Compression-Based Regularization with an Application to Multi-Task Learning

TL;DR

This paper introduces an information theoretic regularization approach for multi-task learning that balances model complexity and risk, demonstrating an optimal tradeoff with empirical and hierarchical text categorization applications.

Contribution

It formulates multi-task learning within an information theoretic framework using lossy source coding principles, providing an iterative algorithm with convergence guarantees.

Findings

Existence of an optimal information rate minimizing excess risk.

Algorithm effectively balances risk and model complexity.

Application to hierarchical text categorization shows practical benefits.

Abstract

This paper investigates, from information theoretic grounds, a learning problem based on the principle that any regularity in a given dataset can be exploited to extract compact features from data, i.e., using fewer bits than needed to fully describe the data itself, in order to build meaningful representations of a relevant content (multiple labels). We begin by introducing the noisy lossy source coding paradigm with the log-loss fidelity criterion which provides the fundamental tradeoffs between the \emph{cross-entropy loss} (average risk) and the information rate of the features (model complexity). Our approach allows an information theoretic formulation of the \emph{multi-task learning} (MTL) problem which is a supervised learning framework in which the prediction models for several related tasks are learned jointly from common representations to achieve better generalization performance. Then, we present an iterative algorithm for computing the optimal tradeoffs and its global convergence is proven provided that some conditions hold. An important property of this algorithm is that it provides a natural safeguard against overfitting, because it minimizes the average risk taking into account a penalization induced by the model complexity. Remarkably, empirical results illustrate that there exists an optimal information rate minimizing the \emph{excess risk} which depends on the nature and the amount of available training data. An application to hierarchical text categorization is also investigated, extending previous works.