James Wu

James Wu

Computational Statistics & Machine Learning @ UCL

Blog posts

2023

Generalised Variational Inference

13 minute read

Published:

Generalised Variational Inference (GVI) is a framework motivated by the breakdown of the Bayesian posterior interpretation in larger-scaled models like Bayesian Neural Networks. In this post, I will discuss how GVI addresses this issue by re-framing Bayesian inference in a wider context of constrainted optimisation. I will also discuss how the GVI posterior ensures the existence of a unique minimiser, providing theoretical guarantees that can be used for understanding larger-scaled modelling in the context of learning theory.

Expectation Maximisation

5 minute read

Published:

Expectation maximisation is a powerful algorithm that can be applied to a wide variety of problems, including clustering, mixture models, and hidden Markov models. In this post, I will present the general formulation of the algorithm and apply it to the k-means clustering problem as an example.

2022

The Kernel Stein Discrepancy

11 minute read

Published:

Stein discrepancies (SDs) calculate a statistical divergence between a known density \(\mathbb{P}\) and samples from an unknown distribution \(\mathbb{Q}\). In this post, we will introduce the Stein discrepancy, in particular the Langevin Kernel Stein Discrepancy (KSD), a common form of Stein discrepancy.

2021

Gaussian Processes: A Hands On Introduction

6 minute read

Published:

There are many online resources for understanding Gaussian Processes. In this post, I present a more hands on way of introducing the topic that I found quite helpful and intuitive for myself.