Related papers: Exactness of Belief Propagation for Some Graphical…
The Bethe approximation, or loopy belief propagation algorithm is a successful method for approximating partition functions of probabilistic models associated with a graph. Chertkov and Chernyak derived an interesting formula called Loop…
Belief propagation (BP) is a popular method for performing probabilistic inference on graphical models. In this work, we enhance BP and propose self-guided belief propagation (SBP) that incorporates the pairwise potentials only gradually.…
We propose an original particle-based implementation of the Loopy Belief Propagation (LPB) algorithm for pairwise Markov Random Fields (MRF) on a continuous state space. The algorithm constructs adaptively efficient proposal distributions…
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…
Message-passing algorithms based on belief-propagation (BP) are successfully used in many applications including decoding error correcting codes and solving constraint satisfaction and inference problems. BP-based algorithms operate over…
Tensor network contraction on arbitrary graphs is a fundamental computational challenge with applications ranging from quantum simulation to error correction. While belief propagation (BP) provides a powerful approximation algorithm for…
The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…
We study the performance of different message passing algorithms in the two dimensional Edwards Anderson model. We show that the standard Belief Propagation (BP) algorithm converges only at high temperature to a paramagnetic solution. Then,…
Belief Propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals. The resulting approximations are equivalent to the Bethe-Peierls…
We generalize the belief-propagation algorithm to sparse random networks with arbitrary distributions of motifs (triangles, loops, etc.). Each vertex in these networks belongs to a given set of motifs (generalization of the configuration…
We continue our numerical study of quantum belief propagation initiated in [Phys. Rev. A, 77 (2008), p. 052318]. We demonstrate how the method can be expressed in terms of an effective thermal potential that materializes when the system…
In this paper, we address the inverse problem, or the statistical machine learning problem, in Markov random fields with a non-parametric pair-wise energy function with continuous variables. The inverse problem is formulated by maximum…
We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006) allows to express the exact partition function of a graphical model as a…
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.…
Variational message passing (VMP), belief propagation (BP) and expectation propagation (EP) have found their wide applications in complex statistical signal processing problems. In addition to viewing them as a class of algorithms operating…
A loop series expansion for the partition function of a general statistical model on a graph is carried out. If the auxiliary probability distributions of the expansion are chosen to be a fixed point of the belief-propagation equation, the…
A statistical system is classically defined on a set of microstates $E$ by a global energy function $H : E \to \mathbb{R}$, yielding Gibbs probability measures (softmins) $\rho^\beta(H)$ for every inverse temperature $\beta = T^{-1}$. Gibbs…
Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise…
The belief propagation (BP) algorithm is an efficient way to solve "inference" problems in graphical models, such as Bayesian networks and Markov random fields. The system-state probability distribution of CSMA wireless networks is a Markov…
Statistical Relational Models and, more recently, Probabilistic Programming, have been making strides towards an integration of logic and probabilistic reasoning. A natural expectation for this project is that a probabilistic logic…