Vinayak Rao, Assistant Professor
Department of Statistics | Purdue University
Modeling and computation for continuous-time systems through random time-discretization
A variety of phenomena, from fields such as genetics, social network analysis and computational chemistry, are best described using models operating in continuous time. Such models allow rich and mechanistic system dynamics, but also present significant computational challenges, especially in data-rich settings. A typical approach is to approximate the dynamics by discretizing time, thereby introducing error. In this talk, I will describe work on a class of simple Markov chain Monte Carlo methods that allow efficient computations while still being exact. The core idea is to work with random discretizations of time, allowing methods from discrete-time (like the forward-backward algorithm) to be easily applied, and avoiding the need for expensive operations like matrix exponentiation. I will talk about more recent work that extends these ideas to allow efficient inference over the system parameters, and discuss some convergence properties of the resulting MCMC algorithm. In the last part of the talk, I will outline how such ideas can be used to develop novel machine learning algorithms (like variational inference) for continuous-time dynamical systems, as well as some results modeling genetic and social media data.