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Efficient Estimation of Mutual Information for Strongly Dependent Variables

By Shuyang Gao, Greg Ver Steeg and Aram Galstyan

Abstract

We demonstrate that a popular class of nonparametric mutual information (MI) estimators based on k-nearest-neighbor graphs requires number of samples that scales exponentially with the true MI. Consequently, accurate estimation of MI between two strongly dependent variables is possible only for prohibitively large sample size. This important yet overlooked shortcoming of the existing estimators is due to their implicit reliance on local uniformity of the underlying joint distribution. We introduce a new estimator that is robust to local non-uniformity, works well with limited data, and is able to capture relationship strengths over many orders of magnitude. We demonstrate the superior performance of the proposed estimator on both synthetic and real-world data.Comment: 13 pages, to appear in International Conference on Artificial Intelligence and Statistics (AISTATS) 201

Topics: Computer Science - Information Theory, Physics - Data Analysis, Statistics and Probability, Statistics - Machine Learning
Year: 2015
OAI identifier: oai:arXiv.org:1411.2003

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