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Functional output regression with infimal convolution: exploring the Huber and ε-insensitive losses

Author

Listed:
  • Lambert, Alex
  • Bouche, Dimitri
  • Szabo, Zoltan
  • d'Alché-Buc, Florence

Abstract

The focus of the paper is functional output regression (FOR) with convoluted losses. While most existing work consider the square loss setting, we leverage extensions of the Huber and the ε-insensitive loss (induced by infimal convolution) and propose a flexible framework capable of handling various forms of outliers and sparsity in the FOR family. We derive computationally tractable algorithms relying on duality to tackle the resulting tasks in the context of vector-valued reproducing kernel Hilbert spaces. The efficiency of the approach is demonstrated and contrasted with the classical squared loss setting on both synthetic and real-world benchmarks.

Suggested Citation

  • Lambert, Alex & Bouche, Dimitri & Szabo, Zoltan & d'Alché-Buc, Florence, 2022. "Functional output regression with infimal convolution: exploring the Huber and ε-insensitive losses," LSE Research Online Documents on Economics 115651, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:115651
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    File URL: https://researchonline.lse.ac.uk/id/eprint/115651/
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    References listed on IDEAS

    as
    1. Maronna, Ricardo A. & Yohai, Victor J., 2013. "Robust functional linear regression based on splines," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 46-55.
    2. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    3. Kalogridis, Ioannis & Van Aelst, Stefan, 2019. "Robust functional regression based on principal components," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 393-415.
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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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