approximate message passing algorithm

Optimal errors and phase transitions in high-dimensional generalized linear models

Generalized linear models (GLMs) are used in high-dimensional machine learning, statistics, communications, and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing, …

Streaming Bayesian inference: Theoretical limits and mini-batch approximate message-passing

In statistical learning for real-world large-scale data problems, one must often resort to “streaming” algorithms which operate sequentially on small batches of data. In this work, we present an analysis of the information-theoretic limits of …

Phase Transitions and Sample Complexity in Bayes-Optimal Matrix Factorization

We analyze the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications, such as dictionary learning, blind matrix calibration, sparse …

Variational free energies for compressed sensing

We consider a variational free energy approach for compressed sensing. We first show that the naïve mean field approach performs remarkably well when coupled with a noise learning procedure. We also notice that it leads to the same equations as those …

Phase diagram and approximate message passing for blind calibration and dictionary learning

We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of phase …