Sparse polynomial prediction

Maruri-Aguilar, Hugo and Wynn, Henry ORCID: 0000-0002-6448-1080 (2023) Sparse polynomial prediction. Statistical Papers, 64 (4). 1233 - 1249. ISSN 0932-5026

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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.

Item Type:	Article
Official URL:	https://www.springer.com/journal/362
Additional Information:	© 2023 The Author(s).
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	27 Apr 2023 16:00
Last Modified:	12 Dec 2024 03:43
URI:	http://eprints.lse.ac.uk/id/eprint/118748

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