Mathematics

Permanent URI for this community

https://testres.nu.edu.kz/handle/123456789/511

Browse

Browsing Mathematics by Author "Assylbekov, Zhenisbek"

Now showing 1 - 5 of 5
  • No Thumbnail Available
    ItemOpen Access
    A free/open-source hybrid morphological disambiguation tool for Kazakh
    (DOI: 10.13140/RG.2.2.12467.43045, 2016-04) Assylbekov, Zhenisbek; Washington, Jonathan; Tyers, Francis; Nurkas, Assulan; Sundetova, Aida; Karibayeva, Aidana; Abduali, Balzhan; Amirova, Dina
    This paper presents the results of developing a morphological disambiguation tool for Kazakh. Starting with a previously developed rule-based approach, we tried to cope with the complex morphology of Kazakh by breaking up lexical forms across their derivational boundaries into inflectional groups and modeling their behavior with statistical methods. A hybrid rule-based/statistical approach appears to benefit morphological disambiguation demonstrating a per-token accuracy of 91% in running text.
  • Thumbnail Image
    ItemOpen Access
    Convergence Rate of Fourier Neural Networks
    (Nazarbayev University School of Science and Technology, 2019-04-26) Zhumekenov, Abylay; Assylbekov, Zhenisbek; Tourassis, Vassilios D.
    The paper investigates a convergence rate for 2-layer feedforward Fourier Neural Network (FNN). Such networks are motivated by the approximation properties of wellknown Fourier series. Several implementations of FNNs were proposed since 1990’s: by Gallant and White; A. Silvescu; Tan, Zuo and Cai; Liu. The main focus of this research is Silvescu’s FNN, because such activation function does not fit into the category of networks, where the linearly transformed input is exposed to activation. The latter ones were extensively described by Hornik in 1989. In regard to non-trivial Silvescu’s FNN, its convergence rate is proven to be of order 𝑂(1/𝑛). The paper continues investigating classes of functions approximated by Silvescu FNN, which appeared to be from Schwartz space and space of positive definite functions.
  • Thumbnail Image
    ItemOpen Access
    Copula functions in Credit Metrics’ VaR estimation
    (Nazarbayev University School of Science and Technology, 2019-08-08) Magzanov, Shynggys; Wei, Dongming; Assylbekov, Zhenisbek
    Credit risk modelling of a portfolio of exposures is essential part of activity of every financial institution. However this procedure is complicated since the joint behavior of chosen exposures must be known. In this paper Value at Risk percentile of the portfolio consisting of three corporate bonds issued by Lukoil, Gazprom and Norilsk Nickel was estimated at three different significance levels within the frame of Credit Metrics approach proposed by J.P.Morgan. Following the Asset value model, Monte-Carlo simulations were performed to obtain possible portfolio values in one year time horizon. Where the joint distribution of asset returns of three companies was constructed by means of pair-copula construction method discussed in Aas, Czado, Frigessi,Bakken (2009). Results reveal that for particular portfolio of bonds at 90%, 95% and 99% confidence levels the value of our portfolio will not fall below 2057.915 ,1798.117 and 1375.011 dollars respectively.
  • No Thumbnail Available
    ItemOpen Access
    Experiments with Russian to Kazakh sentence alignment
    (The 4-th International Conference on Computer Processing of Turkic Languages “TurkLang 2016”, 2016) Assylbekov, Zhenisbek; Myrzakhmetov, Bagdat; Makazhanov, Aibek
    Sentence alignment is the final step in building parallel corpora, which arguably has the greatest impact on the quality of a resulting corpus and the accuracy of machine translation systems that use it for training. However, the quality of sentence alignment itself depends on a number of factors. In this paper we investigate the impact of several data processing techniques on the quality of sentence alignment. We develop and use a number of automatic evaluation metrics, and provide empirical evidence that application of all of the considered data processing techniques yields bitexts with the lowest ratio of noise and the highest ratio of parallel sentences.
  • Thumbnail Image
    ItemOpen Access
    Explorations on chaotic behaviors of Recurrent Neural Networks
    (Nazarbayev University School of Science and Technology, 2019-04-29) Myrzakhmetov, Bagdat; Assylbekov, Zhenisbek; Takhanov, Rustem; Tourassis, Vassilios D.
    In this thesis work we analyzed the dynamics of the Recurrent Neural Network architectures. We explored the chaotic nature of state-of-the-art Recurrent Neural Networks: Vanilla Recurrent Network, Recurrent Highway Networks and Structurally Constrained Recurrent Network. Our experiments showed that they exhibit chaotic behavior in the absence of input data. We also proposed a way of removing chaos chaos from Recurrent Neural Networks. Our findings show that initialization of the weight matrices during the training plays an important role, as initialization with the matrices whose norm is smaller than one will lead to the non-chaotic behavior of the Recurrent Neural Networks. The advantage of the non-chaotic cells is stable dynamics. At the end, we tested our chaos-free version of the Recurrent Highway Networks (RHN) in a real-world application. In a sequence-to-sequence modeling experiments, particularly in the language modeling task, chaos-free version of RHN perform on par with the original version by using the same hyperparameters.