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## Introduction to the Theory of Randomized Machine Learning

P. 199-220.

We propose a new machine learning concept called Randomized Machine Learning, in which model parameters are assumed random and data are assumed to contain random errors. Distinction of this approach from “classical” machine learning is that optimal estimation deals with the probability density functions of random parameters and the “worst” probability density of random data errors. As the optimality criterion of estimation, randomized machine learning employs the generalized information entropy maximized on a set described by the system of empirical balances. We apply this approach to text classification and dynamic regression problems. The results illustrate capabilities of the approach.

А. Ю. Попков, Ю. А. Дубнов, Ю. С. Попков, Информатика и автоматизация (Труды СПИИРАН) 2022 Т. 4 № 21 С. 659-677

We propose an approach to estimation of the parameters of non-linear dynamic models using the concept of Randomized Machine Learning (RML), based on the transition from deterministic models to random ones (with random parameters), followed by estimation of the probability distributions of parameters and noises on real data. The main feature of this method is ...

Added: February 5, 2024

Popkov Y., Dubnov Y. A., Volkovich Z. et al., Entropy 2017 Vol. 19(4) No. 178 P. 1-14

A proposal for a new method of classification of objects of various nature, named “2”-soft classification, which allows for referring objects to one of two types with optimal entropy probability for available collection of learning data with consideration of additive errors therein. A decision rule of randomized parameters and probability density function (PDF) is formed, ...

Added: May 26, 2017

Popkov Y., Dubnov Y. A., Попков А. Ю., Информатика и автоматизация (Труды СПИИРАН) 2021 Т. 20 № 5 С. 1010-1033

© St. Petersburg Federal Research Center of the Russian Academy of Sciences.The paper is devoted to the forecasting of the COVID-19 epidemic by the novel method of randomized machine learning. This method is based on the idea of estimation of probability distributions of model parameters and noises on real data. Entropy-optimal distributions correspond to the ...

Added: October 28, 2022

MDPI AG, 2020

Proceedings (ISSN 2504-3900) publishes publications resulting from conferences, workshops and similar events. ...

Added: March 13, 2020

49606783, Dobrokhotov S. Y., Nazaikinskii V. E., Mathematical notes 2016 Vol. 100 No. 5 P. 828-834

We develop the recent research [1] and introduce the notions of volume and entropy in abstract analytic number theory. The introduction of negative numbers in the generalized partition problem, together with the meaning of such a generalization in some applications of the theory, is discussed. ...

Added: February 21, 2017

Shabanov D. A., European Journal of Combinatorics 2015 Vol. 43 P. 185-203

An equitable two-coloring of a hypergraph $H=(V,E)$ is a proper vertex two-coloring such that the cardinalities of color classes differ by at most one. In connection with the property B problem Radhakrishnan and Srinivasan proved that if $H$ is a $k$-uniform hypergraph with maximum vertex degree $\Delta(H)$ satisfying
$$
\Delta(H)\leqslant c\,\frac {2^{k-1}}{\sqrt{k\,\ln k}}
$$
for some absolute constant ...

Added: October 6, 2015

Apenko S.M., Physica A: Statistical Mechanics and its Applications 2012 Vol. 391 No. 1-2 P. 62-77

We present a possible approach to the study of the renormalization group (RG) flow based
entirely on the information theory. The average information loss under a single step of
Wilsonian RG transformation is evaluated as a conditional entropy of the fast variables,
which are integrated out, when the slow ones are held fixed. Its positivity results in the
monotonic ...

Added: October 23, 2014

Popkov Y., Dubnov Y. A., Popkov A. Y., Automation and Remote Control 2018 Vol. 79 No. 11 P. 2038-2051

The direct and inverse projections (DIP) method was proposed to reduce the feature space to the given dimensions oriented to the problems of randomized machine learning and based on the procedure of “direct” and “inverse” design. The “projector” matrices are determined by maximizing the relative entropy. It is suggested to estimate the information losses by ...

Added: February 12, 2019

Skripchenko A., Troubetzkoy S., / Cornell University. Series math "arxiv.org". 2015. No. 1501.04584.

We prove that a polygonal billiard with one-sided mirrors has zero
topological entropy. In certain cases we show sub exponential and for other
polynomial estimates on the complexity. ...

Added: January 26, 2015

Maksim D. Miroshnichenko, Russian Studies in Philosophy 2022 Vol. 60 No. 3 P. 205-230

The paper reconstructs the conception of the Soviet-American psychologist Vladimir Lefebvre as part of the neocybernetic movement. In particular, I propose to consider such components of his research of the 70s-90s as systemic vision, reflexive analysis, search for a holistic configuration, and Janus-cosmology as realizations of neocybernetics. Lefebvre's interest in the reflexive structures of cognition ...

Added: November 29, 2021

Popkov A., Dubnov Y. A., Popkov Y., Информационные технологии и вычислительные системы 2022 № 3 С. 67-78

The work is devoted to application of the theory of Randomized Machine Learning to forecasting of the COVID-19 pandemic based on SIR epidemiological model. We propose two modelling variants, the first is based on estimation of SIR model using real case data, the second is based on the idea of modelling transmission coefficient and its prediction. Comparative study ...

Added: February 5, 2024

Bezhaeva Z., Oseledets V. I., Functional Analysis and Its Applications 2010 Vol. 44 No. 2 P. 83-91

Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. ...

Added: April 12, 2012

В.Н. Азаров, Бойцов Б. В., Ю.И. Гудков et al., Компетентность 2017 № 9-10 С. 46-57

We have examined the main new competencies that should be matched by the specialist — managers of complex techno-technological and socio-economic systems in the era of information (digital) and industrial revolutions. We have also investigated what kind of overprofessional competencies the expert should have and what the system of its preparation includes. Having outlined and ...

Added: January 29, 2018

V.L. Chernyshev, Minenkov D. S., Nazaikinskii V. E., Functional Analysis and Its Applications 2016 Vol. 50 No. 4 P. 291-307

We find the asymptotics of the element counting function for an additive arithmetic semigroup with exponential growth of the counting function of prime generators. ...

Added: October 18, 2015

Vorontsova T., Булеев А. А., Ефимов А. В. et al., В кн. : Межвузовская научно-техническая конференция студентов, аспирантов и молодых специалистов им. Е.В. Арменского. : МИЭМ НИУ ВШЭ, 2018. Гл. 159. С. 220-222.

Added: March 12, 2021

Popkov Y., Popkov A., Dubnov Y. A., Автоматика и телемеханика 2020 № 7 С. 148-172

A randomized forecasting method based on the generation of ensembles of entropy-optimal forecasting trajectories is developed. The latter are generated by randomized dynamic regression models containing random parameters, measurement noises, and a random input. The probability density functions of random parameters and measurement noises are estimated using real data within the randomized machine learning procedure. ...

Added: October 31, 2020

Rubchinskiy A., / Высшая школа экономики. Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2015. No. WP7/2015/09.

An algorithm of solution of the Automatic Classification (AC for brevity) problem is set forth in the paper. In the AC problem, it is required to find one or several partitions, starting with the given pattern matrix or dissimilarity / similarity matrix. The three-level scheme of the algorithm is suggested. The output of the procedure ...

Added: October 19, 2017

Bezhaeva Z., Oseledets V. I., / The Erwin Schrodinger International Institute for Mathematical Physics. Series "ESI preprints". 2008. No. 2087.

Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. ...

Added: April 12, 2012

Levshina N., Namboodiripad S., Allassonnière-Tang M. et al., Linguistics 2023 Vol. 61 No. 4 P. 825-883

This paper argues for a gradient approach to word order, which treats word order preferences, both within and across languages, as a continuous variable. Word order variability should be regarded as a basic assumption, rather than as something exceptional. Although this approach follows naturally from the emergentist usage-based view of language, we argue that it ...

Added: October 12, 2021

Kelbert E., World Literature Studies 2021 Vol. 13 No. 4 P. 55-70

This study considers the dialogue in the USSR between semiotics, cybernetics, and information theory, as a case study of the complexities of conceptual transfer between disciplines. Yuri Lotman’s use of the concept of entropy in literary criticism is especially telling. Information theory defines entropy in terms of a system’s complexity and predictability, while its metaphoric ...

Added: January 25, 2022

Kolesnikov A., Kosov E., Theory of Stochastic Processes 2017 Vol. 22 No. 38 P. 47-61

Let γ be the standard Gaussian measure on Rn and let Pγ be the space of probability measures that are absolutely continuous with respect to γ. We study lower bounds for the functional Fγ(µ) = Ent(µ) − 1 2W2 2 (µ, ν), where µ ∈ Pγ, ν ∈ Pγ, Ent(µ) = R log µ γ ...

Added: August 21, 2018

Zhukova G., Сметанин Ю. Г., Ulyanov M., , in : 2019 International Conference on Engineering Technologies and Computer Science (EnT). : IEEE, 2019. P. 43-47.

A qualitative analysis refers to the identification of the qualitative characteristics of a time series, such as its periodicity, final periodicity or near periodicity, convergence to the limit state, randomness, etc. For such an analysis, methods of symbolic dynamics are used, with the time series being represented as a sequence of symbols from a finite ...

Added: October 22, 2019

Demidovskij A., Bakhchina A., Sozinov A., International Journal of Psychophysiology 2016 Vol. 108 P. 148-149

The approach and withdrawal behaviors can be superficially similar. Howether, they differ in a number of cognitive, neurological and physiological characteristics (Carver et al., 2000; Elliot, 2006; Brunia et al., 2011; Franzen et al., 2015). The critical assumption for the present study is that these two types of behaviour are supported by distinct asymmetric domains ...

Added: October 15, 2018

Gromoff A., Bilinkis (Stavenko) J., Информационные технологии в проектировании и производстве 2011 № 3 С. 28-35

This article discusses and applies an approach to solution of business process monitoring task on the basis of study of entropy characters of an acting business system information field, which is considered from a view of behavior and modeling of open systems. Process flow continuity in time is taken to account. A method of stability ...

Added: December 10, 2012