212 citations · 370 across the 6 of their papers we have counts for
4 papers · 1 filter
The Layered Structure of Tensor Estimation and its Mutual Information
Jean Barbier, Nicolas Macris, Léo Miolane
We consider rank-one non-symmetric tensor estimation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat i…
Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models
Jean Barbier, Florent Krzakala, Nicolas Macris +2
Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is…
Fundamental limits of low-rank matrix estimation: the non-symmetric case
Léo Miolane
We consider the high-dimensional inference problem where the signal is a low-rank matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-r…
Statistical and computational phase transitions in spiked tensor estimation
Thibault Lesieur, Léo Miolane, Marc Lelarge +2
We consider tensor factorizations using a generative model and a Bayesian approach. We compute rigorously the mutual information, the Minimal Mean Squared Error (MMSE), and unveil…