approximation theory

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 …

Decoding from pooled data: Phase transitions of message passing

We consider the problem of decoding a discrete signal of categorical variables from the observation of several histograms of pooled subsets of it. We present an Approximate Message Passing (AMP) algorithm for recovering the signal in the random dense …

Multi-layer generalized linear estimation

We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP) algorithm for …

Replica analysis and approximate message passing decoder for superposition codes

Superposition codes are efficient for the additive white gaussian noise channel. We provide here a replica analysis of the performances of these codes for large signals. We also consider a Bayesian approximate message passing decoder based on a …

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 …