Neural McKean-Vlasov Processes: Inferring Distributional Dependence

Haoming Yang, Ali Hasan, Yuting Ng, Vahid Tarokh

Keywords: McKean-Vlasov, stochastic process, ito diffusion

TL;DR: We investigate how distributional dependence in stochastic differential equations affects modeling capabilities.

Abstract:

McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical description of the behavior of an infinite number of interacting particles by imposing a dependence on the particle density.
These processes differ from standard Ito-SDEs to the extent that MV-SDEs include distributional information in their individual particle parameterization.
As such, we study the influence of explicitly including distributional information in the parameterization of the SDE.
We first propose a series of semi-parametric methods for representing MV-SDEs, and then propose corresponding estimators for inferring parameters from data based on the underlying properties of the MV-SDE.
By analyzing the properties of the different architectures and estimators, we consider their relationship to standard Ito-SDEs and consider their applicability in relevant machine learning problems.
We empirically compare the performance of the different architectures on a series of real and synthetic datasets for time series and probabilistic modeling.
The results suggest that including the distributional dependence in MV-SDEs is an effective modeling framework for temporal data under an exchangeability assumption while maintaining strong performance for standard Ito-SDE problems due to the richer class of probability flows associated with MV-SDEs.

Submission Number: 3903