PML
swMATH ID:  34605 
Software Authors:  Pavlichin, Dmitri S.; Jiao, Jiantao; Weissman, Tsachy 
Description:  Approximate profile maximum likelihood. We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML has appealing theoretical properties, but is difficult to compute exactly. Inspired by observations gleaned from exactly solvable cases, we look for an approximate PML solution, which, intuitively, clumps comparably frequent symbols into one symbol. This amounts to lowerbounding a certain matrix permanent by summing over a subgroup of the symmetric group rather than the whole group during the computation. We extensively experiment with the approximate solution, and the empirical performance of our approach is competitive and sometimes significantly better than stateoftheart performances for various estimation problems. 
Homepage:  https://arxiv.org/abs/1712.07177 
Source Code:  https://github.com/dmitrip/PML 
Keywords:  profile maximum likelihood; dynamic programming; sufficient statistic; partition of multipartite numbers; integer partition 
Related Software:  GitHub; OEIS 
Cited in:  2 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Approximate profile maximum likelihood. Zbl 1441.62041 Pavlichin, Dmitri S.; Jiao, Jiantao; Weissman, Tsachy 
2019

Cited by 5 Authors
1  Anari, Nima 
1  Jiao, Jiantao 
1  Pavlichin, Dmitri S. 
1  Rezaei, Alireza 
1  Weissman, Tsachy 
Cited in 2 Serials
1  SIAM Journal on Computing 
1  Journal of Machine Learning Research (JMLR) 
all
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