The Bethe and Sinkhorn Permanents of Low Rank Matrices and Implications for Profile Maximum Likelihood
Nima Anari,
Moses Charikar,
Kirankumar Shiragur
et al.
Abstract:In this paper we consider the problem of computing the likelihood of the profile of a discrete distribution, i.e., the probability of observing the multiset of element frequencies, and computing a profile maximum likelihood (PML) distribution, i.e., a distribution with the maximum profile likelihood. For each problem we provide polynomial time algorithms that given n i.i.d. samples from a discrete distribution, achieve an approximation factor of exp (−O( √ n log n)), improving upon the previous best-known boun… Show more
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