Related papers: Belief Propagation on the random $k$-SAT model
Random $K$-satisfiability ($K$-SAT) is a paradigmatic model system for studying phase transitions in constraint satisfaction problems and for developing empirical algorithms. The statistical properties of the random $K$-SAT solution space…
Infinite-range spin-glass models with Levy-distributed interactions show a spin-glass transition with similarities to both the Sherrington-Kirkpatrick model and to disordered spin systems on finite connectivity random graphs. Despite the…
In this paper we derive the equations for Loop Corrected Belief Propagation on a continuous variable Gaussian model. Using the exactness of the averages for belief propagation for Gaussian models, a different way of obtaining the…
A heuristic model procedure for determining satisfiability of CNF-formulae is set up and described by nonlinear recursion relations for m (number of clauses), n (number of variables) and clause filling k. The system mimicked by the…
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…
When belief propagation (BP) converges, it does so to a stationary point of the Bethe free energy $F$, and is often strikingly accurate. However, it may converge only to a local optimum or may not converge at all. An algorithm was recently…
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…
The ability to understand and solve high-dimensional inference problems is essential for modern data science. This article examines high-dimensional inference problems through the lens of information theory and focuses on the standard…
By controlling quantum fluctuations via the Falk-Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick model with a transverse magnetic field if the temperature…
Belief propagation (BP) is a powerful tool to solve distributed inference problems, though it is limited by short cycles in the corresponding factor graph. Such cycles may lead to incorrect solutions or oscillatory behavior. Only for…
This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean…
Belief Propagation (BP) is a simple probabilistic inference algorithm, consisting of passing messages between nodes of a graph representing a probability distribution. Its analogy with a neural network suggests that it could have…
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. We present a polynomial time algorithm that finds a satisfying assignment of F with high probability for constraint densities m/n<(1-eps_k)2^k\ln(k)/k,…
The commonly assumed cosmological history of our universe is that at early-times and high-temperatures the universe went through an ElectroWeak Phase Transition (EWPT). Assuming an EWPT, and depending on its strength, there are many…
Compressed sensing (CS) demonstrates that sparse signals can be recovered from underdetermined linear measurements. We focus on the joint sparse recovery problem where multiple signals share the same common sparse support sets, and they are…
Many datasets give partial information about an ordering or ranking by indicating which team won a game, which item a user prefers, or who infected whom. We define a continuous spin system whose Gibbs distribution is the posterior…
During the past decade, phase-transition phenomena in the random 3-satisfiability (3-SAT) problem has been intensively studied by statistical physics methods. In this work, we study the random 3-SAT problem by the mean-field first-step…
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access.…
Gaussian belief propagation (BP) has been widely used for distributed inference in large-scale networks such as the smart grid, sensor networks, and social networks, where local measurements/observations are scattered over a wide…