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

Nima Anari, Moses Charikar, Kirankumar Shiragur, Aaron Sidford
2020 arXiv   pre-print
We achieve these results by providing new bounds on the quality of approximation of the Bethe and Sinkhorn permanents (Vontobel, 2012 and 2014).  ...  maximum likelihood (PML) distribution, i.e., a distribution with the maximum profile likelihood.  ...  We thank the anonymous reviewer for pointing out the alternative proof of the quality of scaled Sinkhorn and Bethe approximations on approximating the permanent of matrices with a bounded number of distinct  ... 
arXiv:2004.02425v1 fatcat:ueqgbx6oundqtamybbor4ptj6i

Instance Based Approximations to Profile Maximum Likelihood [article]

Nima Anari, Moses Charikar, Kirankumar Shiragur, Aaron Sidford
2020 arXiv   pre-print
In this paper we provide a new efficient algorithm for approximately computing the profile maximum likelihood (PML) distribution, a prominent quantity in symmetric property estimation.  ...  We provide an algorithm which matches the previous best known efficient algorithms for computing approximate PML distributions and improves when the number of distinct observed frequencies in the given  ...  Acknowledgments We thank Alon Orlitsky and Yi Hao for helpful clarifications and discussions. Sources of Funding  ... 
arXiv:2011.02761v1 fatcat:4wofj4gqbvcanln2gnprz4ryke