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We investigate approximating joint distributions of random processes withcausal dependence tree distributions. Such distributions are particularlyuseful in providing parsimonious representation when there exists causaldynamics among processes. By extending the results by Chow and Liu ondependence tree approximations, we show that the best causal dependence treeapproximation is the one which maximizes the sum of directed informations onits edges, where best is defined in terms of minimizing the KL-divergencebetween the original and the approximate distribution. Moreover, we describe alow-complexity algorithm to efficiently pick this approximate distribution.

Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes