###Neural Bayesian model selection
Project ID: 2228bd1015 (You will need this ID for your application)
Research Theme: Artificial Intelligence and Robotics
UCL Lead department: Space and Climate Physics (MSSL)
Lead Supervisor: Jason McEwen
Project Summary:
While deep learning has undergone remarkable progress in recent years, it typically lacks a principled statistical basis. Probabilistic deep learning has emerged recently but the field remains nascent. And while the outputs of probabilistic deep learning approaches may exhibit the mathematical properties of probabilities, they usually do not satisfy the rigorous statistical interpretation of either frequentist or Bayesian statistical frameworks. Moreover, in science the most pertinent questions are often those of model selection, e.g. what is the nature of dark energy and dark matter, what is the origin of structure in our Universe, what is the best physical model to describe gravitational wave signals from black hole mergers? Model selection is typically neglected in probabilistic deep learning frameworks. In this project we will develop deep learning approaches to Bayesian model selection.
Bayesian model selection requires the computation of the marginal likelihood (aka. model evidence), the average likelihood of a model over its prior probability space, which is an extremely challenging computational problem. We will develop deep learning techniques integrated into Markov chain Monte Carlo (MCMC) sampling approaches in order to: (i) accelerate the computation of the marginal likelihood to scale to high dimensional settings; and (ii) incorporate learned data-driven priors. To achieve these goals we will develop techniques leveraging normalizing flows and generative diffusion models. Furthermore, we will develop techniques to compute the marginal likelihood in variational inference frameworks in order to provide dramatically accelerated model selection. While the focus of the project is on methodological developments, we will showcase the application of the techniques developed on cosmological problems to address the science questions posed above.
The student should have a strong mathematical background and be proficient in coding, particularly in Python. Expertise in either statistics or deep learning is an advantage (cosmological background not required).