Logo PTI Logo FedCSIS

Communication Papers of the 17th Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 32

An Optimized Monte Carlo Approach for Multidimensional Integrals Related to Intelligent Systems

, , , , ,

DOI: http://dx.doi.org/10.15439/2022F84

Citation: Communication Papers of the 17th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 32, pages 101–104 ()

Full text

Abstract. 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.

References

  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.