Research output: Contribution to journal › Article › peer-review
Quasi-deterministic processes with monotonic trajectories and unsupervised machine learning. / Orekhov, Andrey V.
In: Mathematics, Vol. 9, No. 18, 2301, 17.09.2021.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Quasi-deterministic processes with monotonic trajectories and unsupervised machine learning
AU - Orekhov, Andrey V.
N1 - Publisher Copyright: © 2021 by the author. Licensee MDPI, Basel, Switzerland.
PY - 2021/9/17
Y1 - 2021/9/17
N2 - 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 (statis-tics) 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.
AB - 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 (statis-tics) 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.
KW - Approximation
KW - Approximation-estimation test
KW - Integral-estimation test
KW - Least-squares method
KW - Markov chain with mem-ory
KW - Markov decision process
KW - Markov moment
KW - Quasi-deterministic process
KW - Unsupervised machine learning
KW - CRITERIA
KW - approximation
KW - NUMBER
KW - Markov chain with memory
KW - approximation-estimation test
KW - REAL-TIME PCR
KW - integral-estimation test
KW - unsupervised machine learning
KW - quasi-deterministic process
KW - least-squares method
UR - http://www.scopus.com/inward/record.url?scp=85115296582&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/259a21b2-20dc-33cf-9e28-b252982dd7cf/
U2 - 10.3390/math9182301
DO - 10.3390/math9182301
M3 - Article
AN - SCOPUS:85115296582
VL - 9
JO - Mathematics
JF - Mathematics
SN - 2227-7390
IS - 18
M1 - 2301
ER -
ID: 85898765