A systematic presentation of the randomized machine learning problem: from data processing, through structuring randomized models and algorithmic procedure, to the solution of applications-relevant problems in different fields. Provides new numerical methods for random global optimization and computation of multidimensional integrals. A universal algorithm for randomized machine learning.

This monograph aspires to lay the foundations of a new scientific discipline, demoeconomics, representing the synthesis of demography and spatial economics. This synthesis is performed in terms of interaction between population and its economic activity. The monograph appears a unique research work having no analogs in scientific literature. Demoeconomic systems are studied involving the macrosystems approach which combines the generalized entropy maximization principle and the local equilibria principle. Demoeconomic systems operate in an uncertain environment; thus and so, the monograph develops the methodology and technique of probabilistic modeling and forecasting of their evolution.

Macrosystems are systems in which the stochastic behaviour of the elements is transformed into deterministic behaviour of the system as a whole. This publication discusses equilibrium in these systems. Mathematical models of stationary states using the principle of maximum entropy are presented. This is developed and generalized for macrosystems with constrained resources. Parametric properties which characterize a model's response to data variations are discussed. The author has developed new computational methods for the computer-aided realization of stationary state models. Algorithms and computer experiments are evaluated. Mathematical modelling methods are applied to problems of hierarchical structures, interregional product exchange and image reconstruction.