Experimental Study of an Approximate Method for Calculating Entropy-Optimal Distributions in Randomized Machine Learning Problems

Alexey Yu. Popkov, Yuri A. Dubnov (), Ilya V. Sochenkov and Yuri S. Popkov
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Alexey Yu. Popkov: Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 44/2 Vavilova, 119333 Moscow, Russia
Yuri A. Dubnov: Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 44/2 Vavilova, 119333 Moscow, Russia
Ilya V. Sochenkov: Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 44/2 Vavilova, 119333 Moscow, Russia
Yuri S. Popkov: Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 44/2 Vavilova, 119333 Moscow, Russia

Mathematics, 2025, vol. 13, issue 11, 1-14

Abstract: This paper is devoted to the experimental study of the integral approximation method in entropy optimization problems arising from the application of the Randomized Machine Learning method. Entropy-optimal probability density functions contain normalizing integrals from multivariate exponential functions; as a result, when computing these distributions in the process of solving an optimization problem, it is necessary to ensure efficient computation of these integrals. We investigate an approach based on the approximation of integrand functions, which are applied to the solution of several configurations of problems with model and real data with linear static models using a symbolic computation mechanism. Computational studies were carried out under the same conditions, with the same initial data and values of hyperparameters of the used models. They have shown the performance and efficiency of the proposed approach in the Randomized Machine Learning problems based on linear static models.

Keywords: randomized machine learning; entropy; optimization; symbolic computations; symbolic integration; numerical methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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