Approximate Profile Maximum Likelihood
This addresses the problem of efficient statistical estimation for researchers and practitioners, offering an incremental improvement over existing PML methods.
The paper tackles the computational difficulty of profile maximum likelihood (PML) by proposing an efficient approximate algorithm that clumps symbols with comparable frequencies, resulting in competitive or significantly better empirical performance than state-of-the-art methods for various estimation problems.
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 find the empirical performance of our approach is competitive and sometimes significantly better than state-of-the-art performance for various estimation problems.