The Geometric Statistics Research Group is part of the Computational Statistics and Machine Learning research theme based at the Department of Statistical Science, University College London.
Our focus is on statistical methods that recognize and exploit the geometric structure of data and parameters.
Members:
My research is centred on leveraging the geometric structure of the data and models to develop computationally tractable methodologies with theoretical guarantees. Key areas of interest include numerical integration, model inference, and interpretable deep learning for biomedical applications.
My research interest focuses on defining meaningful geometrical embeddings and statistical methods for complex data, mostly graphs and images. My work has focused on metric spaces, quotient space, stratified spaces, and beyond manifold embeddings in general. I am especially interested in modelling questions that are motivated by real-world challenges. For example, I have worked on applications involving cardiac fibrosis, pancreatic tubular structures, brain connectivity, public transport systems, and other domains where graphs and images provide rich and informative representations.
My research focuses on exploiting geometry in the data structure. Examples include diffusions on the manifold of positive definite matrices for financial applications and physical symmetries leading to complex projective space as parameter space in electron nuclear double resonance spectroscopy.
My work focuses on the development and analysis of efficient, scalable algorithms for sampling, inference, and learning in computational statistics and machine learning, drawing on the geometric structure of the space of probability distributions. Particular areas of interest include Bayesian posterior sampling, generative modelling, simulation-based inference, and parameter estimation in interacting particle systems.
Geometric Statistics Research Group 