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fastMI: a fast and consistent copula-based estimator of mutual information

Soumik PurkayasthaPeter X.K. Song
Dec 2022
摘要
As a fundamental concept in information theory, mutual information (MI) hasbeen commonly applied to quantify association between random variables. Mostexisting estimators of MI have unstable statistical performance since theyinvolve parameter tuning. We develop a consistent and powerful estimator,called fastMI, that does not incur any parameter tuning. Using a copulaformulation, fastMI estimates MI by leveraging Fast Fouriertransformation-based estimation of the underlying density. Extensive simulationstudies reveal that fastMI outperforms state-of-the-art estimators withimproved estimation accuracy and reduced run time for large data sets. fastMInot only provides a powerful test for independence that controls type I error,it may be used for further inference purposes. We establish asymptoticnormality of fastMI for dependent random variables using a new data-splittinganalytic argument. Anticipating that fastMI will be a powerful tool inestimating mutual information in a broad range of data, we develop an R packagefastMI for broader dissemination.
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