Learning Using Privileged Information: SVM+ and Weighted SVM

TL;DR

This paper explores how privileged information can enhance learning algorithms like SVM+ and demonstrates that weighted SVMs can replicate SVM+ solutions, highlighting their relationship and limitations.

Contribution

It establishes the connection between privileged information and importance weighting, showing weighted SVMs can emulate SVM+ and discusses weight selection without privileged features.

Findings

Weighted SVMs can replicate SVM+ solutions.

Privileged features can be encoded as example weights.

Limitations of SVM+ are demonstrated with a counterexample.

Abstract

Prior knowledge can be used to improve predictive performance of learning algorithms or reduce the amount of data required for training. The same goal is pursued within the learning using privileged information paradigm which was recently introduced by Vapnik et al. and is aimed at utilizing additional information available only at training time -- a framework implemented by SVM+. We relate the privileged information to importance weighting and show that the prior knowledge expressible with privileged features can also be encoded by weights associated with every training example. We show that a weighted SVM can always replicate an SVM+ solution, while the converse is not true and we construct a counterexample highlighting the limitations of SVM+. Finally, we touch on the problem of choosing weights for weighted SVMs when privileged features are not available.