Gaussian Process Regression

Consider fitting a Gaussian Process to fixed training pairs (0, 0) and (1, 1). We use a zero prior mean and a unit-amplitude Radial Basis Function (RBF) kernel defined as k(x,z) = exp(-(x-z)^2 / (2 * ell^2)), where ell is the length scale.

Experiment

This visualization allows you to explore the effect of GP hyperparameters on the predictive distribution. View the module here: Gaussian Process Regression.

1. Set Length scale to 1, Noise variance to 0 and Query x to 0.5. Read mean 0.549318, latent variance 0.030456 and standard deviation 0.174518.
2. Set Noise variance to 1. The matrix diagonal becomes 2, mean becomes 0.338571 and latent variance becomes 0.402423. The variance control is added once, not squared.
3. Restore noise to 0 and set Length scale to 0.5. At the midpoint, read mean 0.534230 and latent variance 0.351946.
4. Set Query x to 0: the noise-free training point has mean and variance zero. Set length scale to 2 and query to 1: read mean one and variance zero.
5. Drag the plot or use arrow keys, then Home or Reset view. View changes preserve the matrix and posterior readouts.