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 …

Many questions of fundamental interest in today's science can be formulated as inference
problems: some partial, or noisy, observations are performed over a set of variables and the …

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

Graph neural networks (GNNs) have become increasingly popular for classification tasks on
graph-structured data. Yet, the interplay between graph topology and feature evolution in …

These notes survey and explore an emerging method, which we call the low-degree
method, for understanding statistical-versus-computational tradeoffs in high-dimensional …

In this review article we discuss connections between the physics of disordered systems,
phase transitions in inference problems, and computational hardness. We introduce two …

A common graph mining task is community detection, which seeks an unsupervised
decomposition of a network into groups based on statistical regularities in network …

This book presents a unified theory of random matrices for applications in machine learning,
offering a large-dimensional data vision that exploits concentration and universality …

Community detection, the decomposition of a graph into essential building blocks, has been
a core research topic in network science over the past years. Since a precise notion of what …

Inverse problems correspond to a certain type of optimization problems formulated over
appropriate input distributions. Recently, there has been a growing interest in understanding …