Bayesian Optimization in Action

3 Customizing a Gaussian process with the mean and covariance functions

This chapter covers

• Controlling the expected behavior of a GP using mean functions
• Controlling the smoothness of a GP using covariance functions
• Learning the optimal hyperparameters of a GP using gradient descent

In chapter 2, we saw that the mean and covariance functions are the two core components of a Gaussian process (GP). Even though we used the zero mean and the RBF covariance function when implementing our GP, you can choose from many options when it comes to these two components.

By going with a specific choice for either the mean or the covariance function, we are effectively specifying prior knowledge for our GP. Incorporating prior knowledge into prediction is ...