PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

A Unified Algorithmic Approach for Efficient Online Label Ranking
Shai Shalev-Shwartz and Yoram Singer
In: AISTAT 2007(2007).

Abstract

Label ranking is the task of ordering labels with respect to their relevance to an input instance. We describe a unified approach for the online label ranking task. We do so by casting the online learning problem as a game against a competitor who receives all the examples in advance and sets its label ranker to be the optimal solution of a constrained optimization problem. This optimization problem consists of two terms: the empirical label-ranking loss of the competitor and a complexity measure of the competitor's ranking function. We then describe and analyze a framework for online label ranking that {\em incrementally} ascends the dual problem corresponding to the competitor's optimization problem. The generality of our framework enables us to derive new online update schemes. In particular, we use the relative entropy as a complexity measure to derive efficient multiplicative algorithms for the label ranking task. Depending on the specific form of the instances, the multiplicative updates either have a closed form or can be calculated very efficiently by tailoring an interior point procedure to the label ranking task. We demonstrate the potential of our approach in a few experiments with email categorization tasks.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Natural Language Processing
Theory & Algorithms
ID Code:4064
Deposited By:Shai Shalev-Shwartz
Deposited On:25 February 2008