Estimating directed information to infer causal relationships between neural spike trains and approximating discrete probability distributions with causal dependence trees

摘要

This work examines an information theoretic quantity known as directed information,which measures statistically causal influences between processes. It is shown to be a general quantity, applicable to arbitrary probability distributions. It is interpreted in terms of prediction, communication with feedback,source coding with feed forward, control over noisy channels, and other settings. It is also shown to be consistent with Granger's philosophical definition. The concepts of direct and indirect causation in a network of processesare formalized. Next, two applications of directed information are investigated.Neuroscience researchers have been attempting to identify causal relationships between neural spike trains in electrode recordings, but have been doing so with correlation measures and measures based on Granger causality. Wediscuss why these methods are not robust, and do not have statistical guarantees. We use a point process GLM model and MDL (as a model order selection tool) for consistent estimation of directed information between neuralspike trains. We have successfully applied this methodology to a network of simulated neurons and electrode array recordings.This work then develops a procedure, similar to Chow and Liu's, for fi nding the "best" approximation (in terms of KL divergence) of a full, jointdistribution over a set of random processes, using a causal dependence tree distribution. Chow and Liu's procedure had been shown to be equivalent to maximizing a sum of mutual informations, and the procedure presented hereis shown to be equivalent to maximizing a sum of directed informations. An algorithm is presented for efficiently finding the optimal causal tree, similarto that in Chow and Liu's work.