I am a PhD student in Mathematics at Imperial College London supervised by Andrew Duncan and Greg Pavliotis.

Summary

My research focuses on developing and analysing robust methodologies for unsupervised machine learning based on techniques from physics, mathematical analysis, and optimisation. Currently, I am working on an improved training methodology for energy-based models for generative modelling and inference.

Projects

How to train your EBM without Markov Chain Monte Carlo

We propose a new training methodology for energy-based models based on Energy Discrepancy (ED) which does not rely on sampling (like contrastive divergence, short CD) or Stein scores (as in score-based methods, short SM). The goal are robust unbiased models for high-dimensional data. Our paper “Energy Discrepancies: A Score-Independent Loss for Energy-Based Models” can be accessed here. An extension to energy-based models on discrete spaces has been presented at the ICML 2023 workshop Sampling and Optimisation in Discrete Spaces and can be found here

Variational Inference as a gradient flow in a kernelised Wasserstein geometry

Variational Inference optimises a training objective with gradient descent to infer optimal parameters in a parametric family of distributions, for example, to compute an approximate Bayesian posterior distribution. For my Master thesis, I formulated the training dynamics as a gradient flow in a kernelised Wasserstein geometry based on the results on Stein geometries and a relationship between gradient flows and black box variational inference