Related papers: Belief Propagation on replica symmetric random fac…
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 study interacting particle systems on the real line which generalize the Hammersley process [D. Aldous and P. Diaconis, Prob. Theory Relat. Fields 103, 199-213 (1995)]. Particles jump to the right to a randomly chosen point between their…
One of the main applications of free probability is to show that for appropriately chosen independent copies of $d$ random matrix models, any noncommutative polynomial in these $d$ variables has a spectral distribution that converges…
The Bethe approximation is a successful method for approximating partition functions of probabilistic models associated with a graph. Recently, Chertkov and Chernyak derived an interesting formula called Loop Series Expansion, which is an…
In this brief technical communication it is demonstrated how using Bethe ansatz technique the explicit expression for the two-point free energy distribution function in (1+1) directed polymers can be derived in rather simple way. Obtained…
An "element-free" probability distribution is what remains of a probability distribution after we forget the elements to which the probabilities were assigned. These objects naturally arise in Bayesian statistics, in situations where…
Belief propagation is an algorithm that is known from statistical physics and computer science. It provides an efficient way of calculating marginals that involve large sums of products which are efficiently rearranged into nested products…
Fixing $\beta \ge 0$ and an integer $q \ge 2$, consider the ferromagnetic $q$-Potts measures $\mu_n^{\beta,B}$ on finite graphs ${\sf G}_n$ on $n$ vertices, with external field strength $B \ge 0$ and the corresponding random cluster…
Accurate phase diagram calculation from molecular dynamics requires systematic treatment and convergence of statistical averages. In this work we propose a Gaussian process regression based framework for reconstructing the free energy…
Scale-free networks play a fundamental role in the study of complex networks and various applied fields due to their ability to model a wide range of real-world systems. A key characteristic of these networks is their degree distribution,…
We introduce a simple time-triggered protocol to achieve communication-efficient non-Bayesian learning over a network. Specifically, we consider a scenario where a group of agents interact over a graph with the aim of discerning the true…
The maximum energy of the EPR model on a weighted graph is known to be upper-bounded by the sum of the total weight and the value of maximum-weight fractional matching~(MWFM). Recently, Apte, Parekh and Sud~(APS) conjecture that the bound…
Three models of growing random networks with fitness dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is built by connecting incoming nodes to nodes…
We study the free energy of a most used deep architecture for restricted Boltzmann machines, where the layers are disposed in series. Assuming independent Gaussian distributed random weights, we show that the error term in the so-called…
A general random graph evolution mechanism is defined. The evolution is a combination of the preferential attachment model and the interaction of N vertices (N>=3). A vertex in the graph is characterized by its degree and its weight. The…
Motivated by the need to analyze large, decentralized datasets, distributed Bayesian inference has become a critical research area across multiple fields, including statistics, electrical engineering, and economics. This paper establishes…
We present a detailed study on application of factor graphs and the belief propagation (BP) algorithm to the power system state estimation (SE) problem. We start from the BP solution for the linear DC model, for which we provide a detailed…
Belief propagation (BP) is a message-passing heuristic for statistical inference in graphical models such as Bayesian networks and Markov random fields. BP is used to compute marginal distributions or maximum likelihood assignments and has…
We consider belief propagation (BP) as an efficient and scalable tool for state estimation and optimization problems in supply networks such as power grids. BP algorithms make use of factor graph representations, whose assignment to the…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…