On Information Regularization

TL;DR

This paper introduces an information regularization principle for semi-supervised classification that constrains conditional distributions using unlabeled data, extending previous work to multiple dimensions and providing complexity measures.

Contribution

It extends the information regularization framework to multiple dimensions with a regularizer independent of space covering, and demonstrates its use in logistic regression with unlabeled data.

Findings

Provides a regularizer that penalizes unnecessary information between data points and labels.

Establishes a sample-complexity bound for classification with unlabeled data.

Shows practical application in logistic regression models using unlabeled examples.

Abstract

We formulate a principle for classification with the knowledge of the marginal distribution over the data points (unlabeled data). The principle is cast in terms of Tikhonov style regularization where the regularization penalty articulates the way in which the marginal density should constrain otherwise unrestricted conditional distributions. Specifically, the regularization penalty penalizes any information introduced between the examples and labels beyond what is provided by the available labeled examples. The work extends Szummer and Jaakkola's information regularization (NIPS 2002) to multiple dimensions, providing a regularizer independent of the covering of the space used in the derivation. We show in addition how the information regularizer can be used as a measure of complexity of the classification task with unlabeled data and prove a relevant sample-complexity bound. We illustrate the regularization principle in practice by restricting the class of conditional distributions to be logistic regression models and constructing the regularization penalty from a finite set of unlabeled examples.