Related papers: Deep Gaussian Markov Random Fields

Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…

Current approaches for modeling discrete-valued outcomes associated with spatially-dependent areal units incur computational and theoretical challenges, especially in the Bayesian setting when full posterior inference is desired. As an…

Estimation of spatially-varying parameters for computationally expensive forward models governed by partial differential equations is addressed. A novel multiscale Bayesian inference approach is introduced based on deep probabilistic…

We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…

Bayesian inference of Gibbs random fields (GRFs) is often referred to as a doubly intractable problem, since the likelihood function is intractable. The exploration of the posterior distribution of such models is typically carried out with…

In this paper, we consider Bayesian image denoising based on a Gaussian Markov random field (GMRF) model, for which we propose an new algorithm. Our method can solve Bayesian image denoising problems, including hyperparameter estimation, in…

The wide adoption of Convolutional Neural Networks (CNNs) in applications where decision-making under uncertainty is fundamental, has brought a great deal of attention to the ability of these models to accurately quantify the uncertainty in…

This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by…

Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally.…

Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network…

This paper addresses the challenge of Neural Field (NeF) generalization, where models must efficiently adapt to new signals given only a few observations. To tackle this, we propose Geometric Neural Process Fields (G-NPF), a probabilistic…

Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…

Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…

Gaussian process-based latent variable models are flexible and theoretically grounded tools for nonlinear dimension reduction, but generalizing to non-Gaussian data likelihoods within this nonlinear framework is statistically challenging.…

The present paper aims to demonstrate the usage of Convolutional Neural Networks as a generative model for stochastic processes, enabling researchers from a wide range of fields (such as quantitative finance and physics) to develop a…

The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…

Neural fields have emerged as a powerful framework for representing continuous multidimensional signals such as images and videos, 3D and 4D objects and scenes, and radiance fields. While efficient, achieving high-quality representation…

We introduce the Contextual Graph Markov Model, an approach combining ideas from generative models and neural networks for the processing of graph data. It founds on a constructive methodology to build a deep architecture comprising layers…

Graph Neural Networks (GNNs) are information processing architectures for signals supported on graphs. They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph…