postFitStatistics

Compute post-fit statistics for the exact Gaussian process regression model

Syntax

loores = postFitStatistics(gprMdl) [loores,neff] = postFitStatistics(gprMdl)

Description

loores = postFitStatistics(gprMdl) returns the leave-one-out residuals, loores, for the trained Gaussian process regression (GPR) model.

[loores,neff] = postFitStatistics(gprMdl) also returns the number of effective parameters, neff.

Input Arguments

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`gprMdl` — Gaussian process regression model
`RegressionGP` object

Gaussian process regression model, specified as a RegressionGP object.

Output Arguments

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`loores` — Leave-one-out residuals
n-by-1 matrix

Leave-one-out residuals, returned as an n-by-1 matrix, where n is the number of observations in the training data.

`neff` — Number of effective parameters
n-by-1 matrix

Number of effective parameters, returned as an n-by-1 matrix, where n is the number of observations in the training data.

Examples

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Compute Post-Fit Statistics

Open Live Script

Generate sample data.

rng(0,'twister'); % For reproducibility
n = 1500;
x = linspace(-10,10,n)';
y = sin(3*x).*cos(3*x) + sin(2*x).*cos(2*x) + sin(x) + cos(x) + 0.2*randn(n,1);

Fit a GPR model using the exact method for fitting and prediction.

gprMdl = fitrgp(x,y,'Basis','linear','FitMethod','exact',...
'PredictMethod','exact','KernelFunction','matern52');

Compute the leave-one-out residuals and the effective number of parameters in the trained model.

[loores,neff] = postFitStatistics(gprMdl);

Predict the responses using the trained model.

ypred = resubPredict(gprMdl);

Plot the true and predicted responses, and display effective number of parameters in the fit.

figure()
plot(x,y,'r.');
hold on;
plot(x,ypred,'b'); 
xlabel('x');
ylabel('y');
legend('Data','GPR prediction','Location','Best');
title(['Effective number of parameters = ',num2str(neff)]);
hold off

Plot leave-one-out residuals.

figure()
plot(x,loores,'r.-');
xlabel('x');
ylabel('leave-one-out residuals');

Tips

You can only compute the post-fit statistics when PredictMethod is 'exact'.
If FitMethod is 'exact', then postFitStatistics accounts for the fact that the fixed basis function coefficients are estimated from the data.
If FitMethod is different than 'exact', then postFitStatistics treats the fixed basis function coefficients as known.
For all PredictMethod and FitMethod options, postFitStatistics treats the estimated kernel parameters and noise standard deviation as known.