Search results for “analysis”

Наивная теория множеств и парадокс Рассела, упорядоченная пара по Куратовскому и декартово произведение, функция как подмножество произведения, композиция, инъекции, сюръекции и биекции, группа биекций и вложение в неё любой группы, равномощность и индикаторы, теоремы Кантора–Бернштейна и Кантора.

Topic modeling is an area of text analysis actively developing over the past 20 years. A probabilistic topic model (PTM) finds a set of hidden topics from a collection of text documents. It defines each topic as a probability distribution over words and describes each document as a probability mixture of topic distributions. Learning algorithms for topic models are usually based on Bayesian inference or log-likelihood maximization. In both cases, EM-like algorithms are used. In this paper, we propose to replace the logarithm in the log-likelihood by an arbitrary smooth loss function. We prove that such a modification preserves both the structure of the algorithm and compatibility with any regularizers in terms of additive regularization of topic models (ARTM). Moreover, in the case of a linear loss, the Estep becomes much faster due to the omission of a normalization. We study combinations of the fast and usual E-steps and compare them to regularization using different number of topics in both offline and online versions of EM-algorithm. For an empirical comparison of the algorithms, we estimate perplexity, coherence, and learning time. We use an efficient parallel implementation of the EM-algorithm from the BigARTM open-source library. We show that in most cases the two-stage strategy wins, which uses fast E-steps at the beginning of iterations, then proceeds with usual E-steps.

Probabilistic topic modeling of text collections is a powerful tool for statistical text analysis based on the preferential use of graphical models and Bayesian learning. Additive regularization for topic modeling (ARTM) is a recent semiprobabilistic approach, which provides a simpler inference for many models previously studied only in the Bayesian settings. ARTM reduces barriers to entry into topic modeling research field and facilitates combination of topic models. In this paper we develop the multimodal extension of ARTM approach and implement it in BigARTM open source project for online parallelized topic modeling. We demonstrate the ability of non-Bayesian regularization to combine modalities, languages and multiple criteria to find sparse, diverse, and interpretable topics.

This article proposes a new approach for building topic models on unbalanced collections in topic modelling, based on the existing methods and our experiments with such methods. Real-world data collections contain topics in various proportions, and often documents of the relatively small theme become distributed all over the larger topics instead of being grouped into one topic. To address this issue, we design a new regularizer for and matrices in probabilistic Latent Semantic Analysis (pLSA) model. We make sure this regularizer increases the quality of topic models, trained on unbalanced collections. Besides, we conceptually support this regularizer by our experiments.

Movielens dataset has become a default choice for recommender systems evaluation. In this paper we analyze the best strategies of a Reinforcement Learning agent on Movielens (1M) dataset studying the balance between precision and diversity of recommendations. We found that trivial strategies are able to maximize ranking quality criteria, but useless for users of the recommendation system due to the lack of diversity in final predictions. Our proposed method stimulates the agent to explore the environment using the stochasticity of Ornstein-Uhlenbeck processes. Experiments show that optimization of the Ornstein-Uhlenbeck process drift coefficient improves the diversity of recommendations while maintaining high nDCG and HR criteria. To the best of our knowledge, the analysis of agent strategies in recommendation environments has not been studied excessively in previous works.

With the increasing popularity of cashless payment methods for everyday, seasonal and special expenses popular banks accumulate huge amount of data about customer operations. In the article, we report a successful application of topic modelling to extract behaviour patterns from the data. The resulting models are built with BigARTM framework: flexible and efficient tool for topic modelling. The framework allows us to experiment with various models including PLSA, LDA and beyond. Results demonstrate ability of the approach to aggregate information about behaviour patterns of different customer groups. The results analysis allows to see the topics of such people clusters varying from travellers to mortgage holders. Moreover, low-dementional embeddings of the customers, which was given with topic model, were studied. We display that the client vector representations store demographic information as well as source data. We also test for a best way of preparing data for the model with metric above in mind.

The article examines the issue of representing municipal government in the media space, followed by the proposed solution for automatically identifying signs of destructive and constructive positioning of communicative types of municipal employees in the public information space. The definition of the concept of the communicative type “municipal employee” with verification features is introduced. The results of the analysis of the organization of local self-government on the example of the Moscow region allowed us to conclude that the communicative type “municipal employee” reflects a diversified system of territorial communicative position within the regional government. The information obtained during the analysis of public information space attitudes regarding the activities of municipal employees can be automated with the method of identifying linguistic markers of emotivity to determine the communicative position of territorial authorities. The suggested methodology for effective automation of the studied subject area in the humanities has been verified as possessing a high scientific potential for further research. It is concluded that the development of technology for monitoring and forecasting public threats based on “soft power” methods through automatic and expert work to identify markers of evaluative presentation of communicative types of municipal employees is designed to help regional authorities achieve the desired results in ensuring territorial identity.

The Millennium Meeting, Paris, 24 May 2000, at which the seven problems were announced.

Three general methods for obtaining exact bounds on the probability of overfitting are proposed within statistical learning theory: a method of generating and destroying sets, a recurrent method, and a blockwise method. Six particular cases are considered to illustrate the application of these methods. These are the following model sets of predictors: a pair of predictors, a layer of a Boolean cube, an interval of a Boolean cube, a monotonic chain, a unimodal chain, and a unit neighborhood of the best predictor. For the interval and the unimodal chain, the results of numerical experiments are presented that demonstrate the effects of splitting and similarity on the probability of overfitting.

It is shown that computationally tight bounds for the probability of overfitting can be obtained only by simultaneous consideration of the following two properties of classifier sets: splitting into error levels and similarity of classifiers. For a set consisting of only two classifiers, an exact bound is obtained for the probability of overfitting. This is the simplest learning task that exhibits overfitting and the effects of splitting and similarity, which reduce the probability of overfitting. For a more complex case—a chain of classifiers—an experiment is carried out in which the effects of splitting and similarity are estimated separately. It is shown that reasonably low probabilities of overfitting can be obtained only for the sets that possess both properties.

Two methods for solving a SLAE — Cramer's rule via determinants and the universal Gaussian elimination method, with examples.

How to bring up a twenty-year-old Unix TCAD package under emulation on an ARM Mac, drive it from Jupyter, and parse its data formats in Python

Recommended for publication at the Journal of Algebraic Geometry; under review.

Linear systems in matrix form, the Kronecker–Capelli theorem, homogeneous systems, and the fundamental system of solutions.