Efficient Estimation of Mutual Information for Strongly Dependent Variables
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Publication:6256214
arXiv1411.2003MaRDI QIDQ6256214
Greg Ver Steeg, Shuyang Gao, Aram Galstyan
Publication date: 7 November 2014
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.
Has companion code repository: https://gitlab.com/ita-ml/pyhard
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