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

arXiv: https://arxiv.org/abs/2206.08220 · HTML: https://mlsanity.com/paper/2206.08220/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 16 Jun 2022.

## Builds on (most cited first, 5 of 5)

- [Operator-valued Kernels for Learning from Functional Response Data](https://mlsanity.com/paper/1510.08231/) (2015)
- [Functional Regression](https://mlsanity.com/paper/1406.4068/) (2014)
- [Fast Function to Function Regression](https://mlsanity.com/paper/1410.7414/) (2014)
- [Nonlinear Functional Output Regression: a Dictionary Approach](https://mlsanity.com/paper/2003.01432/) (2020)
- [Robust functional regression based on principal components](https://mlsanity.com/paper/1807.00135/) (2018)

## Built on by (most cited first, 1 of 1)

- [Extending Kernel PCA through Dualization: Sparsity, Robustness and Fast Algorithms](https://mlsanity.com/paper/2306.05815/) (2023)

## Abstract (arXiv)

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.