Empirical risk minimization and complexity of dynamical models
Speaker: James Carzon
Abstract: A dynamical model consists of a continuous self-map of a compact state space and a continuous observation function. In this talk, I will start by surveying some interesting general problems of statistical inference for dynamical systems (cf. [1]). My focus will be on translating some central concepts in the study of real-valued dynamical systems to familiar statistical settings. Then I will highlight some results on the consistency of parameter estimation under dynamical models (cf. [2]). [1] https://projecteuclid.org/journals/statistics-surveys/volume-9/issue-none/Statistical-inference-for-dynamical-systems-A-review/10.1214/15-SS111.full [2] https://projecteuclid.org/journals/annals-of-statistics/volume-48/issue-4/Empirical-risk-minimization-and-complexity-of-dynamical-models/10.1214/19-AOS1876.full