Functional Output Regression with Infimal Convolution: Exploring the Huber and $ε$-insensitive Losses

Alex Lambert, Dimitri Bouche, Zoltan Szabo, Florence D’Alché-Buc
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:11844-11867, 2022.

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 $\epsilon$-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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-lambert22a, title = {Functional Output Regression with Infimal Convolution: Exploring the Huber and $ε$-insensitive Losses}, author = {Lambert, Alex and Bouche, Dimitri and Szabo, Zoltan and D'Alch{\'e}-Buc, Florence}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {11844--11867}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/lambert22a/lambert22a.pdf}, url = {https://proceedings.mlr.press/v162/lambert22a.html}, 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 $\epsilon$-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.} }
Endnote
%0 Conference Paper %T Functional Output Regression with Infimal Convolution: Exploring the Huber and $ε$-insensitive Losses %A Alex Lambert %A Dimitri Bouche %A Zoltan Szabo %A Florence D’Alché-Buc %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-lambert22a %I PMLR %P 11844--11867 %U https://proceedings.mlr.press/v162/lambert22a.html %V 162 %X 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 $\epsilon$-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.
APA
Lambert, A., Bouche, D., Szabo, Z. & D’Alché-Buc, F.. (2022). Functional Output Regression with Infimal Convolution: Exploring the Huber and $ε$-insensitive Losses. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:11844-11867 Available from https://proceedings.mlr.press/v162/lambert22a.html.

Related Material