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Cross-validated regression model


RegressionPartitionedModel is a set of regression models trained on cross-validated folds. Estimate the quality of regression by cross validation using one or more “kfold” methods: kfoldPredict, kfoldLoss, and kfoldfun. 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.



You can create a RegressionPartitionedModel object in two ways:

  • Create a cross-validated model from a regression tree model object RegressionTree by using the crossval object function.

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


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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';
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.

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

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

Data Types: char

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

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

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

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

Response variable name, specified as a character vector.

Data Types: char

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

Trained learners, returned as a cell array of compact regression models.

Data Types: cell

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

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

This property is read-only.

Row classifications corresponding to the rows of 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

gatherGather properties of Statistics and Machine Learning Toolbox object from GPU
kfoldLossLoss for cross-validated partitioned regression model
kfoldPredictPredict responses for observations in cross-validated regression model
kfoldfunCross-validate function for regression


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Load the sample data. Create a variable X containing the Horsepower and Weight data.

load carsmall
X = [Horsepower Weight];

Construct a regression tree using the sample data.

cvtree = fitrtree(X,MPG,'crossval','on');

Evaluate the cross-validation error of the carsmall data using Horsepower and Weight as predictor variables for mileage (MPG).

L = kfoldLoss(cvtree)
L = 25.5338

Extended Capabilities

Version History

Introduced in R2011a