Work

Optimal prediction of vector-valued functions from point samples

Year: 2025

Type: article

Abstract: Predicting the value of a function f at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when f produces several values depending on one another, e.g. when it outputs a probability vector. 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 the vector-valued function f . 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.

Source: Journal of Complexity

DOI: 10.1016/j.jco.2025.101981

Author: Simon Foucart

Institution: Texas A&M University

Language: English

Topic: Machine Learning and Algorithms

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,680

Funders: National Science Foundation, Multidisciplinary University Research Initiative, Office of Naval Research, Heilbronn Institute for Mathematical Research