Use a regressionGP model (from fitrgp()) to predict the gradient with uncertainty

I'm working with the Gaussian Process Regression functions in MATLAB to produce a fitted curve to a discrete set of observations: (X,y). I'm able to produce a fit with uncertainties using fitrgp(X,y) to generate a regressionGP object and then [output, uncertainties] = predict(regressionGP) to get the result. However, what I'm really after is the gradient of the fit with its uncertainties. Is there a simple way to compute this using MATLAB?

Thank you for your help.

Answer 1

[Aditya]

Hi Evan,

To compute the gradient of a Gaussian Process Regression (GPR) fit along with its uncertainties in MATLAB, you can follow these steps:

% Sample data (replace with your actual data)
X = linspace(0, 10, 100)'; % Predictor variable
y = sin(X) + 0.1 * randn(size(X)); % Response variable with noise

% Fit the Gaussian Process Model
regressionGP = fitrgp(X, y);

% Predict the mean and standard deviation
[xGrid, yPred, ySD] = predict(regressionGP, X);

% Compute the gradient of the predicted mean
dy_dx = gradient(yPred, X);

% Compute the gradient of the standard deviation (uncertainty in the gradient)
dSD_dx = gradient(ySD, X);

% Plot the results
figure;
subplot(2, 1, 1);
plot(X, y, 'o', X, yPred, '-');
xlabel('X');
ylabel('Predicted y');
title('Gaussian Process Regression Fit');
legend('Data', 'GPR Fit');

subplot(2, 1, 2);
plot(X, dy_dx, '-');
hold on;
plot(X, dy_dx + dSD_dx, '--', X, dy_dx - dSD_dx, '--');
xlabel('X');
ylabel('Gradient of Predicted y');
title('Gradient and Uncertainty');
legend('Gradient', 'Gradient + Uncertainty', 'Gradient - Uncertainty');