An efficient algorithm for the computation of average mutual information: Validation and implementation in Matlab

• Present an efficient computational algorithm programmed in Matlab to compute average mutual information between two time-series.
• Assess the validity against other readily available alternatives in three scenarios.
• Discuss a potential application to EEG connectivity.

Average mutual information (AMI) measures the dependence between pairs of random variables. It has been used in many applications including blind source separation, data mining, neural synchronicity assessment, and state space reconstruction in human movement studies. Presently, several algorithms and computational code exist to estimate AMI. However, most are difficult to use and/or understand the manner by which AMI is calculated. We offer a straightforward and implementable function in Matlab (Mathworks, Inc.) for the computation of AMI in relatively modest sized data streams (N<∼15,000N<∼15,000). Our algorithm incorporates some best practices for statistical estimation that improves accuracy over other readily available options. We present three validation tests: (i) recovery of a known theoretical expected mutual information in a bivariate Gaussian random variable, (ii) invariance with respect to marginal distribution characteristics, and (iii) optimum time-delay selection in state space reconstruction.