4 papers
Optimal Algorithms for Nonlinear Estimation with Convex Models
Simon Foucart
A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well…
Learning the Maximum of a Hölder Function from Inexact Data
Simon Foucart
Within the theoretical framework of Optimal Recovery, one determines in this article the {\em best} procedures to learn a quantity of interest depending on a Hölder function acquir…
Optimal Prediction of Multivalued Functions from Point Samples
Simon Foucart
Predicting the value of a function at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when produces multiple values…
Radius of Information for Two Intersected Centered Hyperellipsoids and Implications in Optimal Recovery from Inaccurate Data
Simon Foucart, Chunyang Liao
For objects belonging to a known model set and observed through a prescribed linear process, we aim at determining methods to recover linear quantities of these objects that are op…