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 …

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 …

Uniqueness of BP fixed point for the Potts model and applications to community detection

Y Gu, Y Polyanskiy - The Thirty Sixth Annual Conference on …, 2023 - proceedings.mlr.press
In the study of sparse stochastic block models (SBMs) one often needs to analyze a
distributional recursion, known as the belief propagation (BP) recursion. Uniqueness of the …

Breakdown of a concavity property of mutual information for non-Gaussian channels

A Kireeva, JC Mourrat - Information and Inference: A Journal of …, 2024 - academic.oup.com
Let and be two independent and identically distributed random variables, which we interpret
as the signal, and let and be two communication channels. We can choose between two …

Searching for (sharp) thresholds in random structures: Where are we now?

W Perkins - Bulletin of the American Mathematical Society, 2025 - ams.org
We survey the current state of affairs in the study of thresholds and sharp thresholds in
random structures on the occasion of the recent proof of the Kahn–Kalai conjecture by Park …

Optimal inference in contextual stochastic block models

O Duranthon, L Zdeborová - arxiv preprint arxiv:2306.07948, 2023 - arxiv.org
The contextual stochastic block model (cSBM) was proposed for unsupervised community
detection on attributed graphs where both the graph and the high-dimensional node …

Critical point representation of the mutual information in the sparse stochastic block model

T Dominguez, JC Mourrat - arxiv preprint arxiv:2406.15233, 2024 - arxiv.org
We consider the problem of recovering the community structure in the stochastic block
model. We aim to describe the mutual information between the observed network and the …

Channel Comparison Methods and Statistical Problems on Graphs

Y Gu - 2023 - dspace.mit.edu
Initially driven by channel coding, information theory has developed a large collection of
tools for measuring and comparing effectiveness of information channels. These tools have …

Adversarially-Robust Inference on Trees via Belief Propagation

SB Hopkins, A Li - The Thirty Seventh Annual Conference on …, 2024 - proceedings.mlr.press
We introduce and study the problem of posterior inference on tree-structured graphical
models in the presence of a malicious adversary who can corrupt some observed nodes. In …

[PDF][PDF] Robust recovery for stochastic block models, simplified and generalized

S Mohanty, P Raghavendra, DX Wu - Proceedings of the 56th Annual …, 2024 - dl.acm.org
We study the problem of robust community recovery: efficiently recovering communities in
sparse stochastic block models in the presence of adversarial corruptions. In the absence of …