Experimentation for Engineers

Appendix C Gaussian process regression

Gaussian process regression (GPR) is a method of estimating function values directly from a set of measurements. In the context of Bayesian optimization, we imagine there exists a true function, business metric versus parameter, from which we take a few measurements. GPR estimates the value of the business metric at parameters for which we haven’t taken measurements. It forms these estimates from the measurements we have already taken.

Let’s call the parameter x (a vector of all the system parameters) and the business metric y (a scalar, a number). Let’s say we’ve already taken N measurements. We’ll index them by i and call the measurements x_i , y_i. Note that each x_i is a vector.

Our task is to estimate ...