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We apply Guo and Wang's relaxed belief propagation (BP) method to the estimation of a random vector from linear measurements followed by a componentwise probabilistic measurement channel. Relaxed BP uses a Gaussian approximation in standard…
Approximate Message Passing (AMP) algorithms are a class of iterative procedures for computationally-efficient estimation in high-dimensional inference and estimation tasks. Due to the presence of an 'Onsager' correction term in its…
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)…
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…
Approximate Message Passing (AMP) algorithms are a family of iterative algorithms based on large random matrices with the special property of tracking the statistical properties of their iterates. They are used in various fields such as…
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…
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 introduces a stochastic plug-and-play (PnP) sampling algorithm that leverages variable splitting to efficiently sample from a posterior distribution. The algorithm based on split Gibbs sampling (SGS) draws inspiration from the…
Message-passing (MP) is a powerful tool for finding an approximate solution in optimization. We generalize it to nonlinear product-sum form, and numerically show the fast convergence for the minimum feedback vertex set and the minimum…
This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian…
Recent result shows how to compute distributively and efficiently the linear MMSE for the multiuser detection problem, using the Gaussian BP algorithm. In the current work, we extend this construction, and show that operating this algorithm…
Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal -- sometimes greatly so. This paper develops generalized approximate message passing (GAMP) algorithms for…
This paper focuses on the distributed static estimation problem and a Belief Propagation (BP) based estimation algorithm is proposed. We provide a complete analysis for convergence and accuracy of it. More precisely, we offer conditions…
Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from…
Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this…
Quantifying predictive uncertainty of neural networks has recently attracted increasing attention. In this work, we focus on measuring uncertainty of graph neural networks (GNNs) for the task of node classification. Most existing GNNs model…
The Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter is an almost exact closed-form approximation to the Bayes-optimal multi-target tracking algorithm. Due to its optimality guarantees and ease of implementation, it has been…
Estimating the probability of collision between spacecraft is crucial for risk management and collision-avoidance strategies. Current methods often rely on Gaussian assumptions and simplifications, which can be inaccurate in highly…
In this paper, we use belief-propagation techniques to develop fast algorithms for image inpainting. Unlike traditional gradient-based approaches, which may require many iterations to converge, our techniques achieve competitive results…
Recently, message-passing Neural networks (MPNN) provide a promising tool for dealing with molecular graphs and have achieved remarkable success in facilitating the discovery and materials design with desired properties. However, the…