Related papers: Double-Edge Factor Graphs: Definition, Properties,…
[...] In this thesis, we are interested in generalizing factor graphs and the relevant methods toward describing quantum systems. Two generalizations of classical graphical models are investigated, namely double-edge factor graphs (DeFGs)…
For standard factor graphs (S-FGs) with non-negative real-valued local functions, Vontobel provided a combinatorial characterization of the Bethe approximation of the partition function, also known as the Bethe partition function, using…
Message passing on factor graphs is a powerful framework for probabilistic inference, which finds important applications in various scientific domains. The most wide-spread message passing scheme is the sum-product algorithm (SPA) which…
One of the most common types of functions in mathematics, physics, and engineering is a sum of products, sometimes called a partition function. After "normalization," a sum of products has a natural graphical representation, called a normal…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
We consider the application of the factor graph framework for symbol detection on linear inter-symbol interference channels. Based on the Ungerboeck observation model, a detection algorithm with appealing complexity properties can be…
Many quantities of interest in communications, signal processing, artificial intelligence, and other areas can be expressed as the partition sum of some factor graph. Although the exact calculation of the partition sum is in many cases…
This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.…
We propose the use of hyperedge replacement graph grammars for factor graphs, or factor graph grammars (FGGs) for short. FGGs generate sets of factor graphs and can describe a more general class of models than plate notation, dynamic…
Approximating the permanent of a complex-valued matrix is a fundamental problem with applications in Boson sampling and probabilistic inference. In this paper, we extend factor-graph-based methods for approximating the permanent of…
We present in this article the model Function-described graph (FDG), which is a type of compact representation of a set of attributed graphs (AGs) that borrow from Random Graphs the capability of probabilistic modelling of structural and…
A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…
The natural Hilbert Space of quantum particles can implement maximum-likelihood (ML) decoding of classical information. The 'Quantum Product Algorithm' (QPA) is computed on a Factor Graph, where function nodes are unitary matrix operations…
To allow for tractable probabilistic inference with respect to domain sizes, lifted probabilistic inference exploits symmetries in probabilistic graphical models. However, checking whether two factors encode equivalent semantics and hence…
This paper presents a factor graph formulation and particle-based sum-product algorithm (SPA) for robust sequential localization in multipath-prone environments. The proposed algorithm jointly performs data association, sequential…
We introduce and study a loopless multigraph associated with a split graph $S$: the factor graph of $S$, denoted by $\Phi(S)$, which encodes the combinatorial information about 2-switch transformations over $S$. This construction provides a…
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…
This paper explores the use of factor graphs as an inference and analysis tool for Bayesian peer-to-peer decentralized data fusion. We propose a framework by which agents can each use local factor graphs to represent relevant partitions of…
A numerical semigroup $S$ is an additively-closed set of non-negative integers, and a factorization of an element $n$ of $S$ is an expression of $n$ as a sum of generators of $S$. It is known that for a given numerical semigroup $S$, the…
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…