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Advanced Stochastic Approaches for Multidimensional Integrals in Neural Networks

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Recent Advances in Computational Optimization (WCO 2020)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 986))

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Abstract

A very important problem in the area of neural networks and machine learning is the accurate evaluation of multidimensional integrals. An introduction to the theory of the stochastic approaches with a special choice of 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 100-dimensions. It is shown that the progress in the area of machine learning is strictly related to the progress in reliable algorithms for multidimensional integration.

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Acknowledgements

The work is supported by Project KP-06-Russia/17 “New Highly Efficient Stochastic Simulation Methods and Applications” funded by National Science Fund - Bulgaria. Venelin Todorov is supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICT in SES)”, contract No DO1-205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria and by the Bulgarian National Science Fund under Project DN 12/5-2017 “Efficient Stochastic Methods and Algorithms for Large-Scale Problems”. Stoyan Apostolov is supported by the Bulgarian National Science Fund under Young Scientists Project KP-06-M32/2 - 17.12.2019 “Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics”.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Department of Information Modeling, Acad. Georgi Bonchev Str., Block 8, 1113, Sofia, Bulgaria

    Venelin Todorov & Stoyan Poryazov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Department of Parallel Algorithms, Acad. G. Bonchev Str., Block 25 A, 1113, Sofia, Bulgaria

    Venelin Todorov, Stefka Fidanova & Ivan Dimov

  3. Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria

    Stoyan Apostolov

  4. Department of Electrical Power Engineering, University of Ruse “Angel Kanchev”, Ruse, Bulgaria

    Daniel Todorov

Authors
  1. Venelin Todorov
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  2. Stefka Fidanova
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  3. Ivan Dimov
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  4. Stoyan Poryazov
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  5. Stoyan Apostolov
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  6. Daniel Todorov
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Corresponding author

Correspondence to Venelin Todorov .

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Editors and Affiliations

  1. Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

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Todorov, V., Fidanova, S., Dimov, I., Poryazov, S., Apostolov, S., Todorov, D. (2022). Advanced Stochastic Approaches for Multidimensional Integrals in Neural Networks. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. WCO 2020. Studies in Computational Intelligence, vol 986. Springer, Cham. https://doi.org/10.1007/978-3-030-82397-9_22

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