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## Robust Feature Selection using Distributions of Mutual Information

Author:Marco Zaffalon and Marcus Hutter (2002) Comments:8 two-column pages Subj-class:Artificial Intelligence; Learning ACM-class:I.2 Reference:Proceedings of the 14th International Conference on Uncertainty in Artificial Intelligence (UAI-2002) Report-no:IDSIA-08-02 and cs.AI/0206006 Paper:LaTeX - PostScript - PDF - Html/Gif Slides:PowerPoint - PDF

Keywords:Robust feature selection, naive Bayes classifier, Mutual Information, Cross Entropy, Dirichlet distribution, Second order distribution, expectation and variance of mutual information.

Abstract:Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must consider sample-to-population inferential approaches. This paper deals with the distribution of mutual information, as obtained in a Bayesian framework by a second-order Dirichlet prior distribution. The exact analytical expression for the mean and an analytical approximation of the variance are reported. Asymptotic approximations of the distribution are proposed. The results are applied to the problem of selecting features for incremental learning and classification of the naive Bayes classifier. A fast, newly defined method is shown to outperform the traditional approach based on empirical mutual information on a number of real data sets. Finally, a theoretical development is reported that allows one to efficiently extend the above methods to incomplete samples in an easy and effective way.

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## Table of Contents

- Introduction
- Distribution of Mutual Information
- Feature Selection
- Experimental Analysis
- Extensions
- Conclusions

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@InProceedings{Hutter:02feature, author = "Marco Zaffalon and Marcus Hutter", title = "Robust Feature Selection using Distributions of Mutual Information", year = "2002", pages = "577--584", booktitle = "Proceedings of the 18th International Conference on Uncertainty in Artificial Intelligence (UAI-2002)", editor = "A. Darwiche and N. Friedman", publisher = "Morgan Kaufmann", address = "San Francisco, CA.", report = "IDSIA-08-02 and cs.AI/0206006", url = "http://www.hutter1.net/ai/feature.htm", url2 = "http://arxiv.org/abs/cs.AI/0206006", ftp = "ftp://ftp.idsia.ch/pub/techrep/IDSIA-08-02.ps.gz", categories = "I.2. [Artificial Intelligence]", keywords = "Robust feature selection, naive Bayes classifier, Mutual Information, Cross Entropy, Dirichlet distribution, Second order distribution, expectation and variance of mutual information.", abstract = "Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must consider sample-to-population inferential approaches. This paper deals with the distribution of mutual information, as obtained in a Bayesian framework by a second-order Dirichlet prior distribution. The exact analytical expression for the mean and an analytical approximation of the variance are reported. Asymptotic approximations of the distribution are proposed. The results are applied to the problem of selecting features for incremental learning and classification of the naive Bayes classifier. A fast, newly defined method is shown to outperform the traditional approach based on empirical mutual information on a number of real data sets. Finally, a theoretical development is reported that allows one to efficiently extend the above methods to incomplete samples in an easy and effective way.", }

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