Statistical limits of dictionary learning: random matrix theory and the spectral replica method
We consider increasingly complex models of matrix denoising and dictionary learning in the
Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank …
Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank …
Nonconvex interactions in mean-field spin glasses
JC Mourrat - Probability and Mathematical Physics, 2021 - msp.org
We propose a conjecture for the limit free energy of mean-field spin glasses with a bipartite
structure, and show that the conjectured limit is an upper bound. The conjectured limit is …
structure, and show that the conjectured limit is an upper bound. The conjectured limit is …
On the free energy of vector spin glasses with non-convex interactions
HB Chen, JC Mourrat - arXiv preprint arXiv:2311.08980, 2023 - arxiv.org
The limit free energy of spin-glass models with convex interactions can be represented as a
variational problem involving an explicit functional. Models with non-convex interactions are …
variational problem involving an explicit functional. Models with non-convex interactions are …
The solution of the deep Boltzmann machine on the Nishimori line
The deep Boltzmann machine on the Nishimori line with a finite number of layers is exactly
solved by a theorem that expresses its pressure through a finite dimensional variational …
solved by a theorem that expresses its pressure through a finite dimensional variational …
Estimating rank-one matrices with mismatched prior and noise: universality and large deviations
We prove a universality result that reduces the free energy of rank-one matrix estimation
problems in the setting of mismatched prior and noise to the computation of the free energy …
problems in the setting of mismatched prior and noise to the computation of the free energy …
Community detection with contextual multilayer networks
Z Ma, S Nandy - IEEE Transactions on Information Theory, 2023 - ieeexplore.ieee.org
In this paper, we study community detection when we observe sparse networks and a high
dimensional covariate matrix, all encoding the same community structure among subjects. In …
dimensional covariate matrix, all encoding the same community structure among subjects. In …
Mutual information for the sparse stochastic block model
T Dominguez, JC Mourrat - The Annals of Probability, 2024 - projecteuclid.org
We consider the problem of recovering the community structure in the stochastic block
model with two communities. We aim to describe the mutual information between the …
model with two communities. We aim to describe the mutual information between the …
An inference problem in a mismatched setting: a spin-glass model with Mattis interaction
The Wigner spiked model in a mismatched setting is studied with the finite temperature
Statistical Mechanics approach through its representation as a Sherrington-Kirkpatrick …
Statistical Mechanics approach through its representation as a Sherrington-Kirkpatrick …
Statistical inference of finite-rank tensors
H Chen, JC Mourrat, J Xia - Annales Henri Lebesgue, 2022 - numdam.org
Statistical inference of finite-rank tensors Page 1 Annales Henri Lebesgue 5 (2022) 1161-1189
HONGBIN CHEN JEAN-CHRISTOPHE MOURRAT JIAMING XIA STATISTICAL INFERENCE …
HONGBIN CHEN JEAN-CHRISTOPHE MOURRAT JIAMING XIA STATISTICAL INFERENCE …
Statistical mechanics of mean-field disordered systems: a Hamilton-Jacobi approach
T Dominguez, JC Mourrat - arXiv preprint arXiv:2311.08976, 2023 - arxiv.org
The goal of this book is to present new mathematical techniques for studying the behaviour
of mean-field systems with disordered interactions. We mostly focus on certain problems of …
of mean-field systems with disordered interactions. We mostly focus on certain problems of …