A Visual Exploration of Gaussian Processes

A Visual Exploration of Gaussian Processes

In particular, given a normal probability distribution P(X,Y) over vectors of random variables X, and Y, we can determine their marginalized probability distributions in the following way:

The interpretation of this equation is that each partition X and Y only depends on its corresponding entries in μ and Σ. The following figure shows an example of this for two dimensions:

Now, the goal of Gaussian processes is to learn this underlying distribution from training data. Since we want to predict the function values at ∣X∣=N test points, the corresponding multivariate Gaussian distribution is also N -dimensional.

Source: distill.pub