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Paper Detail

Paper IDD3-S2-T3.3
Paper Title On maximum-likelihood estimation in the all-or-nothing regime
Authors Luca Corinzia, Paolo Penna, ETH Zurich, Switzerland; Wojciech Szpankowski, Purdue University, United States; Joachim M. Buhmann, ETH Zurich, Switzerland
Session D3-S2-T3: Inference & Learning
Chaired Session: Wednesday, 14 July, 22:20 - 22:40
Engagement Session: Wednesday, 14 July, 22:40 - 23:00
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.