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Title:Estimating directed information to infer causal relationships between neural spike trains and approximating discrete probability distributions with causal dependence trees
Author(s):Quinn, Christopher J.
Advisor(s):Coleman, Todd P.; Kiyavash, Negar
Department / Program:Electrical & Computer Eng
Discipline:Electrical & Computer Engr
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):information theory
computational neuroscience
Bayesian networks
Abstract: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 processes are 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. We discuss 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 neural spike 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, joint distribution 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 here is shown to be equivalent to maximizing a sum of directed informations. An algorithm is presented for efficiently finding the optimal causal tree, similar to that in Chow and Liu's work.
Issue Date:2010-05-18
Rights Information:Copyright 2010 Christopher John Quinn
Date Available in IDEALS:2010-05-18
Date Deposited:May 2010

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