14:00 – 15:00 – Joaquin Miguez (Universidad Carlos III de Madrid)
Title: A simple class of invariant statistics and their application to adaptive particle filtering and implicit generative modelling
Abstract: Assume that we draw n independent and identically distributed samples x(1), x(2), …, x(n) from a common probability distribution P and then we sort them in ascending order to obtain x[1] < x[2] < … < x[n]. These so-called rank statistics have some intrinsic properties that depend on independence and the existence of a common distribution P, rather than the specific form of that distribution. Using those properties, it is possible to derive more elaborate statistics that remain invariant with respect to P and can be used to assess, or calibrate, both probabilistic models and the inference algorithms built on them.
In this talk we construct a simple class of such invariant statistics and then proceed to explore two applications. First, we take the problem of Bayesian filtering for nonlinear/non-Gaussian state-space models. This problem does not admit exact solutions, so approximate numerical algorithms are used in practical filtering applications ranging from target tracking in the battlefield to numerical weather predictions. Particle filters are a popular class of such algorithms. They are sequential Monte Carlo schemes and, as such, their computational cost and accuracy depend on the number of Monte Carlo samples that can be generated (and propagated over time). We show how rank-based statistics can be used to automatically adapt the computational effort of particle filters and assess their accuracy with a general (model invariant) procedure that imposes very little computational overhead on the original algorithm.
The proposed class of invariant statistics can also be leveraged to train implicit generative models. In particular, it is possible to quantitatively compare samples from a target data distribution with synthetic samples from a parametric generative model (e.g., a deep neural network with a random input) in terms of the distribution of the proposed rank-based statistics. This yields a rather simple (and likelihood-free) discrepancy measure that can be minimised to train the network parameters. In the talk, we discuss why this methodology is well-principled and present the results of some illustrative computer experiments, including comparisons with other implicit generative models (GANs, transformers and others).
Refreshments available between 15:00 – 15:30, Huxley Common Room (HXLY 549)