Article
Bayesian inference for spectral projectors of the covariance matrix
Let X_1,…,X_n be an i.i.d. sample in R^p with zero mean and the covariance matrix \Sigma^{*}. The classical PCA approach recovers the projector \P_J^{*} onto the principal eigenspace of \Sigma^{*} by its empirical counterpart \hat \P_J. Recent paper [24] investigated the asymptotic distribution of the Frobenius distance between the projectors \|\hat \P_J - \P_J^{*}\|_2, while [27] offered a bootstrap procedure to measure uncertainty in recovering this subspace \P_J^{*} even in a finite sample setup. The present paper considers this problem from a Bayesian perspective and suggests to use the credible sets of the pseudo-posterior distribution on the space of covariance matrices induced by the conjugated Inverse Wishart prior as sharp confidence sets. This yields a numerically efficient procedure. Moreover, we theoretically justify this method and derive finite sample bounds on the corresponding coverage probability. Contrary to [24, 27], the obtained results are valid for non-Gaussian data: the main assumption that we impose is the concentration of the sample covariance \hat \Sigma in a vicinity of \Sigma^{*}. Numerical simulations illustrate good performance of the proposed procedure even on non-Gaussian data in a rather challenging regime.
In this paper we improve the speed of the nearest neighbor classifiers of a set of points based on sequential analysis of high-dimensional feature vectors. Each input object is associated with a sequence of principal component scores of aggregated features extracted by deep neural network. The number of components in each element of this sequence is dynamically chosen based on explained proportion of total variance for the training set.We propose to process the next element with higher explained variance only if the decision for the current element is unreliable. This reliability is estimated by matching of the ratio of the minimum distance and all other distances with a certain threshold. Experimental study for face recognition with the Labeled Faces in the Wild and YouTube Faces datasets demonstrates the decrease of running time up to 10 times when compared to conventional instance-based learning.
The paper studies salient features of systemic risk in a sample of 22 European (EU and non-EU) countries during January 2010–March 2016. Building on a novel dataset and conducting an empirical horse race, we determine pivotal systemic risk measures for the sample countries. SRISK and volatility indicator tend to lead other metrics, followed by leverage. In contrast to the conventional wisdom, composite systemic risk measures aggregated with the aid of principal and independent component analysis perform worse. The leading systemic risk measures exhibit a high degree of connectedness. The VIX index, TED spread, the Composite Index of Systemic Stress (CISS) and long-term interest rates underlie their dynamics. Two clusters within the sample are identified, with CISS and long-term interest rates being crucial to distinguish between them. There is only scarce evidence for causal linkages between systemic risk and industrial production in the sample countries, based on the concurring results of standard and nonparametric Granger causality tests.
The paper is focused on the problem of balanced information and communication technologies development in modern society and its measures. Existing indices allow estimating the progress of this development, but they are mostly constructed for between countries comparison. At the lower level, we face the problem of different data set structure that does not allow us to use same indices immediately. Another problem is a lack of measures that provide both the estimation of the overall progress in ICT and the progress in its particular aspects at the regional level. Additional attention should be paid to the possible increase of regional differentiation in order to prevent its transformation into extreme form of digital divide. We propose the model in the form of hierarchical system of indices that includes the advantages of information development measurement in particular aspects and as a whole. Sub-indices in the system are just orthogonal, and widely used principal component analysis is not functional for their aggregation. That is why a measure of closeness of the aggregate indicator to the best possible value is used to create the main index. The output oriented data envelopment analysis is used along with the aggregate indicator construction technique to compare the positions of the most advanced regions. We also introduce the method of measuring the differentiation in some aspects of information and communication development to assess the dynamics of this differentiation. The results of the study can be used to stimulate progress in information and communication development that prevents an excessive increase in regional differentiation.
The authors attempted to establish methodology for constructing composite indicator to estimate the value and dynamic characteristics of the digital inequality. The trend of the modern development of the countries all over world is the course on the formation of the digital economy Вопросы статистики. 2018. Т. 25. № 4. С.75-87 76 Математико-статистические методы в оценке и анализе Введение Развитие технологий и стремительное изменение информационного пространства, породившие феномен «цифровой экономики», способствуют формированию новой инфраструктуры и бизнес-среды, открывают дополнительные возможности развития индивидов и социальных групп, обусловливают повышение качества жизни населения [1]. Вместе с тем появляются и новые вызовы и угрозы развитию общества. Меняется привычная среда жизнедеятельности людей, происходит трансформация рынка труда, меняются социальные отношения. Информация становится не просто средством производства, но и оказывает влияние на мировоззрение людей, становится мощным инструментом политического воздействия. Развитие цифровой экономики в свою очередь требует технологической модернизации и совершенствования социальной структуры общества: создания развитой инфраструктуры, технологий и платформ, обеспечивающих получение, обработку и хранение больших объемов информации; подготовки квалифицированных кадров; предоставления доступа к источникам информации для всех граждан при соблюдении законных интересов владельцев данных. Согласно принятым к 2017 г. документам долгосрочного планирования, к которым относятся «Стратегия развития информационного общества в Российской Федерации на 2017-2030 годы» (от 09.05.2017), а также программа «Цифровая экономика Российской Федерации», предусмотрены меры, направленные на стимулирование развития информационных и коммуникационных технологий и их использование в различных секторах экономики. Это свидетельствует об особом внимании к развитию цифровой экономики, а также потребности в адекватной оценке социально-экономических изменений, связанных с реализацией данных программ. Происходящие в обществе изменения в процессе перехода к цифровой экономике пока еще недостаточно изучены и требуют разработки и использования как новых показателей, позволяющих изучать современные процессы цифровой экономики, так и новых подходов и методик по изучению происходящих изменений на различных уровнях иерархии и эффектов от их воздействия на социальную среду. Основные этапы становления информационного общества Зарождение термина «информационное общество» произошло в Японии в 1960-е годы. В основу легло определение, данное в первой книге по указанной тематике Ю. Хаяши в 1969 г. «Информационное общество: от жесткого общества к мягкому» [2]. В 1983 г. Й. Масуда выпустил «Информационное общество как постиндустриальное общество» [3] - книгу, сразу же переведенную на английский язык и получившую широкую огласку в англоговорящем сообществе. С 1969 г. and the development of socio-economic relations based on digital interactions. In this regard the adoption of the «Strategy for the Development of the Information Society in the Russian Federation for 2017-2030» and the program «Digital Economy of the Russian Federation» proves to be relevant. The more so in the context of quite a noticeable socio-economic differentiation, there is a risk of the «digital divide» effect of the Russian regions, which will create additional difficulties for their development. After a brief historical overview of science and technology development stages (related to the digital economy) of the last decade and the reflection of this process in the scientific and professional literature and state programs of a number of countries, the authors review evolutionary aspects and challenges associated with implementation of programs such as the Nationwide program for informatization of society in Russia. The consolidated index of readiness of Russian regions to the information society, proposed by the Institute for the Development of the Information Society, has a number of shortcomings, which hinders its direct use for assessing digital inequality and comparing the regions of Russia according to the level of informatization in dynamics. The article examines the possibility of implementing the author’s idea of the improved integral indicator that would allow studying not only the development of the information society and Information and communication technologies (ICT) as a whole but also the interregional digital divide. The development of the new index considered the possibility of reflecting the degree of access of the population to ICT in the regions, taking into account technological factors.
Paper presents the computer simulation of laser gyros behavior under vibrations at the designing early stages. It allows for savings on repetitive tests and re-designing, finally improves reliability and economic efficiency of development and production.
We study the Gaussian and robust covariance estimation, assuming the true covariance matrix to be a Kronecker product of two lower dimensional square matrices. In both settings we define the estimators as solutions to the constrained maximum likelihood programs. In the robust case, we consider Tyler’s estimator defined as the maximum likelihood estimator of a certain distribution on a sphere. We develop tight sufficient conditions for the existence and uniqueness of the estimates and show that in the Gaussian scenario with the unknown mean, p/q+q/p+2 samples are almost surely enough to guarantee the existence and uniqueness, where p and q are the dimensions of the Kronecker product factors. In the robust case with the known mean, the corresponding sufficient number of samples is max[p/q,q/p]+1.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traffic is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the final node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a finite-dimensional system of differential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of differential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
For a class of optimal control problems and Hamiltonian systems generated by these problems in the space l 2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space l 2 forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.
The problem of minimizing the root mean square deviation of a uniform string with clamped ends from an equilibrium position is investigated. It is assumed that the initial conditions are specified and the ends of the string are clamped. The Fourier method is used, which enables the control problem with a partial differential equation to be reduced to a control problem with a denumerable system of ordinary differential equations. For the optimal control problem in the l2 space obtained, it is proved that the optimal synthesis contains singular trajectories and chattering trajectories. For the initial problem of the optimal control of the vibrations of a string it is also proved that there is a unique solution for which the optimal control has a denumerable number of switchings in a finite time interval.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.