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Abstract: The paper substantiates the concept of autoencoders focused on automatic generation of compressed images. We propose a solution to the problem of synthesizing such autoencoders in the context of machine learning methods, understood here as learning based on the input images themselves (in the bootstrap spirit). For these purposes, a special representation of images has been developed using samples of counts of a controlled size (sampling representations). Based on the specifics of this representation, a generative model of autoencoders is formalized, which is then specified to a probabilistic parametric sampling model in the form of a mixture of components. Based on the concept of receptive fields, a reduction of the general model of a mixture of components to a grid model of finite components of an exponential family is discussed. This allows the synthesis of computationally realistic coding algorithms. PubDate: 2022-12-01
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Abstract: We propose a procedure for developing an adaptive soft sensor using the example of an analyzer for a nonstationary mass-exchange process. The accuracy of the process output prediction is maximized (mean square error is minimized) by the process model error prediction, which is used as a correction to the process performance estimate. In the case of measurements of process characteristics equidistant in time, a measure of the proximity of the error spectrum distribution to the uniform distribution is used as an adaptation criterion. Such a criterion is essentially a “measure of proximity” of the process model to the optimal one. The advantage of the proposed criterion in comparison with the traditional ones, which measure the characteristics of the error spread, is that changes in the characteristics of the error spread of the model can be caused by reasons not related to the adequacy of the model. With nonequidistant measurements, the amplitudes of the harmonic components of the process are found, which permits one to reconstruct the values of the process characteristics at equidistant points in time using the inverse Fourier transform. In contrast to the traditionally used interpolation, this approach does not distort the spectrum of the process under consideration. PubDate: 2022-12-01
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Abstract: This thematic issue presents selected articles of the 20th All-Russian Conference with international participation “Mathematical Pattern Recognition Methods” (MPRM) held on December 7–10, 2021 in Moscow. PubDate: 2022-12-01 DOI: 10.1134/S00051179220120013
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Abstract: The paper presents a study of equilibrium in a two-sided market for network platforms with cross externalities between buyers and sellers. The proposed model is a generalization of Armstrong’s (2006) monopoly model for the case of a duopoly in a two-sided market for network platforms located on a plane. The paper solves the problem of optimal pricing and investigates the question of the optimal location of platforms in the market, provided that the heterogeneous utility of agents of both groups (buyers and sellers) is formed taking into account the Hotelling specification with the Manhattan metric. PubDate: 2022-12-01 DOI: 10.1134/S00051179220120128
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Abstract: Modern natural language processing models such as transformers operate multimodal data. In the present paper, multimodal data is explored using multimodal topic modeling on transactional data of bank corporate clients. A definition of the importance of modality for the model is proposed on the basis of which improvements are considered for two modeling scenarios: preserving the maximum amount of information by balancing modalities and automatic selection of modality weights to optimize auxiliary criteria based on topic representations of documents. A model is proposed for adding numerical data to topic models in the form of modalities: each topic is assigned a normal distribution with learning parameters. Significant improvements are demonstrated in comparison with standard topic models on the problem of modeling bank corporate clients. Based on the topic representations of the bank’s customers, a 90-day delay on the loan is predicted. PubDate: 2022-12-01 DOI: 10.1134/S00051179220120050
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Abstract: Сontrolling the docking of noncooperative spacecraft requires information about the relative position of the active and passive spacecraft. This problem is solved by relative optical navigation systems that analyze visible images, identify (recognize) the observed spacecraft, and measure relative linear and angular coordinates. Since the aspect at which the passive spacecraft is observed can vary over a wide range (up to a full sphere), the image of the passive spacecraft itself changes accordingly over a wide range. Therefore, to solve the identification and measurement problems, a sufficiently large number of reference images is required. The article proposes a way to considerably reduce the number of reference images used to form a cover of the uncertainty area. PubDate: 2022-12-01 DOI: 10.1134/S00051179220120062
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Abstract: The paper considers the problem of classifying 3553 English-language comments from the social network Reddit based on various approaches to the vectorization of comment texts, including bag of words, TF–IDF, bigrams analysis based on pointwise mutual information (PMI) and sentiments, and the deep model BERT of the language representation. The use of a hybrid approach based on text vectorization using BERT and bigrams analysis have made it possible to improve the quality of comments classification up to 91%. Based on a cluster analysis of 1857 English-language comments describing anxiety, clusters were identified using BERT+k-means. The study proposes a hybrid approach based on the use of the LDA topic modeling method, the VADER sentiments analysis method, pointwise mutual information, and parts of speech analysis and permitting one to select bigrams and trigrams to describe clusters of comments. To visualize the extracted patterns in the form of trigrams, a knowledge graph was constructed that describes the subject area, and a comparison of the words of the selected target trigrams with the words of a custom dictionary describing various affective disorders has made it possible to determine the types of psychosocial stressors associated with affective disorders. PubDate: 2022-12-01 DOI: 10.1134/S00051179220120025
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Abstract: We consider a new method to improve the quality of training in gradient boosting as well as to increase its generalization performance based on the use of modified loss functions. In computational experiments, the possible applicability of this method to improve the quality of gradient boosting when solving various classification and regression problems on real data is shown. PubDate: 2022-12-01 DOI: 10.1134/S00051179220120074
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Abstract: Interval systems of linear algebraic equations (ISLAE) are considered as a tool for constructing linear models based on data with interval uncertainty. Sufficient conditions for the boundedness and convexity of the admissible domain of ISLAE and its belonging to only one orthant of the \(n \) -dimensional space are proposed that are verifiable in polynomial time by methods of computational linear algebra. In this case, the admissible domain of ISLAE turns out to be a convex bounded polyhedron that lies entirely in some orthant. These properties of the admissible domain of ISLAE allow one, first, to find solutions to the corresponding ISLAE in polynomial time by linear programming methods (while the search for solutions to ISLAE of a general form is an NP-hard problem). Second, the coefficients of the linear model obtained by solving the corresponding ISLAE have an analog of the property of significance of the coefficient of the linear model, since the coefficients of the linear model do not change their sign within the admissible domain of ISLAE. The statement and proof of the corresponding theorem and an illustrative numerical example are presented. PubDate: 2022-12-01 DOI: 10.1134/S00051179220120037
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Abstract: To solve machine learning problems, we have developed a method to identify closed sets of common features of objects (patterns) of the training sample. The novelty of the method lies in the fact that it is implemented within the concept of constraint programming and uses a new type of table constraints—compressed tables of the \(D \) -type—for internal representation and processing of the training sample. Search reduction is achieved by applying the proposed method of branching the search tree and using partial order relations on sets of objects (features) to prune unpromising branches. The method has a computational complexity estimate that for some types of input data is better than the estimates obtained for the studied prototypes. PubDate: 2022-12-01 DOI: 10.1134/S00051179220120116
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Abstract: For a discrete-time superreplication problem, a guaranteed deterministic formulation is considered: the problem is to ensure the cheapest coverage of the contingent claim on an option under all scenarios that are set using a priori defined compacts depending on the price history. Price increments at each moment of time must lie in the corresponding compact sets. We consider a market with trading constraints and no transaction costs. The statement of the problem is game-theoretic in nature and leads directly to the Bellman–Isaacs equations. In this article, we introduce a mixed extension of the “market” pure strategies. Several results concerning game equilibrium are obtained. PubDate: 2022-12-01 DOI: 10.1134/S0005117922012013X
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Abstract: We consider the problem of data clustering using a heterogeneous ensemble with the use of a co-association matrix. A probabilistic model is stated that takes into account the correlation of evaluation functions with the help of which relationships are found between the characteristics of the ensemble and the quality indicators of the final solution. An expression for the optimal weights of basic algorithms for which the upper bound on the clustering error probability estimate is minimal is found. An experimental study of the proposed method has been carried out showing the method to be advantageous over a number of similar methods. PubDate: 2022-12-01 DOI: 10.1134/S00051179220120086
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Abstract: Machine translation is a natural language text processing task that aims to automatically translate input text from one language into another language. The currently known machine translation models show a fairly high quality of translation between large languages, but for smaller language areas, represented by less data, the problem is still not solved. Different methods are used to deal with various errors in automatic translation systems. This paper discusses approaches that use translation models of reverse language directions and improve consistency between translations of the same text using direct and reverse translation models. The paper presents a general theoretical justification for such methods in terms of solving the likelihood maximization problem and also proposes a method for stable training of modern models using cyclic translations. PubDate: 2022-12-01 DOI: 10.1134/S00051179220120049
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Abstract: We consider the problem of minimizing the fuel consumption of a subsonic turbojet passenger aircraft at the climb phase. In addition to fuel consumption, the objective function to be optimized includes the time spent at the climb phase, since climb optimization is part of the optimization problem for the entire flight with the requirement to arrive at a given point at a given time. Since at the end of the phase it is necessary to reach the given values of speed and altitude from which the cruising flight should begin, penalties for not reaching these values are added to the objective function. The value of the objective function is the result of a numerical solution of a system of differential equations; therefore, for optimization, a gradient-free search method is proposed using candidate points and taking into account constraints. An example of optimizing fuel consumption in comparison with a standard climb profile is considered for two options for the possible implementation of the control system: thrust and pitch control or only pitch control at a constant value of thrust control. PubDate: 2022-11-01 DOI: 10.1134/S00051179220110030
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Abstract: We consider the problem of a zero-sum differential tracking game with a quadratic performance functional in which the plant subjected to uncontrolled disturbances is described by a nonlinear ordinary differential equation. The synthesis of optimal controls is known to necessitate online solving a scalar Bellman–Isaacs partial differential equation that contains information about the trajectory of the process to be monitored. The lack of information about this process over the entire control interval makes the synthesized controls unimplementable. An algebraic method is proposed for solving the Bellman-Isaacs equation, which contains the current value of the monitored process. As an illustration of the results obtained, we give the simulation of the behavior of a nonlinear system with two players with an open control horizon. PubDate: 2022-11-01 DOI: 10.1134/S00051179220110042
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Abstract: We prove the existence of a Stackelberg equilibrium (in the style of M.S. Nikol’skii) for a nonlinear Volterra functional operator equation controlled by two players with the help of finite-dimensional program controls with integral objective functionals. On this way, we use our formerly proved results on the continuous dependence of the state and functionals on finite-dimensional controls and also the classical Weierstrass theorem. The property of being a singleton for the minimizer set of the first player is proved by M.S. Nikol’skii’s scheme applied earlier to a linear ordinary differential equation. PubDate: 2022-11-01 DOI: 10.1134/S00051179220110091
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Abstract: The present paper is a continuation of the series of articles [1, 2] and is devoted to solving the problem of estimating the parameters of hidden Markov models. The hidden state is a homogeneous Markov jump process with a finite set of states. The available observations are indirect and contain Wiener processes whose intensities are different and depend on the hidden state. Both the intensity matrix of Markov state transitions and the drift and diffusion parameters of the observations are subject to estimation. For identification, an iterative algorithm based on smoothing the state of the system based on observations over a fixed time interval is proposed. Then, according to these estimates, the parameters are reconstructed. The paper describes in detail all the numerical schemes for estimating the state and for identifying the parameters. A set of illustrative numerical examples is presented, demonstrating the high quality of the proposed identification estimates. PubDate: 2022-11-01 DOI: 10.1134/S00051179220110054
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Abstract: The article contains a survey of publications studying problems characterized by the presence of fast variables with various rates of change (time scales). We consider the passage to the limit from the solution of a perturbed problem to the solution of a degenerate one, asymptotic solutions of initial and boundary value problems, stability and controllability, asymptotic solutions of optimal control problems, and problems with “hidden” multi-tempo variables. In addition, problems with control constraints, game problems, and stochastic systems are given. The last section presents practical problems with multi-tempo fast motions. PubDate: 2022-11-01 DOI: 10.1134/S00051179220110017
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Abstract: We consider the game-theoretic problem of choosing optimal strategies for agents of the oligopoly market under a linear demand function and nonlinear agent cost functions. The influence of reflexive behavior on the number and properties of equilibria in the game is studied for agents with different types of cost functions: concave, corresponding to positive returns to scale, and convex, corresponding to a negative effect. It is proved that in the case of convex cost functions there is only one equilibrium, and in the case of concave cost functions there can be two equilibria, one less and the other greater than the equilibrium for linear costs. It has been established that for convex cost functions the equilibrium action increases with the growth of the agent’s reflexion and decreases with the growth of the environment’s reflexion, as in the model with linear cost functions. For concave cost functions, the influence of reflexion depends on the sign of the sum of conjectural variations \(S\) : with an increase in the agent’s reflexion, the greater equilibrium increases, while the smaller one decreases for \(S<0 \) , and vice versa for \(S>0 \) . PubDate: 2022-11-01 DOI: 10.1134/S00051179220110066
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