Generalization Bounds for Learning with Linear, Polygonal, Quadratic and Conic Side Knowledge
This work addresses generalization improvement for machine learning practitioners by incorporating domain knowledge, but it is incremental as it extends existing bounds to new constraint types.
The paper tackles the problem of improving generalization in supervised learning by incorporating side knowledge about unlabeled examples, which reduces the hypothesis space and leads to tighter generalization bounds. It provides bounds for quadratic and conic constraints, showing tightness for the quadratic case.
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.