# Stability of Multi-Task Kernel Regression Algorithms

arXiv: https://arxiv.org/abs/1306.3905 · HTML: https://mlsanity.com/paper/1306.3905/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2013.

## Built on by (most cited first, 2 of 2)

- [Differentially Private Shapley Values for Data Evaluation](https://mlsanity.com/paper/2206.00511/) (2022)
- [Learning in RKHM: a C^*-Algebraic Twist for Kernel Machines](https://mlsanity.com/paper/2210.11855/) (2022)

## Abstract (arXiv)

We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning prob- lems with nonscalar outputs like multi-task learning and structured out- put prediction. We show that multi-task kernel regression algorithms are uniformly stable in the general case of infinite-dimensional output spaces. We then derive under mild assumption on the kernel generaliza- tion bounds of such algorithms, and we show their consistency even with non Hilbert-Schmidt operator-valued kernels . We demonstrate how to apply the results to various multi-task kernel regression methods such as vector-valued SVR and functional ridge regression.