Efficient Approximate Minimum Entropy Coupling of Multiple Probability Distributions

Given a collection of probability distributions p 1 , xmlns:xlink="http://www.w3.org/1999/xlink">⋯ ,p xmlns:xlink="http://www.w3.org/1999/xlink">m the minimum entropy coupling is X ,X ( xmlns:xlink="http://www.w3.org/1999/xlink">i ~ ) with smallest H(X ). While this problem known to be NP-hard, we present an efficient algorithm for computing within 2 bits from optimal value. More precisely, construct greatest lower bound respect majorization. This construction also valid when infinite, and supports are infinite. Potential applications our results include random number generation, entropic causal inference, functional representation variables.