Codes and Expansions (CodEx) Seminar

Simon Foucart (Texas A&M University)
Integrating Observation Errors in Optimal Recovery

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 an affirmative answer to 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.