On maximum-likelihood estimation in the all-or-nothing regime
Not on the map. Why?
Abstract (arXiv)
We study the problem of estimating a rank-1 additive deformation of a Gaussian tensor according to the 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 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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 8 of its 21 references that are in the map. First posted on arXiv 25 Jan 2021.
Builds on
8 of 21 references.
References · 8
- 2015Statistical physics of inference: Thresholds and algorithmscited by 128
- 2014A statistical model for tensor PCAcited by 72
- 2015Tensor principal component analysis via sum-of-squares proofscited by 35
- 2016Statistical limits of spiked tensor modelscited by 28
- 2016Mutual information for symmetric rank-one matrix estimation: A proof of the replica formulacited by 26
- 2020All-or-nothing statistical and computational phase transitions in sparse spiked matrix estimationcited by 16
- 2019How to iron out rough landscapes and get optimal performances: Averaged Gradient Descent and its application to tensor PCAcited by 14
- 2020Statistical and computational thresholds for the planted k-densest sub-hypergraph problemcited by 5
Built on by
Not cited yet.