In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional regression, to multi-layer case handling of cascaded problem such as matrix-factorization arising in relay communication among others. Assuming statistically independent matrix entries with known priors, new algorithm called ML-BiGAMP could general sum-produ...

This paper determines the computational strength of the shared memory abstraction (a register) emulated over a message passing system, and compares it with fundamental message passing abstractions like consensus and various forms of reliable broadcast. We introduce the notion of Quorum failure detectors and show that this notion captures the exact amount of information about failures needed to ...

Most optimization problems in applied sciences realistically involve uncertainty in the parameters defining the cost function, of which only statistical information is known beforehand. Here we provide an in-depth discussion of how message passing algorithms for stochastic optimization based on the cavity method of statistical physics can be constructed. We focus on two basic problems, namely t...

We study the gossip problem in a message-passing environment: When a process receives a message, it has to decide whether the sender has more recent information on other processes than itself. This problem is at the heart of many distributed algorithms, and it is tightly related to questions from formal methods concerning the expressive power of distributed automata. We provide a non-determinis...

The message passing paradigm underlies many important families of programs—for instance programs in the area of high performance computing that support science and engineering research. Unfortunately, very few formal methods researchers are involved in developing formal analysis tools and techniques for message passing programs. This paper summarizes research being done in our groups in support...

Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.This thesis studies inference in discrete graphical models from an “algebraic perspective” and the ways inference can be used to express and approximate NP-har...

The MPI Forum This paper presents an overview of mpi, a proposed standard message passing interface for MIMD distributed memory concurrent computers. The design of mpi has been a collective eeort involving researchers in the United States and Europe from many organizations and institutions. mpi includes point-to-point and collective communication routines, as well as support for process groups,...

Unifying logical and probabilistic reasoning is a longstanding goal of AI. While recent work in lifted belief propagation, handling whole sets of indistinguishable objects together, are promising steps towards achieving this goal that even scale to realistic domains, they are not tailored towards solving combinatorial problems such as determining the satisfiability of Boolean formulas. Recent r...

The principal submatrix localization problem deals with recovering a K ×K principal submatrix of elevated mean μ in a large n × n symmetric matrix subject to additive standard Gaussian noise. This problem serves as a prototypical example for community detection, in which the community corresponds to the support of the submatrix. The main result of this paper is that in the regime Ω( √ n) ≤ K ≤ ...