A New Optimized Stochastic Approach for Multidimensional Integrals in Machine Learning

• Autorzy: Todorov Venelin , Apostolov Stoyan , Dimov Ivan , Fidanova Stefka

Identyfikatory

DOI

10.15439/2020F110

• Konferencja: Federated Conference on Computer Science and Information Systems (15 ; 06-09.09.2020 ; Sofia, Bulgaria)
• Języki publikacji: EN

Abstrakty

EN

Stochastic techniques have been developed over many years in a range of different fields, but have only recently been applied to the problems in machine learning. A fundamental problem in this area is the accurate evaluation of multidimensional integrals. An introduction to the theory of the stochastic optimal generating vectors has been given. A new optimized lattice sequence with a special choice of the optimal generating vector have been applied to compute multidimensional integrals up to 30-dimensions. Clearly, the progress in the area of machine learning is closely related to the progress in reliable algorithms for multidimensional integration.

Słowa kluczowe

EN

integration; artificial intelligence; optimisation; stochastic processes; vectors

PL

integracja; sztuczna inteligencja; optymalizacja; procesy stochastyczne; wektory

• Wydawca: Polskie Towarzystwo Informatyczne
• Czasopismo: Annals of Computer Science and Information Systems
• Rocznik: 2020
• Tom: Vol. 21
• Strony: 337--340
• Opis fizyczny: Bibliogr. 10 poz., wz., tab.

Twórcy

autor

Todorov Venelin

• Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, ul. G. Bonchev 8, 1113 Sofia, Bulgaria
• Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, ul. G. Bonchev 25A, 1113 Sofia, Bulgaria

autor

Apostolov Stoyan

• Sofia University, Faculty of Mathematics and Informatics, 1764 Sofia, Bulgaria

autor

Dimov Ivan

• Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, ul. G. Bonchev 25A, 1113 Sofia, Bulgaria

autor

Fidanova Stefka

• Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, ul. G. Bonchev 25A, 1113 Sofia, Bulgaria

Bibliografia

• 1. N. Bahvalov (1959) On the approximate calculation of multiple integrals, Journal of Complexity, Volume 31, Issue 4, 2015, Pages 502-516, ISSN 0885-064X, https://doi.org/10.1016/j.jco.2014.12.003.
• 2. Dimov I., Monte Carlo Methods for Applied Scientists, New Jersey, London, Singapore, World Scientific, 2008, 291p.
• 3. Hua, L.K. and Wang, Y., Applications of Number Theory to Numerical analysis, 1981.
• 4. Lin S., “Algebraic Methods for Evaluating Integrals in Bayesian Statistics,” Ph.D. dissertation, UC Berkeley, May 2011.
• 5. Lin, S., Sturmfels B., Xu Z.: Marginal Likelihood Integrals for Mixtures of Independence Models, Journal of Machine Learning Research, Vol. 10, pp. 1611-1631, 2009, https://doi/10.5555/1577069.1755838.
• 6. Kuo, F.Y., Nuyens, D. Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation. Found Comput Math 16, 16311696 (2016). https://doi.org/10.1007/s10208-016-9329-5.
• 7. Sloan I.H. and Kachoyan P.J., Lattice methods for multiple integration: Theory, error analysis and examples, SIAM J. Numer. Anal. 24, pp. 116–128, 1987, https://doi.org/10.1137/0724010.
• 8. Wang Y., Hickernell F.J. (2002) An Historical Overview of Lattice Point Sets. In: Fang KT., Niederreiter H., Hickernell F.J. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56046-010.
• 9. Watanabe S., Algebraic analysis for nonidentifiable learning machines. NeuralComput.(13), pp. 899-933, April 2001, https://doi.org/10.1162/089976601300014402.
• 10. Zheleva, I., Georgiev, I., Filipova, M., & Menseidov, D. (2017, October). Mathematical modeling of the heat transfer during pyrolysis process used for end-of-life tires treatment. In AIP Conference Proceedings (Vol. 1895, No. 1, p. 030008). AIP Publishing LLC, https://doi.org/10.1063/1.5007367.

Uwagi

1. Track 1: Artificial Intelligence

2. Technical Session: 13th International Workshop on Computational Optimization

3. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).