Statistics seminar

Abstract: Inference in stochastic interacting particle systems is increasingly important due to applications in social sciences, physics, and machine learning. In this talk, we focus on learning the interaction kernel from observations of a single particle. We adopt a semi-parametric approach, expressing the kernel as a generalized Fourier series with orthogonal polynomials tailored to the problem. The Fourier coefficients are estimated via a variation of the method of moments applied to the invariant measure of the mean-field dynamics, resulting in a linear system based on moments approximated from the particle trajectory. We analyze the approximation error and asymptotic behavior of the estimator in the limits of infinite observation time, large particle number, and increasing number of Fourier coefficients. Numerical experiments illustrate the effectiveness of the approach. This work is joint with Grigorios A. Pavliotis (Imperial College London).