Computational Methods of Randomized Machine Learning
Yuri S. Popkov, Alexey Yu. Popkov, Yuri A. Dubnov, Alexander Yu. Mazurov · 2022
Chapter 7 focuses on the computational methods of randomized machine learning that are intended to solve the functional entropy-linear programming problems of randomized parametric models and the entropy-nonlinear programming problems to estimate the probabilities of belonging of the nonrandomized model parameters to corresponding intervals. The optimality conditions of these problems are formulated as the nonlinear empirical balance equations. For the functional entropy-linear programming problems, these equations contain integral terms. Our idea is to solve the equations by minimizing a residual function, i.e., the solution is reduced to a minimization problem on a compact set. A considerable part of calculations consists in the numerical integration of nonlinear exponential functions using the Monte Carlo method. The solution procedure of this system also employs the packet Monte Carlo iterations.