PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Conditional Likelihood Maximisation: A Unifying Framework for Information Theoretic Feature Selection
Gavin Brown, Adam Pocock, Ming-Jie Zhao and Mikel Lujan
Journal of Machine Learning Research Volume 13, Number 1, pp. 26-66, 2012.

Abstract

We present a unifying framework for information theoretic feature selection, bringing almost two decades of research on heuristic filter criteria under a single theoretical interpretation. This is in response to the question: "what are the implicit statistical assumptions of feature selection criteria based on mutual information?". To answer this, we adopt a different strategy than is usual in the feature selection literature−instead of trying to define a criterion, we derive one, directly from a clearly specified objective function: the conditional likelihood of the training labels. While many hand-designed heuristic criteria try to optimize a definition of feature 'relevancy' and 'redundancy', our approach leads to a probabilistic framework which naturally incorporates these concepts. As a result we can unify the numerous criteria published over the last two decades, and show them to be low-order approximations to the exact (but intractable) optimisation problem. The primary contribution is to show that common heuristics for information based feature selection (including Markov Blanket algorithms as a special case) are approximate iterative maximisers of the conditional likelihood. A large empirical study provides strong evidence to favour certain classes of criteria, in particular those that balance the relative size of the relevancy/redundancy terms. Overall we conclude that the JMI criterion (Yang and Moody, 1999; Meyer et al., 2008) provides the best tradeoff in terms of accuracy, stability, and flexibility with small data samples.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Machine Vision
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:9102
Deposited By:Gavin Brown
Deposited On:21 February 2012