Optimal Prediction of Multivalued Functions from Point Samples
Optimization and Control
2024-12-16 v1 Functional Analysis
Abstract
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 that depend on one another, e.g. when it outputs likelihoods or concentrations. Considering the points as fixed (not random) entities and focusing on the worst-case, this article uncovers a prediction procedure that is optimal relatively to some model-set information about . When the model sets are convex, this procedure turns out to be an affine map constructed by solving a convex optimization program. The theoretical result is specified in the two practical frameworks of (reproducing kernel) Hilbert spaces and of spaces of continuous functions.
Cite
@article{arxiv.2412.09894,
title = {Optimal Prediction of Multivalued Functions from Point Samples},
author = {Simon Foucart},
journal= {arXiv preprint arXiv:2412.09894},
year = {2024}
}