Validate gaussian process regression model with leave-one-out cross validation

Dear all,

I have a dataset with:

X = Torque (the input variable)

Y1 = Response 1

Y2 = Response 2

Y3 = Response 3

I want to use the method of leave-one-out cross-validation (LOOCV) to validate the gaussian process regression model. Then, I want to asses the quality of the model by using the root mean squared error (RMSE) and coefficient of determination (R2). How can I do this?

Answer 1

[Paras Gupta]

Hi Tessa,

To validate and assess a Gaussian Process Regression (GPR) model using the LOOCV Method, you can iteratively compute the RMSE and R2 values for each of the respone variables. The following code illustrates one way to achieve the same for the response variable 'Y1':

load('dataset.mat');

Y = Y1;
n = length(Y); % Number of observations
predictions = zeros(n, 1); % Preallocate predictions vector

for i = 1:n
    % Indices for the training set (all data points except the ith)
    trainIdx = [1:i-1, i+1:n];
    
    % Create a Gaussian process regression model
    gprMdl = fitrgp(X(trainIdx, :), Y(trainIdx), 'Basis', 'constant', 'FitMethod', ...
        'exact', 'PredictMethod', 'exact');
    
    % Predict the left-out observation
    predictions(i) = predict(gprMdl, X(i, :));
end

% Calculate RMSE
rmse = sqrt(mean((Y - predictions).^2));

% Calculate R^2
SStot = sum((Y - mean(Y)).^2);
SSres = sum((Y - predictions).^2);
rSquared = 1 - (SSres / SStot);

fprintf('RMSE: %f\n', rmse);

RMSE: 0.010725

fprintf('R^2: %f\n', rSquared);

R^2: 0.991260

You can refer to the following documentations for more information on the functions used in the code above:

• 'fitrgp' - https://www.mathworks.com/help/stats/fitrgp.html
• 'predict' - https://www.mathworks.com/help/stats/linearmodel.predict.html

Hope this answers your query.