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Sparse polynomial prediction

Author

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  • Maruri-Aguilar, Hugo
  • Wynn, Henry

Abstract

In numerical analysis, sparse grids are point configurations used in stochastic finite element approximation, numerical integration and interpolation. This paper is concerned with the construction of polynomial interpolator models in sparse grids. Our proposal stems from the fact that a sparse grid is an echelon design with a hierarchical structure that identifies a single model. We then formulate the model and show that it can be written using inclusion–exclusion formulæ. At this point, we deploy efficient methodologies from the algebraic literature that can simplify considerably the computations. The methodology uses Betti numbers to reduce the number of terms in the inclusion–exclusion while achieving the same result as with exhaustive formulæ.

Suggested Citation

  • Maruri-Aguilar, Hugo & Wynn, Henry, 2023. "Sparse polynomial prediction," LSE Research Online Documents on Economics 118748, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:118748
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    File URL: http://eprints.lse.ac.uk/118748/
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    Cited by:

    1. Huicong Zhong & Xiaobing Feng, 2023. "An Efficient and Fast Sparse Grid Algorithm for High-Dimensional Numerical Integration," Mathematics, MDPI, vol. 11(19), pages 1-26, October.

    More about this item

    Keywords

    Betti numbers; inclusion–exclusion; Smolyak grids; sparse designs;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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