Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation
4th March 2022, 3:00 pm – 4:00 pm
Virtual Seminar, Zoom link: TBA
McKean-Vlasov SDEs, which arise naturally as the hydrodynamical limit (N→∞) of systems of N interacting particles, are important in many applications, from mathematical biology (e.g., neuroscience and population dynamics) to the social sciences (e.g., opinion dynamics and cooperative behaviours) to high-dimensional sampling. In this talk, we discuss parameter estimation for a McKean-Vlasov SDE and the associated system of weakly interacting particles. We first establish consistency and asymptotic normality of the offline maximum likelihood estimator for the interacting particle system in the limit as the number of particles N→∞. We then propose an online estimator, which evolves according to a continuous-time stochastic gradient descent algorithm on the asymptotic log-likelihood of the interacting particle system. We obtain various convergence results for this estimator, under assumptions which guarantee ergodicity and uniform-in-time propagation chaos. Our theoretical results are supported via several numerical examples, including a toy linear mean field model and a stochastic opinion dynamics model. This is joint work with Nikolas Kantas, Panos Parpas, and Greg Pavliotis (Imperial College London).