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 find the empirical performance of our approach is competitive and sometimes significantly better than state-of-the-art performance for various estimation problems.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Instance Based Approximations to Profile Maximum Likelihood
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 match…
A new adjusted maximum likelihood method for the Fay–Herriot small area model
In the context of the Fay–Herriot model, a mixed regression model routinely used to combine information from various sources in small area estimation, certain adjustments to a standard likelihood (e.g., profile, residu…
regressionThe Bethe and Sinkhorn Permanents of Low Rank Matrices and Implications for Profile Maximum Likelihood
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 likelih…
Maximum Approximated Likelihood Estimation
Empirical economic research frequently applies maximum likelihood estimation in cases where the likelihood function is analytically intractable. Most of the theoretical literature focuses on maximum simulated likelihood …
On the Efficient Implementation of High Accuracy Optimality of Profile Maximum Likelihood
We provide an efficient unified plug-in approach for estimating symmetric properties of distributions given $n$ independent samples. Our estimator is based on profile-maximum-likelihood (PML) and is sample optimal for es…