Related papers: Stationary Geometric Graphical Model Selection

We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. The benchmark information-theoretic results in the case of d-regular graphs require the number of samples to be at least proportional to…

We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different…

Graphs have become pervasive tools to represent information and datasets with irregular support. However, in many cases, the underlying graph is either unavailable or naively obtained, calling for more advanced methods to its estimation.…

In this paper, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model…

We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…

This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…

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…

This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact…

An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…

Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide…

A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…

We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a…

We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices of the graph is, under mild regularity conditions, a…

Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…

Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…

Machine learning methods on graphs have proven useful in many applications due to their ability to handle generally structured data. The framework of Gaussian Markov Random Fields (GMRFs) provides a principled way to define Gaussian models…