kfoldPredict - Predict responses for observations in cross-validated regression model - MATLAB (original) (raw)

Predict responses for observations in cross-validated regression model

Syntax

Description

[yFit](#mw%5F07f1a040-132a-48ca-b863-13a56a7414dc) = kfoldPredict([CVMdl](#bsu1qp2-1%5Fsep%5Fmw%5F6577e588-b931-4d13-a896-01d344a3d171)) returns responses predicted by the cross-validated regression modelCVMdl. 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.

example

[yFit](#mw%5F07f1a040-132a-48ca-b863-13a56a7414dc) = kfoldPredict([CVMdl](#bsu1qp2-1%5Fsep%5Fmw%5F6577e588-b931-4d13-a896-01d344a3d171),[Name,Value](#namevaluepairarguments)) specifies options using one or more name-value arguments. For example,'IncludeInteractions',true specifies to include interaction terms in computations for generalized additive models.

[[yFit](#mw%5F07f1a040-132a-48ca-b863-13a56a7414dc),[ySD](#mw%5Fdeeb7733-3174-4093-911b-ccbe236226a0),[yInt](#mw%5Fbc65533c-94fb-4ded-8344-a8d179390cdf)] = 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 (GAM) for which the IsStandardDeviationFit property of CVMdl istrue.

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.

load carsmall 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.

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)

Input Arguments

Name-Value Arguments

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Specify optional pairs of arguments asName1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

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 intervalsyInt, 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 whenCVMdl is RegressionPartitionedGAM and the IsStandardDeviationFit property of CVMdl istrue.

Example: 'Alpha',0.01

Data Types: single | double

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

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

Data Types: logical

Since R2023b

Predicted response value to use for observations with missing predictor values, specified as "median", "mean", or a numeric scalar. This argument is valid only for a Gaussian process regression, neural network, or support vector machine model. That is, you can specify this argument only whenCVMdl is a RegressionPartitionedGP,RegressionPartitionedNeuralNetwork, orRegressionPartitionedSVM object.

Example: "PredictionForMissingValue","mean"

Example: "PredictionForMissingValue",NaN

Data Types: single | double | char | string

Output Arguments

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Predicted responses, returned as an n_-by-1 numeric vector, where_n is the number of observations. (n issize(CVMdl.X,1) when observations are in rows.) Each entry ofyFit 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), thenyFit has NaN values for training-fold observations.

Standard deviations of the response variable, evaluated at each observation in the predictor data [CVMdl](#bsu1qp2-1%5Fsep%5Fmw%5F6577e588-b931-4d13-a896-01d344a3d171).X, returned as a column vector of length n, where n is the number of observations in `CVMdl`.X. Theith 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 istrue.

Prediction intervals of the response variable, evaluated at each observation in the predictor data [CVMdl](#bsu1qp2-1%5Fsep%5Fmw%5F6577e588-b931-4d13-a896-01d344a3d171).X, returned as an_n_-by-2 matrix, where n is the number of observations in `CVMdl`.X. Theith row yInt(i,:) contains the estimated100(1 – [Alpha](#mw%5F2e2bf216-bf31-400d-b9b2-07aa80264beb))% prediction interval of the ith response for the ith observation CVMdl.X(i,:) using[ySD](#mw%5Fdeeb7733-3174-4093-911b-ccbe236226a0)(i). The Alpha value is the probability that the prediction interval does not contain the true response valueCVMdl.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 istrue.

Extended Capabilities

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Usage notes and limitations:

• This function fully supports GPU arrays for the following models.
  • RegressionPartitionedEnsemble
  • RegressionPartitionedNeuralNetwork
  • RegressionPartitionedModel object fitted using fitrtree, or by passing aRegressionTree object tocrossval
  • RegressionPartitionedSVM

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

Version History

Introduced in R2011a

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Starting in R2023b, when you predict or compute the loss, some regression models allow you to specify the predicted response value for observations with missing predictor values. Specify the PredictionForMissingValue name-value argument to use a numeric scalar, the training set median, or the training set mean as the predicted value. When computing the loss, you can also specify to omit observations with missing predictor values.

This table lists the object functions that support thePredictionForMissingValue name-value argument. By default, the functions use the training set median as the predicted response value for observations with missing predictor values.

In previous releases, the regression model loss and predict functions listed above used NaN predicted response values for observations with missing predictor values. The software omitted observations with missing predictor values from the resubstitution ("resub") and cross-validation ("kfold") computations for prediction and loss.