Related papers: Loop series expansion with propagation diagrams
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…
Loopy belief propagation performs approximate inference on graphical models with loops. One might hope to compensate for the approximation by adjusting model parameters. Learning algorithms for this purpose have been explored previously,…
In this paper we present a synthesis of the work performed on two inference algorithms: the Pearl's belief propagation (BP) algorithm applied to Bayesian networks without loops (i.e. polytree) and the Loopy belief propagation (LBP)…
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…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
The main objective of this paper is to explore the precise relationship between the Bethe free energy (or entropy) and the Shannon conditional entropy of graphical error correcting codes. The main result shows that the Bethe free energy…
We present a real-time propagation method for computing linear and nonlinear optical properties of molecules based on the Bethe-Salpeter equation. The method follows the time evolution of the one-particle density matrix under an external…
Data association, the problem of reasoning over correspondence between targets and measurements, is a fundamental problem in tracking. This paper presents a graphical model formulation of data association and applies an approximate…
Gradients have been exploited in proposal distributions to accelerate the convergence of Markov chain Monte Carlo algorithms on discrete distributions. However, these methods require a natural differentiable extension of the target discrete…
The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…
We compute the logarithmic asymptotics of the non-existence probability (and more generally the lower-tail probability) for a wide variety of combinatorial problems for a range of parameters in the `critical regime' between the regime…
In this paper we develop a Bethe approximation, based on the cluster variation method, which is apt to study lattice models of branched polymers. We show that the method is extremely accurate in cases where exact results are known as, for…
For standard factor graphs (S-FGs) with non-negative real-valued local functions, Vontobel provided a combinatorial characterization of the Bethe approximation of the partition function, also known as the Bethe partition function, using…
This write-up contains some minor results and notes related to our work [HQ15] (some of them already known in the literature). In particular, it shows the following: - We show that a graph with polynomial expansion have sublinear…
The "expansion by regions" is a method of asymptotic expansion developed by Beneke and Smirnov in 1997. It expands the integrand according to the scaling prescriptions of a set of regions and integrates all expanded terms over the whole…
The sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data…
A Chain Event Graph (CEG) is a graphial model which designed to embody conditional independencies in problems whose state spaces are highly asymmetric and do not admit a natural product structure. In this paer we present a probability…