Related papers: Accuracy Bounds for Belief Propagation
As belief networks are used to model increasingly complex situations, the need to automatically construct them from large databases will become paramount. This paper concentrates on solving a part of the belief network induction problem:…
The assumption that the values of model parameters are known or correctly learned, i.e., the Nishimori condition, is one of the requirements for the detectability analysis of the stochastic block model in statistical inference. In practice,…
The task of CDMA multiuser detection is to simultaneously estimate binary symbols of $K$ synchronous users from the received $N$ base-band CDMA signals. Mathematically, this can be formulated as an inference problem on a complete bipartite…
In this article we present an algorithm to compute bounds on the marginals of a graphical model. For several small clusters of nodes upper and lower bounds on the marginal values are computed independently of the rest of the network. The…
The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…
This paper considers the noisy group testing problem where among a large population of items some are defective. The goal is to identify all defective items by testing groups of items, with the minimum possible number of tests. The focus of…
We focus on belief propagation for the assignment problem, also known as the maximum weight bipartite matching problem. We provide a constructive proof that the well-known upper bound on the number of iterations (Bayati, Shah, Sharma 2008)…
We study the stochastic block model with two communities where vertices contain side information in the form of a vertex label. These vertex labels may have arbitrary label distributions, depending on the community memberships. We analyze a…
Finding the most probable assignment (MAP) in a general graphical model is known to be NP hard but good approximations have been attained with max-product belief propagation (BP) and its variants. In particular, it is known that using BP on…
We consider the reconstruction of a two-dimensional discrete image from a set of tomographic measurements corresponding to the Radon projection. Assuming that the image has a structure where neighbouring pixels have a larger probability to…
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…
We define two algorithms for propagating information in classification problems with pairwise relationships. The algorithms are based on contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is…
We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally…
Survey propagation (SP) is an exciting new technique that has been remarkably successful at solving very large hard combinatorial problems, such as determining the satisfiability of Boolean formulas. In a promising attempt at understanding…
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…
Interval analysis (or interval bound propagation, IBP) is a popular technique for verifying and training provably robust deep neural networks, a fundamental challenge in the area of reliable machine learning. However, despite substantial…
A Monte-Carlo algorithm for discrete statistical models that combines the full power of the Belief Propagation algorithm with the advantages of a detailed-balanced heat bath approach is presented. A sub-tree inside the factor graph is first…
Neural nets have become popular to accelerate parameter inferences, especially for the upcoming generation of galaxy surveys in cosmology. As neural nets are approximative by nature, a recurrent question has been how to propagate the neural…