Related papers: Tutorial on Exact Belief Propagation in Bayesian N…
The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…
Belief Propagation (BP) is an efficient message-passing algorithm widely used for inference in graphical models and for solving various problems in statistical physics. However, BP often yields inaccurate estimates of order parameters and…
We describe expectation propagation for approximate inference in dynamic Bayesian networks as a natural extension of Pearl s exact belief propagation.Expectation propagation IS a greedy algorithm, converges IN many practical cases, but NOT…
We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…
Transformers are the dominant architecture in AI, yet why they work remains poorly understood. This paper offers a precise answer: a transformer is a Bayesian network. We establish this in five ways. First, we prove that every sigmoid…
In this article, we present a visual introduction to Gaussian Belief Propagation (GBP), an approximate probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily structured factor graphs. A special…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian belief networks. By imposing additional assumptions about the nature of the probabilistic models represented in the belief networks, we derive…
Recently, researchers have demonstrated that loopy belief propagation - the use of Pearls polytree algorithm IN a Bayesian network WITH loops OF error- correcting codes.The most dramatic instance OF this IS the near Shannon - limit…
Belief propagation is a well-studied algorithm for approximating local marginals of multivariate probability distribution over complex networks, while tensor network states are powerful tools for quantum and classical many-body problems.…
We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and…
In this manuscript, a general method for deriving filtering algorithms that involve a network of interconnected Bayesian filters is proposed. This method is based on the idea that the processing accomplished inside each of the Bayesian…
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…
Bayesian Belief Networks have been largely overlooked by Expert Systems practitioners on the grounds that they do not correspond to the human inference mechanism. In this paper, we introduce an explanation mechanism designed to generate…
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…
We extend Gaussian networks - directed acyclic graphs that encode probabilistic relationships between variables - to its vector form. Vector Gaussian continuous networks consist of composite nodes representing multivariates, that take…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
The two most important algorithms in artificial intelligence are backpropagation and belief propagation. In spite of their importance, the connection between them is poorly characterized. We show that when an input to backpropagation is…
Belief Propagation (BP) is a widely used approximation for exact probabilistic inference in graphical models, such as Markov Random Fields (MRFs). In graphs with cycles, however, no exact convergence guarantees for BP are known, in general.…
This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions,…
This paper studies the convergence rate of a message-passing distributed algorithm for solving a large-scale linear system. This problem is generalised from the celebrated Gaussian Belief Propagation (BP) problem for statistical learning…