationResults depends on the setting of the Optimizer option in HyperparameterOptimizationOptions when you create the model.

• "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)

NumObservations — Number of observations in training data

Read-only: 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

W — Scaled weights in tree

Read-only: 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

Object Functions

compact	Reduce size of machine learning 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
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
removeLearners	Remove members of compact 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 Boosted Regression Ensemble

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 boosted ensemble of 100 regression trees using the LSBoost method. Specify that Cylinders is a categorical variable.

Mdl = fitrensemble(X,Y,'Method','LSBoost',...
    'PredictorNames',{'W','C'},'CategoricalPredictors',2)

Mdl = 
  RegressionEnsemble
           PredictorNames: {'W'  'C'}
             ResponseName: 'Y'
    CategoricalPredictors: 2
        ResponseTransform: 'none'
          NumObservations: 94
               NumTrained: 100
                   Method: 'LSBoost'
             LearnerNames: {'Tree'}
     ReasonForTermination: 'Terminated normally after completing the requested number of training cycles.'
                  FitInfo: [100×1 double]
       FitInfoDescription: {2×1 cell}
           Regularization: []


  Properties, Methods

Mdl is a RegressionEnsemble model object that contains the training data, among other things.

Mdl.Trained is the property that stores a 100-by-1 cell vector of the trained 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 shallow trees for boosted ensembles of trees.

Predict the fuel economy of 4,000 pound cars with 4, 6, and 8 cylinders.

XNew = [4000*ones(3,1) [4; 6; 8]];
mpgNew = predict(Mdl,XNew)

mpgNew = 3×1

   19.5926
   18.6388
   15.4810

Tips

For an ensemble of regression trees, the Trained property contains 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})

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.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• The following object functions fully support GPU arrays:

  • compact

  • crossval

  • cvshrink

  • gather

  • predictorImportance

  • regularize

  • removeLearners

  • resume

  • shrink

• The following object functions offer limited support for GPU arrays:

  • loss

  • partialDependence

  • plotPartialDependence

  • predict

  • resubLoss

  • resubPredict

• The object functions execute on a GPU if at least one of the following applies:

  • The model was fitted with GPU arrays.

  • The predictor data that you pass to the object function is a GPU array.

  • The response data that you pass to the object function is a GPU array.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2011a