Related papers: Extending Factor Graphs so as to Unify Directed an…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…
We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph…
We consider the following problem: Given an undirected (mixed) network and a set of ordered source-target, or cause-effect pairs, direct all edges so as to maximize the number of pairs that admit a directed source-target path. This is…
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings,…
The factor graph decentralized data fusion (FG-DDF) framework was developed for the analysis and exploitation of conditional independence in {heterogeneous Bayesian decentralized fusion problems, in which robots update and fuse pdfs over…
In recent years, we have witnessed a surge of Graph Neural Networks (GNNs), most of which can learn powerful representations in an end-to-end fashion with great success in many real-world applications. They have resemblance to Probabilistic…
Generative Adversarial Networks (GANs) are modern methods to learn the underlying distribution of a data set. GANs have been widely used in sample synthesis, de-noising, domain transfer, etc. GANs, however, are designed in a model-free…
Foundation models have emerged as critical components in a variety of artificial intelligence applications, and showcase significant success in natural language processing and several other domains. Meanwhile, the field of graph machine…
We describe a graph-based neural acceleration technique for nonnegative matrix factorization that builds upon a connection between matrices and bipartite graphs that is well-known in certain fields, e.g., sparse linear algebra, but has not…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Satellite power system is a complex, highly interconnected hybrid system that exhibit nonlinear and mode switching behaviors. Directed factor graph is an inference model for fault diagnosis using probabilistic reasoning techniques. A novel…
Probabilistic graphical models are widely used to model complex systems under uncertainty. Traditionally, Gaussian directed graphical models are applied for analysis of large networks with continuous variables as they can provide…
Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…
We propose a Bayesian regression method that accounts for multi-way interactions of arbitrary orders among the predictor variables. Our model makes use of a factorization mechanism for representing the regression coefficients of…
We show that the factor graph and certifiable estimation paradigms, which have thus far been treated as essentially independent in the literature, can be naturally synthesized into a unified framework for certifiable factor graph…
Graph signal processing (GSP) advances spectral analysis on irregular domains. However, existing two-dimensional graph fractional Fourier transform (2D-GFRFT) employs a single fractional order for both factor graphs, thereby limiting its…
The analysis of practical probabilistic models on the computer demands a convenient representation for the available knowledge and an efficient algorithm to perform inference. An appealing representation is the influence diagram, a network…
A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, as for…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…