ClassificationBaggedEnsemble

Classification ensemble grown by resampling

Description

ClassificationBaggedEnsemble 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 bagged classification ensemble object (ens) using fitcensemble. Set the name-value pair argument 'Method' of fitcensemble 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

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`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

`ClassNames` — List of elements in `Y` with duplicates removed
categorical array | cell array of character vectors | character array | logical vector | numeric vector

This property is read-only.

List of the elements in Y with duplicates removed, returned as a categorical array, cell array of character vectors, character array, logical vector, or a numeric vector. ClassNames has the same data type as the data in the argument Y. (The software treats string arrays as cell arrays of character vectors.)

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

`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

`Cost` — Cost of classifying a point into class `j` when its true class is `i`
square matrix

Cost of classifying a point into class j when its true class is i, returned as a square matrix. The rows of Cost correspond to the true class and the columns correspond to the predicted class. The order of the rows and columns of Cost corresponds to the order of the classes in ClassNames. The number of rows and columns in Cost is the number of unique classes in the response.

Data Types: double

`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. fitcensemble 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 fitcensemble uses to create the ensemble, returned as a character vector.

Example: 'AdaBoostM1'

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

`Prior` — Prior probabilities for each class
`m`-element vector

Prior probabilities for each class, returned as an m-element vector, where m is the number of unique classes in the response. The order of the elements of Prior corresponds to the order of the classes in ClassNames.

Data Types: double

`ReasonForTermination` — Reason that `fitcensemble` stopped adding weak learners to ensemble
character vector

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

Example: 'Terminated normally after completing the requested number of training cycles.'

Data Types: char

`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

`RowsUsed` — Rows of the original predictor data `X` used for fitting
logical vector

This property is read-only.

Rows of the original predictor data X used for fitting, returned as an n-element logical vector, where n is the number of rows of X. If the software uses all rows of X for constructing the object, then RowsUsed is an empty array ([]).

Data Types: logical

`ScoreTransform` — Function for transforming scores
function handle | name of a built-in transformation function | `'none'`

Function for transforming scores, specified as a function handle or the name of a built-in transformation function. 'none' means no transformation; equivalently, 'none' means @(x)x. For a list of built-in transformation functions and the syntax of custom transformation functions, see fitctree.

Add or change a ScoreTransform function using dot notation:

ctree.ScoreTransform = 'function'
% or
ctree.ScoreTransform = @function

Data Types: char | string | function_handle

`Trained` — Trained classification models
cell vector

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

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 ensemble
numeric vector

This property is read-only.

Scaled weights in the ensemble, returned as a numeric vector. W has length n, the number of rows in the training data. The sum of the elements of W is 1.

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.

Object Functions

`compact`	Reduce size of classification ensemble model
`compareHoldout`	Compare accuracies of two classification models using new data
`crossval`	Cross-validate machine learning model
`edge`	Classification edge for classification ensemble model
`gather`	Gather properties of Statistics and Machine Learning Toolbox object from GPU
`lime`	Local interpretable model-agnostic explanations (LIME)
`loss`	Classification loss for classification ensemble model
`margin`	Classification margins for classification ensemble model
`oobEdge`	Out-of-bag classification edge for bagged classification ensemble model
`oobLoss`	Out-of-bag classification loss for bagged classification ensemble model
`oobMargin`	Out-of-bag classification margins for bagged classification ensemble
`oobPermutedPredictorImportance`	Out-of-bag predictor importance estimates for random forest of classification trees by permutation
`oobPredict`	Predict out-of-bag labels and scores of bagged classification ensemble
`partialDependence`	Compute partial dependence
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
`predict`	Predict labels using classification ensemble model
`predictorImportance`	Estimates of predictor importance for classification ensemble of decision trees
`resubEdge`	Resubstitution classification edge for classification ensemble model
`resubLoss`	Resubstitution classification loss for classification ensemble model
`resubMargin`	Resubstitution classification margins for classification ensemble model
`resubPredict`	Classify observations in classification ensemble by resubstitution
`resume`	Resume training of classification ensemble model
`shapley`	Shapley values
`testckfold`	Compare accuracies of two classification models by repeated cross-validation

Examples

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Train Bagged Ensemble of Classification Trees

Open Live Script

Load the ionosphere data set.

load ionosphere

You can train a bagged ensemble of 100 classification trees using all measurements.

Mdl = fitcensemble(X,Y,'Method','Bag')

fitcensemble uses a default template tree object templateTree() as a weak learner when 'Method' is 'Bag'. In this example, for reproducibility, specify 'Reproducible',true when you create a tree template object, and then use the object as a weak learner.

rng('default') % For reproducibility
t = templateTree('Reproducible',true); % For reproducibiliy of random predictor selections
Mdl = fitcensemble(X,Y,'Method','Bag','Learners',t)

Mdl = 
  ClassificationBaggedEnsemble
             ResponseName: 'Y'
    CategoricalPredictors: []
               ClassNames: {'b'  'g'}
           ScoreTransform: 'none'
          NumObservations: 351
               NumTrained: 100
                   Method: 'Bag'
             LearnerNames: {'Tree'}
     ReasonForTermination: 'Terminated normally after completing the requested number of training cycles.'
                  FitInfo: []
       FitInfoDescription: 'None'
                FResample: 1
                  Replace: 1
         UseObsForLearner: [351x100 logical]

Mdl is a ClassificationBaggedEnsemble model object.

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

Plot a graph of the first trained classification tree.

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

Figure Classification tree viewer contains an axes object and other objects of type uimenu, uicontrol. The axes object contains 60 objects of type line, text. One or more of the lines displays its values using only markers

By default, fitcensemble grows deep decision trees for bagged ensembles.

Estimate the in-sample misclassification rate.

L = resubLoss(Mdl)

L = 
0

L is 0, which indicates that Mdl is perfect at classifying the training data.

Tips

For a bagged ensemble of classification trees, the Trained property of ens stores a cell vector of ens.NumTrained CompactClassificationTree 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 ClassificationEnsemble 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 fitcensemble, the following restrictions apply.
- The value of the ScoreTransform name-value argument cannot be an anonymous function.
- Code generation limitations for the weak learners used in the ensemble also apply to the ensemble. For decision tree weak learners, 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 fitcensemble, you must train an ensemble using tree learners, and the ScoreTransform value cannot be 'invlogit'.
- 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.
- Class labels with the categorical data type are not supported. Both the class label value in the training data (Tbl or Y) and the value of the ClassNames name-value argument cannot be an array with the categorical data type.

For more information, see Introduction to Code Generation.

Version History

Introduced in R2011a

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R2022a: `Cost` property stores the user-specified cost matrix

Starting in R2022a, the Cost property stores the user-specified cost matrix, so that you can compute the observed misclassification cost using the specified cost value. The software stores normalized prior probabilities (Prior) and observation weights (W) that do not reflect the penalties described in the cost matrix. To compute the observed misclassification cost, specify the LossFun name-value argument as "classifcost" when you call the loss, resubLoss, or oobLoss function.

Note that model training has not changed and, therefore, the decision boundaries between classes have not changed.

For training, the fitting function updates the specified prior probabilities by incorporating the penalties described in the specified cost matrix, and then normalizes the prior probabilities and observation weights. This behavior has not changed. In previous releases, the software stored the default cost matrix in the Cost property and stored the prior probabilities and observation weights used for training in the Prior and W properties, respectively. Starting in R2022a, the software stores the user-specified cost matrix without modification, and stores normalized prior probabilities and observation weights that do not reflect the cost penalties. For more details, see Misclassification Cost Matrix, Prior Probabilities, and Observation Weights.

Some object functions use the Cost, Prior, and W properties:

The loss, resubLoss, and oobLoss functions use the cost matrix stored in the Cost property if you specify the LossFun name-value argument as "classifcost" or "mincost".
The loss and edge functions use the prior probabilities stored in the Prior property to normalize the observation weights of the input data.
The resubLoss, resubEdge, oobLoss, and oobEdge functions use the observation weights stored in the W property.

If you specify a nondefault cost matrix when you train a classification model, the object functions return a different value compared to previous releases.

If you want the software to handle the cost matrix, prior probabilities, and observation weights in the same way as in previous releases, adjust the prior probabilities and observation weights for the nondefault cost matrix, as described in Adjust Prior Probabilities and Observation Weights for Misclassification Cost Matrix. Then, when you train a classification model, specify the adjusted prior probabilities and observation weights by using the Prior and Weights name-value arguments, respectively, and use the default cost matrix.

ClassificationBaggedEnsemble

Description

Creation

Properties

BinEdges — Bin edges for numeric predictors cell array of p numeric vectors

CategoricalPredictors — Indices of categorical predictors vector of positive integers | []

ClassNames — List of elements in Y with duplicates removed categorical array | cell array of character vectors | character array | logical vector | numeric vector

CombineWeights — How the ensemble combines weak learner weights 'WeightedAverage' | 'WeightedSum'

Cost — Cost of classifying a point into class j when its true class is i square matrix

ExpandedPredictorNames — Expanded predictor names cell array of character vectors

FitInfo — Fit information numeric array

FitInfoDescription — Description of information in FitInfo character vector | cell array of character vectors

FResample — Fraction of training data resampled during object construction numeric scalar between 0 and 1

HyperparameterOptimizationResults — Description of cross-validation optimization of hyperparameters BayesianOptimization object | table of hyperparameters and associated values

LearnerNames — Names of weak learners in ensemble cell array of character vectors

Method — Method that creates ensemble character vector

ModelParameters — Parameters used in training ensemble EnsembleParams object

NumObservations — Number of observations in the training data positive integer

NumTrained — Number of trained weak learners positive integer

PredictorNames — Predictor names cell array of character vectors

Prior — Prior probabilities for each class m-element vector

ReasonForTermination — Reason that fitcensemble stopped adding weak learners to ensemble character vector

Replace — Indication that ensemble was trained with replacement true | false

ResponseName — Name of the response variable character vector

RowsUsed — Rows of the original predictor data X used for fitting logical vector

ScoreTransform — Function for transforming scores function handle | name of a built-in transformation function | 'none'

Trained — Trained classification models cell vector

TrainedWeights — Trained weak learner weights numeric vector

UseObsForLearner — Indicator that observation was used to train learner N-by-NumTrained real matrix

W — Scaled weights in ensemble numeric vector

X — Predictor values real matrix | table

Y — Class labels categorical array | cell array of character vectors | character array | logical vector | numeric vector

Object Functions

Examples

Train Bagged Ensemble of Classification Trees

Tips

Alternative Functionality

Bootstrap Aggregation Methods

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

Version History

R2022a: Cost property stores the user-specified cost matrix

See Also

Topics

`BinEdges` — Bin edges for numeric predictors
cell array of p numeric vectors

`CategoricalPredictors` — Indices of categorical predictors
vector of positive integers | `[]`

`ClassNames` — List of elements in `Y` with duplicates removed
categorical array | cell array of character vectors | character array | logical vector | numeric vector

`CombineWeights` — How the ensemble combines weak learner weights
`'WeightedAverage'` | `'WeightedSum'`

`Cost` — Cost of classifying a point into class `j` when its true class is `i`
square matrix

`ExpandedPredictorNames` — Expanded predictor names
cell array of character vectors

`FitInfo` — Fit information
numeric array

`FitInfoDescription` — Description of information in `FitInfo`
character vector | cell array of character vectors

`FResample` — Fraction of training data resampled during object construction
numeric scalar between `0` and `1`

`HyperparameterOptimizationResults` — Description of cross-validation optimization of hyperparameters
`BayesianOptimization` object | table of hyperparameters and associated values

`LearnerNames` — Names of weak learners in ensemble
cell array of character vectors

`Method` — Method that creates ensemble
character vector

`ModelParameters` — Parameters used in training ensemble
`EnsembleParams` object

`NumObservations` — Number of observations in the training data
positive integer

`NumTrained` — Number of trained weak learners
positive integer

`PredictorNames` — Predictor names
cell array of character vectors

`Prior` — Prior probabilities for each class
`m`-element vector

`ReasonForTermination` — Reason that `fitcensemble` stopped adding weak learners to ensemble
character vector

`Replace` — Indication that ensemble was trained with replacement
`true` | `false`

`ResponseName` — Name of the response variable
character vector

`RowsUsed` — Rows of the original predictor data `X` used for fitting
logical vector

`ScoreTransform` — Function for transforming scores
function handle | name of a built-in transformation function | `'none'`

`Trained` — Trained classification models
cell vector

`TrainedWeights` — Trained weak learner weights
numeric vector

`UseObsForLearner` — Indicator that observation was used to train learner
`N`-by-`NumTrained` real matrix

`W` — Scaled weights in ensemble
numeric vector

`X` — Predictor values
real matrix | table

`Y` — Class labels
categorical array | cell array of character vectors | character array | logical vector | numeric vector

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

R2022a: `Cost` property stores the user-specified cost matrix