Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation

Release time:2023-06-12Views:174

Title: Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation


Speaker: Louis SharrockLancaster 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.

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