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

As a fundamental concept in information theory, mutual information (MI) has been commonly applied to quantify association between random variables. Most existing estimators of MI have unstable statistical performance since they involve parameter tuning. We develop a consistent and powerful estimator, called fastMI, that does not incur any parameter tuning. Using a copula formulation, fastMI estimates MI by leveraging Fast Fourier transformation-based estimation of the underlying density. Extensive simulation studies reveal that fastMI outperforms state-of-the-art estimators with improved estimation accuracy and reduced run time for large data sets. fastMI not only provides a powerful test for independence that controls type I error, it may be used for further inference purposes. We establish asymptotic normality of fastMI for dependent random variables using a new data-splitting analytic argument. Anticipating that fastMI will be a powerful tool in estimating mutual information in a broad range of data, we develop an R package fastMI for broader dissemination.