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

Alex Lambert (1, 2) , Dimitri Bouche (3, 4, 5) , Zoltan Szabo (6) , Florence d'Alché-Buc (3, 4, 5)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Department of Electrical Engineering - ESAT [Leuven]
3 S2A - Signal, Statistique et Apprentissage
4 IDS - Département Images, Données, Signal
5 IP Paris - Institut Polytechnique de Paris
6 LSE - Department of Statistics - London School of Economics

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-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.

Domains: Statistics [stat]; Machine Learning [stat.ML]

Alex Lambert, Dimitri Bouche, Zoltan Szabo, Florence d'Alché-Buc. Functional Output Regression with Infimal Convolution: Exploring the Huber and -insensitive Losses. International Conference on Machine Learning - 2022, Jul 2022, Baltimore, United States. ⟨hal-03807108⟩