Related papers: Belief Propagation, Bethe Approximation and Polyno…
We introduce two graph polynomials and discuss their properties. One is a polynomial of two variables whose investigation is motivated by the performance analysis of the Bethe approximation of the Ising partition function. The other is a…
In the bayesian analysis of Inverse Problems most relevant cases the forward maps (FM, or regressor function) are defined in terms of a system of (O, P)DE's with intractable solutions. These necessarily involve a numerical method to find…
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Belief propagation (BP) is a useful probabilistic inference algorithm for efficiently computing approximate marginal probability densities of random variables. However, in its standard form, BP is only applicable to the vector-type random…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
We consider the problem of maximum likelihood estimation in linear models represented by factor graphs and solved via the Gaussian belief propagation algorithm. Motivated by massive internet of things (IoT) networks and edge computing, we…
Gaussian Mixture Models (GMMs) commonly arise in communication systems, particularly in bilinear joint estimation and detection problems. Although the product of GMMs is still a GMM, as the number of factors increases, the number of…
We introduce and study the problem of posterior inference on tree-structured graphical models in the presence of a malicious adversary who can corrupt some observed nodes. In the well-studied broadcasting on trees model, corresponding to…
Probabilistic graphs are an abstraction that allow us to study randomized propagation in graphs. In a probabilistic graph, each edge is "active" with a certain probability, independent of the other edges. For two vertices $u,v$, a classic…
Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice,…
We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices $<u, v>$, along with a…
Most algorithms for propagating evidence through belief networks have been exact and exhaustive: they produce an exact (point-valued) marginal probability for every node in the network. Often, however, an application will not need…
Belief propagation (BP) is well-known as a low complexity decoding algorithm with a strong performance for important classes of quantum error correcting codes, e.g. notably for the quantum low-density parity check (LDPC) code class of…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
We consider the task of detecting a hidden bipartite subgraph in a given random graph. This is formulated as a hypothesis testing problem, under the null hypothesis, the graph is a realization of an Erd\H{o}s-R\'{e}nyi random graph over $n$…
We propose PROPAGATE, a fast approximation framework to estimate distance-based metrics on very large graphs such as the (effective) diameter, the (effective) radius, or the average distance within a small error. The framework assigns seeds…
Recently, Vontobel showed the relationship between Bethe free energy and annealed free energy for protograph factor graph ensembles. In this paper, annealed free energy of any random regular, irregular and Poisson factor graph ensembles are…
We propose a new approach to the theoretical analysis of Loopy Belief Propagation (LBP) and the Bethe free energy (BFE) by establishing a formula to connect LBP and BFE with a graph zeta function. The proposed approach is applicable to a…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…