On optimization problems arising from the application of topological data analysis to the search for forecasting algorithms with fixed correctors

Corrective operations (correctors) in multialgorithmic constructions of the algebraic approach can be based on known physical models and/or multilevel descriptions of physical objects. At the same time, within the framework of the topological approach to the analysis of poorly formalized problems, the search for algorithms included in the corrector can be considered as a combinatorial optimization problem or as a problem of minimizing a certain loss function. The study of the neighborhoods of chains in the lattice of subsets of objects made it possible to obtain a number of rank optimization criteria that are promising for solving the problems of predicting numerical target variables. The formalism was tested on the problem of ligand–receptor interaction within the framework of the chemokine analysis of drug molecules (data from ProteomicsDB). The best results of predicting constants were observed when using the obtained rank criteria (correlation coefficient on a sliding control $0.86\pm0.20$ averaging over 300 biological activities).