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Learning with Discrete Least Squares on Multivariate Polynomial Spaces Using Evaluations at Random or Low-Discrepancy Point Sets

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Machine Learning, Optimization, and Big Data (MOD 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9432))

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Abstract

We review the results achieved in previous works [1, 2, 6, 8, 10–12] concerning the analysis of stability and accuracy of discrete least-squares approximation on multivariate polynomial spaces with noiseless evaluations at random points, and the results from [9] concerning the case of noiseless evaluations at low-discrepancy point sets. Afterwards, we present some numerical examples that confirm our theoretical findings and give some insights on their potential applications. The purpose of the numerical section is twofold: on the one hand we compare the performance of discrete least squares using random points versus low-discrepancy points; on the other hand we point out further directions of research, by showing what happens when we choose fewer evaluation points than those prescribed by our theoretical analysis.

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References

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Authors and Affiliations

  1. MATHICSE-CSQI, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Giovanni Migliorati

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  1. Giovanni Migliorati
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Correspondence to Giovanni Migliorati .

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Editors and Affiliations

  1. University of Florida, Gainsville, Florida, USA

    Panos Pardalos

  2. University of Catania, Catania, Italy

    Mario Pavone

  3. University of Catania, Catania, Italy

    Giovanni Maria Farinella

  4. University of Catania, Catania, Italy

    Vincenzo Cutello

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Migliorati, G. (2015). Learning with Discrete Least Squares on Multivariate Polynomial Spaces Using Evaluations at Random or Low-Discrepancy Point Sets. In: Pardalos, P., Pavone, M., Farinella, G., Cutello, V. (eds) Machine Learning, Optimization, and Big Data. MOD 2015. Lecture Notes in Computer Science(), vol 9432. Springer, Cham. https://doi.org/10.1007/978-3-319-27926-8_1

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  • DOI: https://doi.org/10.1007/978-3-319-27926-8_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27925-1

  • Online ISBN: 978-3-319-27926-8

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