Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 464, Issue 2093, Pages 1203-1215Publisher
ROYAL SOC
DOI: 10.1098/rspa.2007.0196
Keywords
mutual information; nearest neighbour analysis; non-parametric estimation
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Mutual information quantifies the determinism that exists in a relationship between random variables, and thus plays an important role in exploratory data analysis. We investigate a class of non-parametric estimators for mutual information, based on the nearest neighbour structure of observations in both the joint and marginal spaces. Unless both marginal spaces are one-dimensional, we demonstrate that a well-known estimator of this type can be computationally expensive under certain conditions, and propose a computationally efficient alternative that has a time complexity of order O(N log N) as the number of observations N -> infinity.
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