Optimal prediction of vector-valued functions from point samples

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2025-08-18 DOI:10.1016/j.jco.2025.101981

Simon Foucart

引用次数: 0

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.

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基于点样本的向量值函数的最优预测

在给定函数f在旧点的值的情况下，预测函数f在新点的值是一项普遍存在的科学努力，当f产生相互依赖的几个值时，例如当它输出一个概率向量时，就不那么发达了。考虑到点是固定的（不是随机的）实体，并关注最坏情况，本文揭示了一个预测过程，相对于关于向量值函数f的一些模型集信息是最优的。当模型集是凸的，这个过程变成了一个通过求解凸优化程序构建的仿射映射。在（再现核）希尔伯特空间和连续函数空间的两个实际框架下，给出了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.