Risk bounds when learning infinitely many response functions by ordinary linear regression

Vincent Plassier, François Portier and Johan Segers ()
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Johan Segers: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2023002, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: Consider the problem of learning a large number of response functions simultaneously based on the same input variables. The training data consist of a single independent random sample of the input variables drawn from a common distribution together with the associated responses. The input variables are mapped into a high-dimensional linear space, called the feature space, and the response functions are modelled as linear functionals of the mapped features, with coefficients calibrated via ordinary least squares. We provide convergence guarantees on the worst-case excess prediction risk by controlling the convergence rate of the excess risk uniformly in the response function. The dimension of the feature map is allowed to tend to infinity with the sample size. The collection of response functions, although potentially infinite, is supposed to have a finite Vapnik–Chervonenkis dimension. The bound derived can be applied when building multiple surrogate models in a reasonable computing time.

Keywords: Control variates; Monte Carlo integration; multitask learning; ordinary least squares; Response surface model (search for similar items in EconPapers)
Pages: 27
Date: 2023-02-01
Note: In: Annales de l'Institut Henri Poincaré : Probabilités et Statistiques, 2023, vol. 59(1), p. 53-78
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2023002

DOI: 10.1214/22-AIHP1259

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