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Published June 2017 | public
Book Section - Chapter

Entropic Causality and Greedy Minimum Entropy Coupling

Abstract

We study the problem of identifying the causal relationship between two discrete random variables from observational data. We recently proposed a novel framework called entropie causality that works in a very general functional model but makes the assumption that the unobserved exogenous variable has small entropy in the true causal direction. This framework requires the solution of a minimum entropy coupling problem: Given marginal distributions of m discrete random variables, each on n states, find the joint distribution with minimum entropy, that respects the given marginals. This corresponds to minimizing a concave function of n^m variables over a convex polytope defined by nm linear constraints, called a transportation polytope. Unfortunately, it was recently shown that this minimum entropy coupling problem is NP-hard, even for 2 variables with n states. Even representing points (joint distributions) over this space can require exponential complexity (in n, m) if done naively. In our recent work we introduced an efficient greedy algorithm to find an approximate solution for this problem. In this paper we analyze this algorithm and establish two results: that our algorithm always finds a local minimum and also is within an additive approximation error from the unknown global optimum.

Additional Information

© 2017 IEEE. This research has been supported by NSF Grants CCF 1344364, 1407278, 1422549, 1618689, 1564167, ONR N000141512009 and ARO YIP W911NF-14-1-0258. The work of Babak Hassibi has been supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA's Jet Propulsion Laboratory through the President and Director's Fund, and by King Abdullah University of Science and Technology.

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024