kfoldPredict

Predict responses for observations in cross-validated regression model

Description

example

yFit = kfoldPredict(CVMdl) returns responses predicted by the cross-validated regression model CVMdl. For every fold, kfoldPredict predicts the responses for validation-fold observations using a model trained on training-fold observations. CVMdl.X and CVMdl.Y contain both sets of observations.

yFit = kfoldPredict(CVMdl,Name,Value) specifies options using one or more name-value arguments. For example, 'IncludeInteractions',true specifies to include interaction terms in computations. This syntax applies only to generalized additive models.

[yFit,ySD,yInt] = kfoldPredict(___) also returns the standard deviations and prediction intervals of the response variable, evaluated at each observation in the predictor data CVMdl.X, using any of the input argument combinations in the previous syntaxes. This syntax applies only to generalized additive models for which the IsStandardDeviationFit property of CVMdl is true.

Examples

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When you create a cross-validated regression model, you can compute the mean squared error (MSE) by using the kfoldLoss object function. Alternatively, you can predict responses for validation-fold observations using kfoldPredict and compute the MSE manually.

Load the carsmall data set. Specify the predictor data X and the response data Y.

X = [Cylinders Displacement Horsepower Weight];
Y = MPG;

Train a cross-validated regression tree model. By default, the software implements 10-fold cross-validation.

rng('default') % For reproducibility
CVMdl = fitrtree(X,Y,'CrossVal','on');

Compute the 10-fold cross-validation MSE by using kfoldLoss.

L = kfoldLoss(CVMdl)
L = 29.4963

Predict the responses yfit by using the cross-validated regression model. Compute the mean squared error between yfit and the true responses CVMdl.Y. The computed MSE matches the loss value returned by kfoldLoss.

yfit = kfoldPredict(CVMdl);
mse = mean((yfit - CVMdl.Y).^2)
mse = 29.4963

Input Arguments

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Cross-validated partitioned regression model, specified as a RegressionPartitionedModel, RegressionPartitionedEnsemble, RegressionPartitionedGAM, or RegressionPartitionedSVM object. You can create the object in two ways:

• Pass a trained regression model listed in the following table to its crossval object function.

• Train a regression model using a function listed in the following table and specify one of the cross-validation name-value arguments for the function.

Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'Alpha',0.01,'IncludeInteractions',false specifies the confidence level as 99% and excludes interaction terms from computations for a generalized additive model.

Significance level for the confidence level of the prediction intervals yInt, specified as a numeric scalar in the range [0,1]. The confidence level of yInt is equal to 100(1 – Alpha)%.

This argument is valid only for a generalized additive model object that includes the standard deviation fit. That is, you can specify this argument only when CVMdl is RegressionPartitionedGAM and the IsStandardDeviationFit property of CVMdl is true.

Example: 'Alpha',0.01

Data Types: single | double

Flag to include interaction terms of the model, specified as true or false. This argument is valid only for a generalized additive model (GAM). That is, you can specify this argument only when CVMdl is RegressionPartitionedGAM.

The default value is true if the models in CVMdl (CVMdl.Trained) contain interaction terms. The value must be false if the models do not contain interaction terms.

Data Types: logical

Output Arguments

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Predicted responses, returned as an n-by-1 numeric vector, where n is the number of observations. (n is size(CVMdl.X,1) when observations are in rows.) Each entry of yFit corresponds to the predicted response for the corresponding row of CVMdl.X.

If you use a holdout validation technique to create CVMdl (that is, if CVMdl.KFold is 1), then yFit has NaN values for training-fold observations.

Standard deviations of the response variable, evaluated at each observation in the predictor data CVMdl.X, returned as a column vector of length n, where n is the number of observations in CVMdl.X. The ith element ySD(i) contains the standard deviation of the ith response for the ith observation CVMdl.X(i,:), estimated using the trained standard deviation model in CVMdl.

This argument is valid only for a generalized additive model object that includes the standard deviation fit. That is, kfoldPredict can return this argument only when CVMdl is RegressionPartitionedGAM and the IsStandardDeviationFit property of CVMdl is true.

Prediction intervals of the response variable, evaluated at each observation in the predictor data CVMdl.X, returned as an n-by-2 matrix, where n is the number of observations in CVMdl.X. The ith row yInt(i,:) contains the estimated 100(1 – Alpha)% prediction interval of the ith response for the ith observation CVMdl.X(i,:) using ySD(i). The Alpha value is the probability that the prediction interval does not contain the true response value CVMdl.Y(i). The first column of yInt contains the lower limits of the prediction intervals, and the second column contains the upper limits.

This argument is valid only for a generalized additive model object that includes the standard deviation fit. That is, kfoldPredict can return this argument only when CVMdl is RegressionPartitionedGAM and the IsStandardDeviationFit property of CVMdl is true.

Extended Capabilities

Introduced in R2011a