Functional Output Regression with Infimal Convolution: Exploring the Huber and $ε$-insensitive Losses
This work addresses robust regression in functional data analysis, offering incremental improvements for applications with noisy or sparse outputs.
The paper tackles functional output regression by extending Huber and ε-insensitive losses via infimal convolution to handle outliers and sparsity, demonstrating improved efficiency over squared loss on synthetic and real-world benchmarks.
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.