The Bethe and Sinkhorn Permanents of Low Rank Matrices and Implications for Profile Maximum Likelihood

6 Apr 2020Nima AnariMoses CharikarKirankumar ShiragurAaron Sidford

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 $\exp\left(-O(\sqrt{n} \log n) \right)$, improving upon the previous best-known bound achievable in polynomial time of $\exp(-O(n^{2/3} \log n))$ (Charikar, Shiragur and Sidford, 2019)... (read more)

PDF Abstract

Code


No code implementations yet. Submit your code now

Tasks


Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods used in the Paper


METHOD TYPE
🤖 No Methods Found Help the community by adding them if they're not listed; e.g. Deep Residual Learning for Image Recognition uses ResNet