On maximum-likelihood estimation in the all-or-nothing regime
Abstract
We study the problem of estimating a rank-1 additive deformation of a Gaussian tensor according to the \emph{maximum-likelihood estimator} (MLE). The analysis is carried out in the sparse setting, where the underlying signal has a support that scales sublinearly with the total number of dimensions. We show that for Bernoulli distributed signals, the MLE undergoes an \emph{all-or-nothing} (AoN) phase transition, already established for the minimum mean-square-error estimator (MMSE) in the same problem. The result follows from two main technical points: (i) the connection established between the MLE and the MMSE, using the first and second-moment methods in the constrained signal space, (ii) a recovery regime for the MMSE stricter than the simple error vanishing characterization given in the standard AoN, that is here proved as a general result.
Keywords
Cite
@article{arxiv.2101.09994,
title = {On maximum-likelihood estimation in the all-or-nothing regime},
author = {Luca Corinzia and Paolo Penna and Wojciech Szpankowski and Joachim M. Buhmann},
journal= {arXiv preprint arXiv:2101.09994},
year = {2021}
}