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

arXiv: https://arxiv.org/abs/1405.7764 · HTML: https://mlsanity.com/paper/1405.7764/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2014.

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

- [On Regularization and Inference with Label Constraints](https://mlsanity.com/paper/2307.03886/) (2023)

## Abstract (arXiv)

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.