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Estimation of mutual information between (multidimensional) real-valuedvariables is used in analysis of complex systems, biological systems, andrecently also quantum systems. This estimation is a hard problem, anduniversally good estimators provably do not exist. Kraskov et al. (PRE, 2004)introduced a successful mutual information estimation approach based on thestatistics of distances between neighboring data points, which empiricallyworks for a wide class of underlying probability distributions. Here we improvethis estimator by (i) expanding its range of applicability, and by providing(ii) a self-consistent way of verifying the absence of bias, (iii) a method forestimation of its variance, and (iv) a criterion for choosing the values of thefree parameter of the estimator. We demonstrate the performance of ourestimator on synthetic data sets, as well as on neurophysiological and systemsbiology data sets.

Estimation of mutual information for real-valued data with error bars and controlled bias