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

Alex Lambert, Dimitri Bouche, Zoltan Szabo and Florence d'Alché-Buc

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

JEL-codes: C1 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2022-07-17
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Published in Proceedings of Machine Learning Research, 17, July, 2022, 162, pp. 11844 - 1186. ISSN: 2640-3498

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:115651

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