Phase retrieval consists in the recovery of a complex-valued signal from intensity-only
measurements. As it pervades a broad variety of applications, many researchers have …

It has been observed that the performances of many high-dimensional estimation problems
are universal with respect to underlying sensing (or design) matrices. Specifically, matrices …

We study a spiked Wigner problem with an inhomogeneous noise profile. Our aim in this
problem is to recover the signal passed through an inhomogeneous low-rank matrix …

We consider the problem of learning a target function corresponding to a single hidden layer
neural network, with a quadratic activation function after the first layer, and random weights …

In a mixed generalized linear model, the objective is to learn multiple signals from unlabeled
observations: each sample comes from exactly one signal, but it is not known which one. We …

We consider the problem of parameter estimation in a high-dimensional generalized linear
model. Spectral methods obtained via the principal eigenvector of a suitable data …

We discuss the inhomogeneous spiked Wigner model, a theoretical framework recently
introduced to study structured noise in various learning scenarios, through the prism of …

In this paper, we study phase retrieval under model misspecification and generative priors.
In particular, we aim to estimate an $ n $-dimensional signal $\mathbf {x} $ from $ m $ iid …

This article unveils a new relation between the Nishimori temperature parametrizing a
distribution P and the Bethe free energy on random Erdős–Rényi graphs with edge weights …

Sparse superposition codes were originally proposed as a capacity-achieving
communication scheme over the gaussian channel, whose coding matrices were made of iid …