相关论文: Quantum Graphical Models and Belief Propagation

We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data…

Quantum Graphical Models (QGMs) generalize classical graphical models by adopting the formalism for reasoning about uncertainty from quantum mechanics. Unlike classical graphical models, QGMs represent uncertainty with density matrices in…

This paper is devoted to expressiveness of hypergraphs for which uncertainty propagation by local computations via Shenoy/Shafer method applies. It is demonstrated that for this propagation method for a given joint belief distribution no…

Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to statistical model representation and software development. Clear communication and representation…

Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…

Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information…

Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…

It is the focus of this work to extend and study the previously proposed quantum-like Bayesian networks to deal with decision-making scenarios by incorporating the notion of maximum expected utility in influence diagrams. The general idea…

One of the major successes in computational biology has been the unification, using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied…

Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational…

Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…

With the wide-spread availability of complex relational data, semi-supervised node classification in graphs has become a central machine learning problem. Graph neural networks are a recent class of easy-to-train and accurate methods for…

Bayesian inference offers a principled account of information processing in natural agents. However, it remains an open question how neural mechanisms perform their abstract operations. We investigate a hypothesis where a distributed form…

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…

Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover…

Recent years have seen a growing interest in the use of belief propagation - an algorithm originally introduced for performing statistical inference on graphical models - for approximate, but highly efficient, tensor network contraction.…

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…

Performing exact inference on Bayesian networks is known to be #P-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values $e$ of evidence variables. Classically,…

Quantum Markov networks are a generalization of quantum Markov chains to arbitrary graphs. They provide a powerful classification of correlations in quantum many-body systems---complementing the area law at finite temperature---and are…

We propose a directed acyclic hypergraph framework for a probabilistic graphical model that we call Bayesian hypergraphs. The space of directed acyclic hypergraphs is much larger than the space of chain graphs. Hence Bayesian hypergraphs…