Bounds for Vector-Valued Function Estimation

TL;DR

This paper develops a general framework for deriving risk bounds in vector-valued learning, applicable to multi-task and multi-category problems, especially with shared representations.

Contribution

It introduces a unified approach to risk bounds for vector-valued functions, covering broad feature maps and loss functions, and analyzes conditions for shared representations to be effective.

Findings

Risk bounds applicable to multi-task and multi-category learning

Shared representations are beneficial under certain conditions

Framework accommodates various feature maps and loss functions

Abstract

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.