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 …

In this review article we discuss connections between the physics of disordered systems,
phase transitions in inference problems, and computational hardness. We introduce two …

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 …

Deep learning has gained great popularity due to its widespread success on many inference
problems. We consider the application of deep learning to the sparse linear inverse …

A key challenge of massive MTC (mMTC), is the joint detection of device activity and
decoding of data. The sparse characteristics of mMTC makes compressed sensing (CS) …

We prove a universality theorem for learning with random features. Our result shows that, in
terms of training and generalization errors, a random feature model with a nonlinear …

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

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

This paper considers the problem of solving systems of quadratic equations, namely,
recovering an object of interest x^ ♮ ∈ R^ nx♮∈ R n from m quadratic equations/samples …

Generalized linear models (GLMs) are used in high-dimensional machine learning,
statistics, communications, and signal processing. In this paper we analyze GLMs when the …