Applied Mathematics Seminar ‘Nonstatistical Learning Theory: the View from Optimal Recovery’
Simon Foucart, Texas A&M University
Thursday 2 March 2023
Abstract: For a function observed through point evaluations, is there an optimal way to recover it or merely to estimate a dependent quantity? I will give affirmative answers to variations of this data-focused question, especially under the assumption that the function belongs to a model set defined by approximation capabilities. In fact, I will uncover computationally implementable linear recovery maps that are optimal in the worst-case setting. I will present some recent and ongoing works extending the theory in several directions, with particular emphasis put on observations that are inexact—adversarially or randomly.