BIMSA > Seminar on Control Theory and Nonlinear Filtering Kolmogorov N-Width of the Likelihood Functions in Nonlinear Filtering
Kolmogorov N-Width of the Likelihood Functions in Nonlinear Filtering
Organizer
Shing Toung Yau
Speaker
Zeju Sun
Time
Friday, September 22, 2023 8:00 PM - 8:30 PM
Venue
Online
Abstract
Kolmogorov n-width is a concept originated from approximation theory, which describes the optimal approximation efficiency for a subset in function space by an n-dimensional subspace. In this talk, the subset we need to approximate stems from the likelihood functions in nonlinear filtering. With the help of polynomial interpolation theory, we can prove that the Kolmogorov n-width of the target subset decay rapidly as the dimension n tends to infinity, which shows that it is practical to use finite-dimensional vector spaces to approximate the subset of likelihood functions.