Generalization Bounds for Learning with Linear, Polygonal, Quadratic and Conic Side Knowledge

TL;DR

This paper develops new generalization bounds for supervised learning models by incorporating various types of side knowledge, such as linear, quadratic, and conic constraints, which tighten the hypothesis space and improve learning guarantees.

Contribution

It introduces a unified framework for analyzing how different side knowledge types affect hypothesis space complexity and provides tight bounds for quadratic constraints.

Findings

Tighter generalization bounds with side knowledge

Explicit bounds for quadratic and conic constraints

Demonstration of the impact of domain knowledge on hypothesis complexity

Abstract

In this paper, we consider a supervised learning setting where side knowledge is provided about the labels of unlabeled examples. The side knowledge has the effect of reducing the hypothesis space, leading to tighter generalization bounds, and thus possibly better generalization. We consider several types of side knowledge, the first leading to linear and polygonal constraints on the hypothesis space, the second leading to quadratic constraints, and the last leading to conic constraints. We show how different types of domain knowledge can lead directly to these kinds of side knowledge. We prove bounds on complexity measures of the hypothesis space for quadratic and conic side knowledge, and show that these bounds are tight in a specific sense for the quadratic case.