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 …

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

How do statistical dependencies in measurement noise influence high-dimensional
inference? To answer this, we study the paradigmatic spiked matrix model of principal …

Over the last decade or so, Approximate Message Passing (AMP) algorithms have become
extremely popular in various structured high-dimensional statistical problems. Although the …

We study generalised linear regression and classification for a synthetically generated
dataset encompassing different problems of interest, such as learning with random features …

Understanding the reasons for the success of deep neural networks trained using stochastic
gradient-based methods is a key open problem for the nascent theory of deep learning. The …

In these Lecture Notes, we provide a comprehensive introduction to the most recent
advances in the application of machine learning methods in quantum sciences. We cover …

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 …

We consider the problem of learning a target function corresponding to a deep, extensive-
width, non-linear neural network with random Gaussian weights. We consider the asymptotic …

The Lasso with general Gaussian designs with applications to hypothesis testing Page 1 The
Annals of Statistics 2023, Vol. 51, No. 5, 2194–2220 https://doi.org/10.1214/23-AOS2327 © …