An optimized Monte Carlo approach for multidimensional integrals related to intelligent systems

• Autorzy: Todorov, Venelin , Dimov, Ivan , Fidanova, Stefka , Georgieva, Rayna , Ostromsky, Tzvetan , Poryazov, Stoyan
• Konferencja: Federated Conference on Computer Science and Information Systems (17 ; 04-07.09.2022 ; Sofia, Bulgaria)
• Języki publikacji: EN

Abstrakty

EN

We study an optimized Monte Carlo algorithm forsolving multidimensional integrals related to intelligent systems. Recently Shaowei Lin consider the difficult task of evaluating multidimensional integrals with very high dimensions which are important to machine learning for intelligent systems. Lin multidimensional integrals with 3 to 30 dimensions, related to applications in machine learning, will be evaluated with the presented optimized Monte Carlo algorithm and some advantageous of the method will be analyzed.

Słowa kluczowe

PL

całka wielowymiarowa; system inteligentny; metoda Sobola; próbkowanie

EN

multidimensional integral; intelligent system; Latin hypercube sampling; Sobol sampling

• Czasopismo: Annals of Computer Science and Information Systems
• Rocznik: 2022
• Tom: Vol. 32
• Strony: 101--104
• Opis fizyczny: Bibliogr. 10 poz., tab., wz.

Twórcy

autor

Todorov, Venelin

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

autor

Dimov, Ivan

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

autor

Fidanova, Stefka

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

autor

Georgieva, Rayna

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

autor

Ostromsky, Tzvetan

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

autor

Poryazov, Stoyan

• Institute of Mathematics and Informatics Bulgarian Academy of Sciences 8 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria,

Bibliografia

• 1. Atanassov E. and Dimov I.T., A new optimal monte carlo method for calculating integrals of smooth functions, Journal of Monte Carlo Methods and Applications 5 (1999), no. 2, 149–167, https://doi.org/10.1515/mcma.1999.5.2.149.
• 2. Bratley P., Fox B., Algorithm 659: Implementing Sobol’s Quasirandom Sequence Generator, ACM Transactions on Mathematical Software, 14 (1), 1988, 88–100.
• 3. Dimov I., Monte Carlo Methods for Applied Scientists, New Jersey, London, Singapore, World Scientific, 2008, 291p.
• 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.
• 6. Minasny B., McBratney B.: A conditioned Latin hypercube method for sampling in the presence of ancillary information Journal Computers and Geosciences archive, Volume 32 Issue 9, November, 2006, Pages 1378-1388.
• 7. Paskov S.H., Computing high dimensional integrals with applications to finance, Technical report CUCS-023-94, Columbia University (1994).
• 8. Pencheva, V., Georgiev, I., & Asenov, A. (2021, February). Evaluation of passenger waiting time in public transport by using the Monte Carlo method. In AIP Conference Proceedings (Vol. 2321, No. 1, p. 030028). AIP Publishing LLC.
• 9. Song, J., Zhao, S., Ermon, S., A-nice-mc: Adversarial training for mcmc. In Advances in Neural Information Processing Systems, pp. 5140-5150, 2017.
• 10. Watanabe S., Algebraic analysis for nonidentifiable learning machines. NeuralComput.(13), pp. 899—933, April 2001.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).

Identyfikatory

DOI

10.15439/2022F84