TY - JOUR

T1 - On the Choice of Regression Basis Functions and Machine Learning

AU - Ermakov, S. M.

AU - Leora, S. N.

PY - 2022/3/1

Y1 - 2022/3/1

N2 - Abstract: As is known, regression-analysis tools are widely used in machine-learning problems to establish the relationship between the observed variables and to store information in a compact manner. Most often, a regression function is described by a linear combination of some given functions fj(X), j = 1, …, m, X ∈ D ⊂ Rs. If the observed data contain a random error, then the regression function reconstructed from the observations contains a random error and a systematic error depending on the selected functions fj. This article indicates the possibility of an optimal, in the sense of a given functional metric, choice of fj, if it is known that the true dependence obeys some functional equation. In some cases (a regular grid, s ≤ 2), close results can be obtained using a technique for random-process analysis. The numerical examples given in this work illustrate significantly broader opportunities for the assumed approach to regression problems.

AB - Abstract: As is known, regression-analysis tools are widely used in machine-learning problems to establish the relationship between the observed variables and to store information in a compact manner. Most often, a regression function is described by a linear combination of some given functions fj(X), j = 1, …, m, X ∈ D ⊂ Rs. If the observed data contain a random error, then the regression function reconstructed from the observations contains a random error and a systematic error depending on the selected functions fj. This article indicates the possibility of an optimal, in the sense of a given functional metric, choice of fj, if it is known that the true dependence obeys some functional equation. In some cases (a regular grid, s ≤ 2), close results can be obtained using a technique for random-process analysis. The numerical examples given in this work illustrate significantly broader opportunities for the assumed approach to regression problems.

KW - approximation

KW - basis functions

KW - machine learning

KW - operator method

KW - regression analysis

UR - http://www.scopus.com/inward/record.url?scp=85131376545&partnerID=8YFLogxK

U2 - 10.1134/S1063454122010034

DO - 10.1134/S1063454122010034

M3 - Article

AN - SCOPUS:85131376545

VL - 55

SP - 7

EP - 15

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -