Related papers: The Inverse G-Wishart Distribution and Variational…
Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes…
We show how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian semiparametric regression models. In particular, this approach is amenable to handling…
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…
A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the…
Factor graphs have recently gained increasing attention as a unified framework for representing and constructing algorithms for signal processing, estimation, and control. One capability that does not seem to be well explored within the…
A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…
The G-Wishart distribution is the conjugate prior for precision matrices that encode the conditional independencies of a Gaussian graphical model. While the distribution has received considerable attention, posterior inference has proven…
A general graph-structured neural network architecture operates on graphs through two core components: (1) complex enough message functions; (2) a fixed information aggregation process. In this paper, we present the Policy Message Passing…
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…
Graph signal processing is a framework to handle graph structured data. The fundamental concept is graph shift operator, giving rise to the graph Fourier transform. While the graph Fourier transform is a centralized procedure, distributed…
Bayesian inference on structured models typically relies on the ability to infer posterior distributions of underlying hidden variables. However, inference in implicit models or complex posterior distributions is hard. A popular tool for…
In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different…
Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the…
Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
Advances in neural variational inference have facilitated the learning of powerful directed graphical models with continuous latent variables, such as variational autoencoders. The hope is that such models will learn to represent rich,…
The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing…
Random factor graphs provide a powerful framework for the study of inference problems such as decoding problems or the stochastic block model. Information-theoretically the key quantity of interest is the mutual information between the…
In this article, we present a visual introduction to Gaussian Belief Propagation (GBP), an approximate probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily structured factor graphs. A special…
The field of Graph Signal Processing (GSP) has proposed tools to generalize harmonic analysis to complex domains represented through graphs. Among these tools are translations, which are required to define many others. Most works propose to…