Related papers: Beyond Belief Propagation: Cluster-Corrected Tenso…
A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such…
In a complete bipartite graph with vertex sets of cardinalities $n$ and $m$, assign random weights from exponential distribution with mean 1, independently to each edge. We show that, as $n\rightarrow\infty$, with $m = \lceil…
This paper develops methods of distributed Bayesian hypothesis tests for fault detection and diagnosis that are based on belief propagation and optimization in graphical models. The main challenges in developing distributed statistical…
In distributed target tracking for wireless sensor networks, agreement on the target state can be achieved by the construction and maintenance of a communication path, in order to exchange information regarding local likelihood functions.…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
This paper studies Graphical SLOPE for precision matrix estimation, with emphasis on its ability to recover both sparsity and clusters of edges with equal or similar strength. In a fixed-dimensional regime, we establish that the root-$n$…
Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…
Cluster expansions for the exponential of local operators are constructed using tensor networks. In contrast to other approaches, the cluster expansion does not break any spatial or internal symmetries and exhibits a very favourable…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference;…
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…
Previous work has suggested that the structural restrictions of graphs from classes of bounded expansion--locally dense pockets in a globally sparse graph--naturally coincide with common properties of real-world networks such as clustering…
As neural networks become more integrated into the systems that we depend on for transportation, medicine, and security, it becomes increasingly important that we develop methods to analyze their behavior to ensure that they are safe to use…
Tensor network contraction is a fundamental mathematical operation that generalizes the dot product and matrix multiplication. It finds applications in numerous domains, such as database systems, graph theory, machine learning, probability…
Behavioral experiments on humans and animals suggest that the brain performs probabilistic inference to interpret its environment. Here we present a new general-purpose, biologically-plausible neural implementation of approximate inference.…
Bipartite Correlation clustering is the problem of generating a set of disjoint bi-cliques on a set of nodes while minimizing the symmetric difference to a bipartite input graph. The number or size of the output clusters is not constrained…
We study the fundamental limits on learning latent community structure in dynamic networks. Specifically, we study dynamic stochastic block models where nodes change their community membership over time, but where edges are generated…
A key idea in coding for the broadcast channel (BC) is binning, in which the transmitter encode information by selecting a codeword from an appropriate bin (the messages are thus the bin indexes). This selection is normally done by solving…
3D perception in point clouds is transforming the perception ability of future intelligent machines. Point cloud algorithms, however, are plagued by irregular memory accesses, leading to massive inefficiencies in the memory sub-system,…
This paper presents an enhanced belief propagation (BP) decoding algorithm and a reinforcement learning-based BP decoding algorithm for polar codes. The enhanced BP algorithm weighs each Processing Element (PE) input based on their signals…