Hi Anurag,
In Gaussian Process (GP) regression, the standard deviation of the observation noise, often denoted as sigma (σ), is typically estimated from the data rather than calculated using a specific formula. The estimation of sigma is an inherent part of the GP regression modeling process.
In GP regression, the observation noise is assumed to be Gaussian and independent. The noise level is estimated by fitting the GP model to the data, and the model automatically estimates the hyperparameters, including sigma, through a process called maximum likelihood estimation.
The maximum likelihood estimation finds the hyperparameters that maximize the likelihood of observing the given data under the assumed noise model. The sigma value that maximizes the likelihood is then considered as the estimate for the standard deviation of the observation noise.
Therefore, in practice, sigma is obtained as an output of the GP regression modeling process rather than being calculated using a specific formula.
Here is an example code snippet that demonstrates how to calculate sigma in MATLAB:
% Load your input features (X) and corresponding target values (y)
load('data.mat', 'X', 'y');
% Fit a Gaussian Process regression model to the data
gpModel = fitrgp(X, y);
% Access the Sigma property to obtain the estimated sigma value
sigma = gpModel.Sigma;
After running this code, the sigma variable will contain the estimated standard deviation of the observation noise in the Gaussian Process regression model.
