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