Many questions of fundamental interest in today's science can be formulated as inference
problems: some partial, or noisy, observations are performed over a set of variables and the …

This chapter surveys recent work in applying ideas from graphical models and message
passing algorithms to solve large-scale regularized regression problems. In particular, the …

The standard linear regression (SLR) problem is to recover a vector x 0 from noisy linear
observations y= Ax 0+ w. The approximate message passing (AMP) algorithm proposed by …

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

Approximate message passing (AMP) is a low-cost iterative signal recovery algorithm for
linear system models. When the system transform matrix has independent identically …

Single-pixel imaging is an alternate imaging technique particularly well-suited to imaging
modalities such as hyper-spectral imaging, depth map**, 3D profiling. However, the single …

We consider the estimation of a random vector observed through a linear transform followed
by a componentwise probabilistic measurement channel. Although such linear mixing …

“Approximate message passing”(AMP) algorithms have proved to be effective in
reconstructing sparse signals from a small number of incoherent linear measurements …

A popular approach for estimating an unknown signal x 0∈ ℝ n from noisy, linear
measurements y= Ax 0+ z∈ ℝ m is via solving a so called regularized M-estimator: x̂:= arg …

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 …