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Regression loss for cross-validated kernel regression model



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 pair arguments. For example, you can specify the regression-loss function or which folds to use for loss calculation.


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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


Input Arguments

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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.

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

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(x)=xβ+b.

    • β is a vector of p coefficients.

    • x is an observation from p predictor variables.

    • b is the scalar bias.

    'epsiloninsensitive'Epsilon-insensitive loss: [y,f(x)]=max[0,|yf(x)|ε]
    'mse'MSE: [y,f(x)]=[yf(x)]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)

    • 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

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

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

Example: 'Mode','individual'

Output Arguments

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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