Vince Velkey

Vince Velkey

PhD Student @ UCL, Gatsby Unit

Vince Velkey

Hi, and welcome to my homepage.

I am a PhD Candidate in Machine Learning at the Gatsby Computational Neuroscience Unit at University College London, advised by Prof. Peter Orbanz.

My research focuses on the probabilistic foundations of machine learning and Bayesian statistics. Currently, I am working on de Finetti-style representation theorems for symmetric random structures, with an emphasis on finite exchangeability and exchangeable structures beyond sequences.

More broadly, I am interested in Bayesian nonparametric methods and statistical aspects of random network models. I also have some interests in optimal transport and causal inference.

Previously, I completed a BA and MMath in mathematics at Cambridge, specialising in pure mathematics, particularly functional analysis. I also took the interdisciplinary Logic Year programme at the ILLC, University of Amsterdam, focusing on machine learning.

Current Research

Exchangeable graphs and predictive Bayesian inference

Building on my previous project, I use the tools from graph limits theory to study martingale posteriors for graph data.

Cocycles under confounding

We extend a recent counterfactual modeling framework based on cocycles that bridges the gap between transport based methods and structural causal models. We seek to cover some classical cases of confounding, such as IV, Back-door or Front-door.

Exchangeability, graph limits and exponential families

I use tools from functional analysis and information theory to study problems in exchangeability theory. My work makes explicit the analogy between de Finetti-style representation theorems for a broad class of symmetric random structures. That includes exchangeable and partially exchangeable sequences, exchangeable graphs. I derive integral representation results for their finite exchangeable counterparts.

Preprint in preparation.

Teaching

Academic Activities