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 Выпуск 82
- Belov M., Novikov D., Rogatkin A. Learning curves estimates
Iterative learning as learning in strictly repeating conditions is one of the simplest varieties of learning; it underlies the formation of human skills, conditioned reflexes in animals, the training of many technical (materialized) and cybernetic (abstract-logical) systems and is the subject of research in pedagogy, psychology and physiology of humans and animals, in control theory and in other sciences. For the model of individual learning in discrete time, upper and lower bounds for learning curves are obtained, their asymptotic behavior in time and parameter values is characterized. For the model of joint learning in continuous time, upper and lower bounds are obtained, as well as a lower asymptotic (by the number of agents) estimate of the aggregated level of learning. Stochastic asymptotic (in time) estimates of the learning process are presented, and confidence intervals for the values of the learning level are obtained.
- Belomestny D., Iosipoi L. On density estimation via Fourier series
In this paper, we consider the classical statistical problem of probability density estimation based on a sample from this distribution. This problem naturally arises in many applications when one aims at investigation of a probability structure in a random process. For instance, it is possible to identify some structure in a complex system using density estimation. In this paper, a new approach to estimate a density function is proposed. This approach is based on approximation of a log-density via Fourier series with coefficients obtained by solving a system of linear equations. Analysis of theoretical properties of such estimate is the main purpose of this work. As the main results, we prove bounds on the difference between target density and its approximation in the supremum norm and the Kullback-Leibler divergence. Obtained rates are parametric and have order with high probability, which is a standard rate in parametric estimation problems. The constants in the rates are obtained up to an absolute factor, which means that we investigated the dependence on all parameters. As a numerical example, we consider a problem of Cauchy density estimation.
- Korneenko V. Optimization method of selecting the resulting ranking of objects presented inrank scale of measurement
At present, there is no optimal method for constructing the resulting ranking, known as the Kemeny-Snell median, according to the matrix criterion between orderings of objects by experts, represented by matrices of binary relations on a set of pairs of objects. However, the task of constructing the resulting ranking according to the matrix criterion between orderings of objects by experts represented by matrices of binary relations on a set of pairs of objects can be reduced to an equivalent optimization problem if the ranking of objects is presented in a ranking scale of measurements. In this case, the distance between the object rankings presented in the form of vector rank ratings, including taking into account the ratings of objects with related ranks, acts as an optimality criterion. The article shows that the introduced distances between the ranking of objects in the rank scale satisfy the traditional axioms of metric space. The validity of the transition from the statement of the problem of constructing the Kemeny-Snell median by the matrix criterion to the statement of the problem by the criterion of proximity between rankings in the rank scale is related to the fact that between the rankings represented by the binary relations matrices on the set of pairs of objects and the rankings in the rank scale, As shown in this article, there is a one-to-one correspondence.
- Tsurko V. Recommender systems in the healthcare
Recommender systems are wide spread in Internet services: contextual advertising, movies and music interesting for an user, selection of goods and services in online stores. Algorithms take into account users' profiles, history of requests and sales and the data about similar users. These algorithms develop very fast and show its effectiveness, its implementation increase the service attendance and sales. Healthcare is the new area of recommender systems application. It is collected a huge amount of medical data such as medical records, mortality and morbidity databases, treatment protocols, and even health data continuously monitored by special sensors. Ones develop intelligent systems for primary care, choosing the treatment, daily human health tracking. The article provides the general introduction to the recommender systems, the literature review of recommender systems usage in the healthcare, and also addresses the problem of building recommender systems for optimizing hospital procurement.
- Pavlov D., Petrov D. The application of the new method for mathematical modelling of abnormal operation of the onboard systems of the spacecraft
The article is devoted to software design of lumped-element simulation models of the spacecraft subsystems. Considered type of engineering systems could be complicated due to 1) non-linear relations impact, 2) bi-directional bonds and 3) distributed structure, including huge element count and complex bonds network. In the previous publications we suggested a new approach for simulation models design to address the items above. Based on the new approach we implemented software package to create simulation models of engineering systems. Unlike known analogues, the package equipped with non-linear solver is capable to model non- linear physics. With this package a model could be constructed just via combining of available physical domains, no additional source code required. Spacecraft thermal control subsystem was modelled with the package. In this article we modified previously developed model of thermal control subsystem to simulate several failures, including the leakage of the hydraulic circuit. This requires to update the models of elements of the subsystem to become adequate at a low liquid pressure. We model the subsystem evolution taking into account considered failures under different external conditions and got expected results.
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