Quasi-Deterministic Processes with Monotonic Trajectories and Unsupervised Machine Learning

Andrey V. Orekhov
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Andrey V. Orekhov: Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, 7–9 Universitetskaya Embankment, 199034 Saint Petersburg, Russia

Mathematics, 2021, vol. 9, issue 18, 1-26

Abstract: This paper aims to consider approximation-estimation tests for decision-making by machine-learning methods, and integral-estimation tests are defined, which is a generalization for the continuous case. Approximation-estimation tests are measurable sampling functions (statistics) that estimate the approximation error of monotonically increasing number sequences in different classes of functions. These tests make it possible to determine the Markov moments of a qualitative change in the increase in such sequences, from linear to nonlinear type. If these sequences are trajectories of discrete quasi-deterministic random processes, then moments of change in the nature of their growth and qualitative change in the process match up. For example, in cluster analysis, approximation-estimation tests are a formal generalization of the “elbow method” heuristic. In solid mechanics, they can be used to determine the proportionality limit for the stress strain curve (boundaries of application of Hooke’s law). In molecular biology methods, approximation-estimation tests make it possible to determine the beginning of the exponential phase and the transition to the plateau phase for the curves of fluorescence accumulation of the real-time polymerase chain reaction, etc.

Keywords: quasi-deterministic process; unsupervised machine learning; Markov decision process; approximation-estimation test; integral-estimation test; Markov moment; Markov chain with memory; approximation; least-squares method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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