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Belief Propagation (BP) is a powerful algorithm for distributed inference in probabilistic graphical models, however it quickly becomes infeasible for practical compute and memory budgets. Many efficient, non-parametric forms of BP have…

In this paper, we present structured message passing (SMP), a unifying framework for approximate inference algorithms that take advantage of structured representations such as algebraic decision diagrams and sparse hash tables. These…

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 rigorous analysis is presented for the dynamics of the algorithm…

Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely…

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)…

This paper introduces a framework for approximate message passing (AMP) in dynamic settings where the data at each iteration is passed through a linear operator. This framework is motivated in part by applications in large-scale,…

In this paper, we propose an information geometry (IG) framework to solve the standard linear regression problem. The proposed framework is an extension of the one for computing the mean of complex multivariate Gaussian distribution. By…

We present a "pull" approach to approximate products of Gaussian mixtures within message updates for Nonparametric Belief Propagation (NBP) inference. Existing NBP methods often represent messages between continuous-valued latent variables…

When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…

We consider the optimal quantization of compressive sensing measurements following the work on generalization of relaxed belief propagation (BP) for arbitrary measurement channels. Relaxed BP is an iterative reconstruction scheme inspired…

This paper is divided into two parts. The first part is devoted to the study of a class of Approximate Message Passing (AMP) algorithms which are widely used in the fields of statistical physics, machine learning, or communication theory.…

Sparse Bayesian learning (SBL) can be implemented with low complexity based on the approximate message passing (AMP) algorithm. However, it is vulnerable to `difficult' measurement matrices as AMP can easily diverge. Damped AMP has been…

In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…

The meta learning few-shot classification is an emerging problem in machine learning that received enormous attention recently, where the goal is to learn a model that can quickly adapt to a new task with only a few labeled data. We…

Efficient learning and model compression algorithm for deep neural network (DNN) is a key workhorse behind the rise of deep learning (DL). In this work, we propose a message passing based Bayesian deep learning algorithm called EM-TDAMP to…

A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica…

Vector Approximate Message Passing (VAMP) provides the means of solving a linear inverse problem in a Bayes-optimal way assuming the measurement operator is sufficiently random. However, VAMP requires implementing the linear minimum mean…

How do statistical dependencies in measurement noise influence high-dimensional inference? To answer this, we study the paradigmatic spiked matrix model of principal components analysis (PCA), where a rank-one matrix is corrupted by…

In this work, we address the problem of estimating sparse communication channels in OFDM systems in the presence of carrier frequency offset (CFO) and unknown noise variance. To this end, we consider a convex optimization problem, including…

Belief propagation is known to perform extremely well in many practical statistical inference and learning problems using graphical models, even in the presence of multiple loops. The iterative use of belief propagation algorithm on loopy…