Title: Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation
Speaker: Louis Sharrock（Lancaster University, UK）
Time: Friday, June 16, 2023, 15:30-16:30
Location: Zoom ID：876 0592 8254, Password：2023
Abstract: McKean-Vlasov SDEs arise in many applications, including mathematical biology, social sciences, and machine learning. In this talk, wewill discuss parameter estimation for a cKean-Vlasov SDE and theassociated system of weakly interacting particles. We first analyse theasymptotic properties of the offline maximum likelihood estimator. Wethen propose a new online estimator, which evolves according to acontinuous-time stochastic gradient descent algorithm on the asymptoticog-likelihood of the interacting particle system. We obtain variousconvergence results for this estimator, under assumptions which guaranteeergodicity and uniform-in-time propagation chaos. Our theoretical resultsare supported via several numerical examples, including a toy linear meanfield model a stochastic Kuramoto model. and a stochastic opiniondynamics model.
Biography: Louis Sharrock is a senior research associate in statisticamachine learning at Lancaster University in the Uk He holds a phDin Mathematics from Imperial College London and an MA in Mathematics from the University of Cambridge. His current research focuseson learning-rate free sampling algorithms. score-based methods forsimulation based inference. and online parameter estimation for interacting particle systems and mean-field equations.
More information about HIT-WHU Seminar on Stochastic Analysis and Algorithms can be found here.
