Hugh Dance
PhD researcher in causal machine learning at the Gatsby Unit, University College London.
I am a PhD researcher in machine learning at the Gatsby Unit, UCL, working primarily on causal and probabilistic machine learning. My research develops representations and algorithms that exploit structure—such as invariance, composition and transport—to make causal inference and generative modelling more robust, interpretable and computationally efficient. Recent work includes counterfactual transports and cocycles, generative modelling of interventional distributions using flow matching, causal uncertainty quantification, and accelerator-efficient Monte Carlo methods. More broadly, I am interested in how causal and statistical structure can help us understand, manipulate and reason about complex learned systems, including questions around representation, identifiability, abstraction and reliable intervention.
Selected Research
Debiased Counterfactual Generation via Flow Matching from Observations
Rather than learning an interventional distribution from scratch, we learn a deconfounding flow from the observed conditional distribution to its counterfactual target. The method combines flow matching with semiparametric debiasing and minimal-energy transports for high-dimensional outcomes.
Counterfactual Cocycles: A Framework for Robust and Coherent Counterfactual Transports
We represent intervention-induced transformations through cocycles: maps with algebraic composition structure that identify coherent systems of interventional and counterfactual distributions. This yields estimators that can avoid unnecessary latent-noise modelling while retaining robustness and efficiency.
Interventional Processes for Causal Uncertainty Quantification
We develop spectral Gaussian-process representations for causal effects that support flexible nonparametric estimation together with calibrated epistemic uncertainty. The resulting framework provides reliable uncertainty quantification for intervention functions and causal decision-making.
Paper · ICML 2026
Efficiently Vectorized MCMC on Modern Accelerators
We recast adaptive MCMC algorithms as finite-state machines so vectorized chains can progress through control flow independently, avoiding synchronization bottlenecks on GPUs and other accelerators. The resulting JAX implementations achieve speed-ups of up to an order of magnitude.
Research Themes
Causal and counterfactual machine learning
I develop methods for interventions and counterfactuals from observational data, including counterfactual transports, causal uncertainty quantification, causal discovery and interventional generation. Current work studies partial identification, using dependence between potential outcomes to sharpen counterfactual bounds.
Generative models and structured dynamical systems
I use transport, flow matching and dynamical-systems perspectives to learn transformations between distributions. Recent work includes debiased flow matching for interventional generation and velocity-based causal discovery; current work develops multi-parameter flows with path independence, composition and low-energy dynamics.
Latent structure, invariance and identifiability
I exploit invariance and compositional structure to remove unnecessary parameterisation while preserving what is needed for inference. Building on counterfactual cocycles, current work studies latent-indexed transformations for dimension reduction, latent identification and extrapolation, with broader links to causal abstraction and learned representations.
Probabilistic machine learning, uncertainty and computation
I develop probabilistic methods for scalable inference and calibrated uncertainty, including Gaussian processes for high-dimensional variable selection and causal uncertainty quantification, and finite-state-machine representations of adaptive MCMC for efficient execution on modern accelerators.
Software
jax-fsm-mcmc
JAX implementations of finite-state-machine MCMC methods designed for efficient vectorized execution on modern accelerators.
Cocycles
Research code for learning and evaluating cocycle-based counterfactual transports across simulations and applied causal-inference problems.
SSVGP
Scalable spike-and-slab variable selection for high-dimensional Gaussian-process models, accompanying the AISTATS 2022 oral paper.
Background
I am completing my PhD in Machine Learning at the Gatsby Computational Neuroscience Unit, UCL, supervised by Professor Peter Orbanz. Before starting the PhD, I spent around five years as an econometrician in PwC’s Economic Consulting team in London, working on causal estimation, high-dimensional forecasting, Bayesian modelling and applied policy research. Earlier training includes an MSc in Computational Statistics and Machine Learning and an MSc in Economics, both from UCL. Selected applied work is available in my industry portfolio.