Аддитивная регуляризация тематических моделей
Probabilistic topic models discover a low-dimensional interpretable representation of text corpora by estimating a multinomial distribution over topics for each document and a multinomial distribution over terms for each topic. A unied family of expectation-maximization (EM) like algorithms with smoothing, sampling, sparsing, and robustness heuristics that can be used in any combinations is considered. The known models PLSA (probabilistic latent semantic analysis), LDA (latent Dirichlet allocation), SWB (special words with background), as well as new ones can be considered as special cases of the presented broad family of models. A new simple robust algorithm suitable for sparse models that do not require to estimate and store a big matrix of noise parameters is proposed. The present authors nd experimentally optimal combinations of heuristics with sparsing strategies and discover that sparse robust model without Dirichlet smoothing performs very well and gives more than 99% of zeros in multinomial distributions without loss of perplexity.
The aim of this article is to analyze the discursive background for the characters of teachers in the Soviet school story of the afterwar period. The 1,8 million words corpus for the study was compiled of the novels about school and schooling by 37 authors, written in 1940-s — 1980-s. The contents of the episodes where the keywords (headmaster, deputy headmaster, teacher, female teacher) were mentioned was analyzed automatically with the help of probabilistic topic modeling (LDA). Topics significantly more or less common in these episodes than in the whole corpus were used to characterize discursive context for the keywords. Judging by the thematic profile the term ‘female teacher’ is opposed to all the rest, Meaningful contrasts distinguishing the thematic ptofiles of the terms are: disourse of the upbringing and everyday schooling, komsomol and pioneers, emotions and gender.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.
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.