kfoldLoss

Regression loss for cross-validated kernel regression model

Syntax

L = kfoldLoss(CVMdl)

L = kfoldLoss(CVMdl,Name,Value)

Description

L = kfoldLoss(CVMdl) returns the regression loss obtained by the cross-validated kernel regression model CVMdl. For every fold, kfoldLoss computes the regression loss for observations in the validation fold, using a model trained on observations in the training fold.

L = kfoldLoss(CVMdl,Name,Value) returns the mean squared error (MSE) with additional options specified by one or more name-value arguments. For example, you can specify the regression-loss function or which folds to use for loss calculation.

Examples

Compute Loss for Cross-Validated Kernel Regression Models

Simulate sample data:

rng(0,'twister'); % For reproducibility
n = 1000;
x = linspace(-10,10,n)';
y = 1 + x*2e-2 + sin(x)./x + 0.2*randn(n,1);

Cross-validate a kernel regression model.

CVMdl = fitrkernel(x,y,'Kfold',5);

fitrkernel implements 5-fold cross-validation. CVMdl is a RegressionPartitionedKernel model. It contains the property Trained, which is a 5-by-1 cell array holding 5 RegressionKernel models that the software trained using the training set.

Compute the epsilon-insensitive loss for each fold for observations that fitrkernel did not use in training the folds.

L = kfoldLoss(CVMdl,'LossFun','epsiloninsensitive','Mode','individual')

L = 5×1

    0.1261
    0.1247
    0.1107
    0.1237
    0.1131

Input Arguments

CVMdl — Cross-validated kernel regression model

RegressionPartitionedKernel model object

Cross-validated kernel regression model, specified as a RegressionPartitionedKernel model object. You can create a RegressionPartitionedKernel model using fitrkernel and specifying any of the cross-validation name-value pair arguments, for example, CrossVal.

Name-Value Arguments

Specify optional pairs of arguments as Name1=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: 'LossFun','epsiloninsensitive','Mode','individual' specifies kfoldLoss to return the epsilon-insensitive loss for each fold.

Folds — Fold indices to use for response prediction

1:CVMdl.KFold (default) | numeric vector of positive integers

Fold indices to use for response prediction, specified as the comma-separated pair consisting of 'Folds' and a numeric vector of positive integers. The elements of Folds must range from 1 through CVMdl.KFold.

Example: 'Folds',[1 4 10]

Data Types: single | double

LossFun — Loss function

'mse' (default) | 'epsiloninsensitive' | function handle

Loss function, specified as the comma-separated pair consisting of 'LossFun' and a built-in loss function name or function handle.

• The following table lists the available loss functions. Specify one using its corresponding character vector or string scalar. Also, in the table, $$f\left(x\right)=x\beta +b.$$

  • β is a vector of p coefficients.

  • x is an observation from p predictor variables.

  • b is the scalar bias.

  Value	Description
  'epsiloninsensitive'	Epsilon-insensitive loss: $$\ell \left[y,f\left(x\right)\right]=\max \left[0,\left|y-f\left(x\right)\right|-\epsilon \right]$$
  'mse'	MSE: $$\ell \left[y,f\left(x\right)\right]={\left[y-f\left(x\right)\right]}^2$$

  'epsiloninsensitive' is appropriate for SVM learners only.

• Specify your own function using function handle notation.

  Assume that n is the number of observations in X. Your function must have this signature

  lossvalue = lossfun(Y,Yhat,W)

  where:

  • The output argument lossvalue is a scalar.

  • You specify the function name (lossfun).

  • Y is an n-dimensional vector of observed responses. kfoldLoss passes the input argument Y in for Y.

  • Yhat is an n-dimensional vector of predicted responses, which is similar to the output of predict.

  • W is an n-by-1 numeric vector of observation weights.

Data Types: char | string | function_handle

Mode — Loss aggregation level

'average' (default) | 'individual'

Loss aggregation level, specified as the comma-separated pair consisting of 'Mode' and 'average' or 'individual'.

Value	Description
'average'	Returns losses averaged over all folds
'individual'	Returns losses for each fold

Example: 'Mode','individual'

PredictionForMissingValue — Predicted response value to use for observations with missing predictor values

"median" (default) | "mean" | "omitted" | numeric scalar

Since R2023b

Predicted response value to use for observations with missing predictor values, specified as "median", "mean", "omitted", or a numeric scalar.

Value	Description
"median"	kfoldLoss uses the median of the observed response values in the training-fold data as the predicted response value for observations with missing predictor values.
"mean"	kfoldLoss uses the mean of the observed response values in the training-fold data as the predicted response value for observations with missing predictor values.
"omitted"	kfoldLoss excludes observations with missing predictor values from the loss computation.
Numeric scalar	kfoldLoss uses this value as the predicted response value for observations with missing predictor values.

If an observation is missing an observed response value or an observation weight, then kfoldLoss does not use the observation in the loss computation.

Example: "PredictionForMissingValue","omitted"

Data Types: single | double | char | string

Output Arguments

L — Cross-validated regression losses

numeric scalar | numeric vector

Cross-validated regression losses, returned as a numeric scalar or vector. The interpretation of L depends on LossFun.

• If Mode is 'average', then L is a scalar.

• Otherwise, L is a k-by-1 vector, where k is the number of folds. L(j) is the average regression loss over fold j.

To estimate L, kfoldLoss uses the data that created CVMdl.

Version History

Introduced in R2018b

R2023b: Specify predicted response value to use for observations with missing predictor values

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 the PredictionForMissingValue name-value argument. By default, the functions use the training set median as the predicted response value for observations with missing predictor values.

Model Type	Model Objects	Object Functions
Gaussian process regression (GPR) model	RegressionGP, CompactRegressionGP	loss, predict, resubLoss, resubPredict
	RegressionPartitionedGP	kfoldLoss, kfoldPredict
Gaussian kernel regression model	RegressionKernel	loss, predict
	RegressionPartitionedKernel	kfoldLoss, kfoldPredict
Linear regression model	RegressionLinear	loss, predict
	RegressionPartitionedLinear	kfoldLoss, kfoldPredict
Neural network regression model	RegressionNeuralNetwork, CompactRegressionNeuralNetwork	loss, predict, resubLoss, resubPredict
	RegressionPartitionedNeuralNetwork	kfoldLoss, kfoldPredict
Support vector machine (SVM) regression model	RegressionSVM, CompactRegressionSVM	loss, predict, resubLoss, resubPredict
	RegressionPartitionedSVM	kfoldLoss, kfoldPredict

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.