Title
Wasserstein Fisher Rao gradient flows: Sequential Monte Carlo & Operator Splitting
Abstract
Wasserstein-Fisher-Rao (WFR) gradient flows have recently been proposed for sampling from a target probability distribution, a task that is common across many areas of machine learning, Bayesian statistics and statistical mechanics. Such gradient flows have been shown to accelerate convergence over pure Wasserstein Gradient flows by combining the benefits of both diffusive-transport (Wasserstein) and reweighting (Fisher-Rao) type gradient flows. We consider a Wasserstein-Fisher-Rao flow for the Kullback-Leibler divergence and connect them to well-known Monte Carlo algorithms. In doing so, we show that these lead to a natural implementation using importance sampling and propose a sequential Monte Carlo based algorithm for solving a WFR gradient flow. We study the algorithm both empirically and theoretically. Additional benefits arising from operator splitting will also be discussed.
Bio
Sahani Pathiraja is a Lecturer in the School of Mathematics and Statistics at the University of New South Wales, Sydney Australia. Her research interests span stochastic filtering, sequential Bayesian inference, McKean-Vlasov SDEs, data assimilation and more recently, sampling and gradient flows.