Loosely speaking, Gaussian processes (GPs) can be thought of as a probabilistic yet non-parametric form of non-linear regression which sit within the Bayesian framework. They are a powerful but less well understood tool that can be used in both a regression and classification setting.

In this article we give a thorough introduction to Gaussian process regression collating many of the excellent references on the topic. We also provide Python code examples.

This article will introduce VAEs, providing a synthesis of many of the excellent explanations that already exist. In particular we will derive the ELBO in 3 different ways as well as list some common questions that arose for me whilst understanding VAEs.

The kernel trick allows us to implicitly perform a calculation in a high-dimensional feature space whilst only working in the original feature space. In this article we explain the kernel trick via a toy example which we follow through in detail to illustrate the trick.