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 …

Signal recovery from unitarily invariant measurements is investigated in this paper. A
message-passing algorithm is formulated on the basis of expectation propagation (EP). A …

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 …

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 …

We consider the phase retrieval problem of reconstructing a $ n $-dimensional real or
complex signal $\mathbf {X}^\star $ from $ m $(possibly noisy) observations $ Y_\mu=|\sum …

Uncertainty quantification is a central challenge in reliable and trustworthy machine
learning. Naive measures such as last-layer scores are well-known to yield overconfident …

Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique
for certain high-dimensional linear systems with non-Gaussian distributions. AMP only …

This paper proposes Bayes-optimal convolutional approximate message-passing (CAMP)
for signal recovery in compressed sensing. CAMP uses the same low-complexity matched …

We consider the problem of estimating a rank-$1 $ signal corrupted by structured rotationally
invariant noise, and address the following question:\emph {how well do inference algorithms …

Orthogonal/vector approximate message-passing (AMP) is a powerful message-passing
(MP) algorithm for signal reconstruction in compressed sensing. This paper proves the …