RegressionPartitionedEnsemble

Cross-validated regression ensemble

Description

RegressionPartitionedEnsemble is a set of regression ensembles trained on cross-validated folds. Estimate the quality of classification by cross validation using one or more “kfold” methods: kfoldfun, kfoldLoss, or kfoldPredict. Every “kfold” method uses models trained on in-fold observations to predict response for out-of-fold observations. For example, suppose you cross validate using five folds. In this case, every training fold contains roughly 4/5 of the data and every test fold contains roughly 1/5 of the data. The first model stored in Trained{1} was trained on X and Y with the first 1/5 excluded, the second model stored in Trained{2} was trained on X and Y with the second 1/5 excluded, and so on. When you call kfoldPredict, it computes predictions for the first 1/5 of the data using the first model, for the second 1/5 of data using the second model and so on. In short, response for every observation is computed by kfoldPredict using the model trained without this observation.

Creation

You can create a RegressionPartitionedEnsemble object in two ways:

• Create a cross-validated model from a RegressionEnsemble or RegressionBaggedEnsemble model object by using the crossval object function.

• Create a cross-validated model by using the fitrensemble function and specifying one of the name-value arguments CrossVal, CVPartition, Holdout, KFold, or Leaveout.

Properties

Cross-Validation Properties

CrossValidatedModel — Name of cross-validated model

character vector

This property is read-only.

Name of the cross-validated model, returned as a character vector.

Data Types: char

KFold — Number of folds in ensemble

positive integer

This property is read-only.

Number of folds in the cross-validated ensemble, returned as a positive integer.

Data Types: double

ModelParameters — Parameters of cross-validated ensemble

object

This property is read-only.

Parameters of the cross-validated ensemble, returned as an object.

NumTrainedPerFold — Number of weak learners used in training each fold of the ensemble

positive integer

This property is read-only.

Number of weak learners used in training each fold of the ensemble, returned as a positive integer.

Data Types: double

Partition — Partition used in cross-validation

CVPartition object

This property is read-only.

Partition used in cross-validation, returned as a CVPartition object.

Trainable — Trained learners

cell array of ensembles

This property is read-only.

The trained learners, returned as a cell array of full ensembles trained on cross-validation folds. Every ensemble is full, meaning it contains its training data and weights.

Data Types: cell

Trained — Trained learners

cell array of compact ensembles

This property is read-only.

The trained learners, returned as a cell array of compact ensembles trained on cross-validation folds.

Data Types: cell

Other Regression 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

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

PredictorNames — Predictor names

cell array of character vectors

This property is read-only.

Predictor names in order of their appearance in the predictor data X, specified as a cell array of character vectors. The length of PredictorNames is equal to the number of columns in X.

Data Types: cell

ResponseName — Response variable name

character vector

This property is read-only.

Response variable name, specified as a character vector.

Data Types: char

ResponseTransform — Function for transforming responses

'none' (default) | function handle

Function for transforming the raw response values (mean squared error), specified as a function handle or 'none'. The default 'none' means no transformation; equivalently, 'none' means @(x)x. A function handle must accept a matrix of response values and return a matrix of the same size.

Add or change a ResponseTransform function using dot notation:

tree.ResponseTransform = @function

Data Types: char | function_handle

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.

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

Object Functions

gather	Gather properties of Statistics and Machine Learning Toolbox object from GPU
kfoldLoss	Loss for cross-validated partitioned regression model
kfoldPredict	Predict responses for observations in cross-validated regression model
kfoldfun	Cross-validate function for regression
resume	Resume training of cross-validated regression ensemble model

Examples

Construct Partitioned Regression Ensemble

Construct a partitioned regression ensemble, and examine the cross-validation losses for the folds.

Load the carsmall data set.

load carsmall;

Create a subset of variables.

XX = [Cylinders Displacement Horsepower Weight];
YY = MPG;

Construct the ensemble model.

rens = fitrensemble(XX,YY);

Create a cross-validated ensemble from rens.

rng(10,'twister') % For reproducibility
cvrens = crossval(rens);

Examine the cross-validation losses.

L = kfoldLoss(cvrens,'mode','individual')

L = 10×1

   21.4489
   48.4388
   28.2560
   17.5354
   29.9441
   49.5254
   51.2372
   31.0152
   31.6388
    8.9607

L is a vector containing the cross-validation loss for each trained learner in the ensemble.

Extended Capabilities

GPU Arrays

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

The object functions of the RegressionPartitionedEnsemble model fully support GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2011a