Greedy additive approximation algorithms for minimum-entropy coupling problem - Rossi, Massimiliano (Proceedings / IEEE International Symposium on Information Theory, 2019)
Given two probability distributions p = (p 1 ,p 2 ,...,p n ) and q = (q 1 ,q 2 ,...,q m ) of two discrete random variables X and Y respectively, the minimum-entropy coupling problem is to find the minimum-entropy joint distribution among all possible joint distributions of X and Y having p and q as marginals. This problem is known to be NP-hard and recently have been proposed greedy algorithms that provide different guarantees, i.e. solutions that are local minimum [Kocaoglu et al. AAAI'17] and 1-bit approximation [Cicalese et al. ISIT'17]. In this paper, we show that the algorithm proposed by Kocaoglu et al. provides, in addition, a 1-bit approximation guarantee in the case of 2 variables. Then, we provide a general criteria for guaranteeing an additive approximation factor of 1 that might be of independent interest in other contexts where couplings are used.