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 lower-bounding 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 state-of-the-art 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 multi-partite 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 1441.62041Pavlichin, 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 top 5 Cited in 6 Fields 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year