Personne
Jean François Emmanuel Barbier
Cette personne n’est plus à l’EPFL
Publications associées (18)
Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method
Nicolas Macris, Jean François Emmanuel Barbier, Chun Lam Chan
We rigorously derive a single-letter variational expression for the mutual information of the asymmetric two-groups stochastic block model in the dense graph regime. Existing proofs in the literature are indirect, as they involve mapping the model to a ran ...
IEEE2019The committee machine: computational to statistical gaps in learning a two-layers neural network
Nicolas Macris, Florent Gérard Krzakala, Lenka Zdeborová, Jean François Emmanuel Barbier
Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks. In this paper, we provide a rigor ...
IOP PUBLISHING LTD2019The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models
Nicolas Macris, Jean François Emmanuel Barbier
In this contribution we give a pedagogic introduction to the newly introduced adaptive interpolation method to prove in a simple and unified way replica formulas for Bayesian optimal inference problems. Many aspects of this method can already be explained ...
IOP PUBLISHING LTD2019Adaptive Path Interpolation for Sparse Systems: Application to a Simple Censored Block Model
Nicolas Macris, Jean François Emmanuel Barbier, Chun Lam Chan
A new adaptive path interpolation method has been recently developed as a simple and versatile scheme to calculate exactly the asymptotic mutual information of Bayesian inference problems defined on dense factor graphs. These include random linear and gene ...
IEEE2018The committee machine: Computational to statistical gaps in learning a two-layers neural network
Nicolas Macris, Florent Gérard Krzakala, Lenka Zdeborová, Jean François Emmanuel Barbier
Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks. In this contribution, we provide ...
NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018Entropy and mutual information in models of deep neural networks
Nicolas Macris, Florent Gérard Krzakala, Lenka Zdeborová, Jean François Emmanuel Barbier, Clément Dominique Luneau
We examine a class of stochastic deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical physics ...
NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices
Nicolas Macris, Florent Gérard Krzakala, Jean François Emmanuel Barbier
There has been definite progress recently in proving the variational single-letter formula given by the heuristic replica method for various estimation problems. In particular, the replica formula for the mutual information in the case of noisy linear esti ...
IEEE2018Scampi: a robust approximate message-passing framework for compressive imaging
Florent Gérard Krzakala, Jean François Emmanuel Barbier
Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an alternative probabil ...
Iop Publishing Ltd2016