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

TL;DR

This paper introduces a flexible framework for functional output regression using Huber and epsilon-insensitive losses, effectively handling outliers and sparsity, with demonstrated efficiency on synthetic and real data.

Contribution

It extends functional output regression to include robust loss functions via infimal convolution, providing computational algorithms and empirical validation.

Findings

Effective handling of outliers and sparsity in FOR

Competitive performance on benchmarks

New algorithms based on duality for vector-valued RKHS

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.