# Bounds for Vector-Valued Function Estimation

arXiv: https://arxiv.org/abs/1606.01487 · HTML: https://mlsanity.com/paper/1606.01487/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2016.

## Built on by (most cited first, 3 of 3)

- [Non-Parametric Representation Learning with Kernels](https://mlsanity.com/paper/2309.02028/) (2023)
- [Fine-grained Generalization Analysis of Vector-valued Learning](https://mlsanity.com/paper/2104.14173/) (2021)
- [Loss Gradient Gaussian Width based Generalization and Optimization Guarantees](https://mlsanity.com/paper/2406.07712/) (2024)

## Abstract (arXiv)

We present a framework to derive risk bounds for vector-valued learning with a broad class of feature maps and loss functions. Multi-task learning and one-vs-all multi-category learning are treated as examples. We discuss in detail vector-valued functions with one hidden layer, and demonstrate that the conditions under which shared representations are beneficial for multi- task learning are equally applicable to multi-category learning.