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Sparse polynomial prediction

Author

Listed:
  • Hugo Maruri-Aguilar

    (Queen Mary University of London)

  • Henry Wynn

    (London School of Economics)

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

  • Hugo Maruri-Aguilar & Henry Wynn, 2023. "Sparse polynomial prediction," Statistical Papers, Springer, vol. 64(4), pages 1233-1249, August.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:4:d:10.1007_s00362-023-01439-8
    DOI: 10.1007/s00362-023-01439-8
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    References listed on IDEAS

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    1. Matthew Plumlee, 2014. "Fast Prediction of Deterministic Functions Using Sparse Grid Experimental Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1581-1591, December.
    2. Gu, Chong, 2014. "Smoothing Spline ANOVA Models: R Package gss," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i05).
    Full references (including those not matched with items on IDEAS)

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