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“Informatics and Applications” scientific journalVolume 19, Issue 2, 2025Content Abstract and Keywords About Authors ESTIMATION OF PARAMETERS OF A MIXTURE OF NORMAL MULTIVARIATE DISTRIBUTIONS WITH CONSTRAINTS ON COVARIANCE MATRICES
Abstract: The formulation and method of solving the problem of finding an estimate of the maximum likelihood of the parameters of a mixture of normal multidimensional distributions that allow excluding the occurrence of "infinitely" large values of the likelihood function are considered. It is proposed to condition the set of possible covariance matrices so that they do not become singular. To do this, a boundary Keywords: mixture of normal multivariate distributions; maximum likelihood estimate; EM-algorithm UNBIASED RISK ESTIMATE FOR THE FIRM SHRINKAGE METHOD OF SOLVING LINEAR INVERSE PROBLEMS
Abstract: Inverse statistical problems arise in such areas as astronomy, plasma physics, computational tomography, etc. In this case, the observed data usually contain noise and, therefore, it is necessary to apply noise suppression methods. In situations where the problem is related to the inversion of a linear homogeneous operator, noise suppression methods based on the wavelet transform and thresholding procedures have proven themselves to be effective. These methods are computationally efficient and adapt well to local features of signals. The most common types of thresholding are hard and soft thresholding. However, hard thresholding produces estimates with a large variance, while soft thresholding introduces additional bias. In an attempt to get rid of these drawbacks, various alternative types of thresholding have been proposed in recent years. This paper considers a thresholding procedure with two thresholds, which behaves like soft thresholding for small values of wavelet coefficients and like hard thresholding for large values. For this type of thresholding, an unbiased estimate of the mean-square risk is constructed and its statistical properties are analyzed. An algorithm for calculating the threshold that minimizes this estimate is also described. Keywords: wavelets; threshold processing; linear homogeneous operator; unbiased risk estimate A MODIFIED EXTENDED KALMAN FILTER BY THE LINEAR PSEUDOMEASUREMENT METHOD
Abstract: The paper proposes a modification of the linear pseudomeasurement method for the Extended Kalman Filter. It is intended for use in a typical discrete stochastic observation system model. The modified filter allows one to use both bearing measurements of a moving object and range measurements. To form linear pseudomeasurements, linearization of trigonometric functions of bearing measurements and approximation (minimax or integral) of measurement errors and linearization errors are performed. The range of applied tasks solved by the modified filter includes typical navigation tasks, in particular, those solved for autonomous aircraft and underwater vehicles. Experimental calculations were performed for a model example describing the movement of an autonomous aircraft observed by a stationary radar system. Keywords: discrete stochastic observation system; linear pseudomeasurement; Extended Kalman Filter; target tracking; radar observations COMPLEX STATISTICAL CRITERION CONDITIONALLY OPTIMAL FILTERING METHODS FOR OBSERVABLE IMPLICIT STOCHASTIC SYSTEMS
Abstract: Paper is devoted to exact and approximate based on complex statistical criterion (CSC) conditionally- optimal filtering (COF) methods for continuous and discrete observable implicit non-Gaussian stochastic systems (StS) reducible to explicit. Survey of COF based on mean square criterion for explicit and implicit StS and CSC COF for explicit StS is given. Reduction methods for smooth and discontinuous implicit functions are presented.
Keywords: conditionally-optimal (in Pugachev sense) filter; normal approximation method (NAM); normal suboptimal filter (NSOF); stochastic process (StP); stochastic system (StS) MATHEMATICAL SUPPORT FOR MONITORING OF STATES AND NUMERICAL CHARACTERISTICS OF NETWORK CONNECTION BASED ON COMPOUND STATISTICAL INFORMATION
Abstract: The paper focuses on the application of optimal filtering methods to estimate the current qualitative states and numerical characteristics of a TCP link. The available statistical information includes measurements of round-trip times, jitter, and the flows of packet losses and timeouts. The evolution of the link state is modeled using a special class of Markov jump processes where one set of components defines the qualitative state of the channel while the other represents its quantitative characteristics. The proposed stochastic model and measurement structure enable the filtering ofboth the state and characteristics of the TCP link, yielding estimates that are optimal in both the class of linear and arbitrary transformations of the available observations. A numerical example is provided to validate the accuracy of these estimates. Keywords: special Markov jump process; optimal filtering estimate; stochastic differential observation system; Kushner-Stratonovich equation; Kalman-Bucy filter ABOUT AN ALGORITHM FOR GEOMETRIC MODELING OF STRUCTURES BASED ON THE RESULTS OF LASER SCANNING
Abstract: Laser scanner technology makes it possible to obtain point images of surfaces with a high degree of detail; so, the task of reconstructing a surface (area) from a point cloud has recently attracted a lot of attention. This is a problem faced in reverse engineering, archaeology, etc. The main difficulty that arises when solving general surface restoration problems is that the surface to be restored is usually not a graph of some scalar function. One of the methods used to solve the reconstruction problem is a method based on wavelets and the Bregman algorithm, which is used to find the coefficients of decomposition of the desired function defining the area by scaling functions.
Keywords: wavelet; wavelet frame; wavelet transform; discrete Fourier transform; geometric modeling; Bregman algorithm METRIZATION OF DISCRETE TOPOLOGICAL SPACES IN THE CONTEXT OF LATTICE THEORY. PART 2. PRACTICAL ANALYSIS OF THE CONSEQUENCES OF THE THEOREM ON REGULARITY AND NORMALITY
Abstract: In the first part, a theorem has been proved that connects the concept of normality of topological spaces and regularity according to Yu. I. Zhuravlev, in the context of the problem of metrization of feature spaces. The consequences of the theorem allow one to systematize the search for the most acceptable problem- oriented metrics. Promising directions for further research have been systematized, including the transition to a lattice of feature values and promising functionals for generating synthetic features. The results of the corresponding computational experiments are presented. Keywords: topological data analysis; algebraic approach of Yu. I. Zhuravlev and K. V. Rudakov; computational experiment; synthetic features MACHINE LEARNING AND TRUST IN CLASSIFICATION RESULTS
Abstract: It is generally accepted that trust in the artificial intelligence system is determined by the confidence of the consumer and regulatory organizations that this system is capable ofperforming the tasks assigned to it with the required quality. In the scientific literature, we are talking only about increasing trust but not about guaranteeing trust in the results ofartificial intelligence. In the interpretation ofincreasing trust, it is natural to believe that there is no trust in the results ofthe work ofartificial intelligence. In this article, a mathematical model is built, within the framework of which it is proved that in the class of artificial intelligence systems built on machine learning, there can be no guarantees of trust. The concept of "the trust in classifier" is defined if it correctly classifies new data with probability 1. The result was obtained under the conditions of the classical data space RL and a set of uniform distributions. The model can be complicated by leaving the space metric and the distributions continuous. In this case, trust does not depend on the capabilities of the classifier and on the generalization property. Keywords: machine learning; trust; classification; causal relationships CONCEPTUAL MODEL FOR PROBLEM STRUCTURE IDENTIFICATION IN HYBRID INTELLIGENT MULTIAGENT SYSTEMS
Abstract: The paper is aimed at developing research in the field of automatic solving of practical problems, the complexity of which is due to the vagueness of their definition and weak formalization; at the time of the problem occurrence, there is often no clear understanding of its essence and boundaries, which requires additional efforts to identify and describe them. One of the traditional approaches to manual and automated solution of practical problems, which is their decomposition into parts that can be solved by existing methods, requires significant time and labor resources. In this paper, based on traditional approaches to problem decomposition, a conceptual model of the method of automatic identification of its structure based on prototype frame models is built for use in hybrid intelligent multiagent systems to reduce labor costs at the initial stage of the solution. Keywords: problem; conceptual model; decomposition; reduction; team of specialists; hybrid intelligent multiagent system
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is introduced for the eigenvalues of the estimated covariance matrices of the elements of the mixture. Correction of small eigenvalues, smaller than  | |
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