Machine learning (ML) encompasses a broad range of algorithms and modeling tools used
for a vast array of data processing tasks, which has entered most scientific disciplines in …

The stochastic block model (SBM) is a random graph model with planted clusters. It is widely
employed as a canonical model to study clustering and community detection, and provides …

Traditionally, community detection in graphs can be solved using spectral methods or
posterior inference under probabilistic graphical models. Focusing on random graph …

Generalized linear models (GLMs) are used in high-dimensional machine learning,
statistics, communications, and signal processing. In this paper we analyze GLMs when the …

Recent years witnessed the development of powerful generative models based on flows,
diffusion, or autoregressive neural networks, achieving remarkable success in generating …

We consider the high-dimensional inference problem where the signal is a low-rank
symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic …

In recent years important progress has been achieved towards proving the validity of the
replica predictions for the (asymptotic) mutual information (or “free energy”) in Bayesian …

Community detection in graphs is the problem of finding groups of vertices which are more
densely connected than they are to the rest of the graph. This problem has a long history, but …

We prove, under an assumption on the critical points of a real-valued function, that the
symmetric Ising perceptron exhibits thefrozen 1-RSB'structure conjectured by Krauth and …

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 …