Related papers: Positivity for Gaussian graphical models
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…
The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical…
Graph-based causal discovery methods aim to capture conditional independencies consistent with the observed data and differentiate causal relationships from indirect or induced ones. Successful construction of graphical models of data…
This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive…
The covariance graph (aka bi-directed graph) of a probability distribution $p$ is the undirected graph $G$ where two nodes are adjacent iff their corresponding random variables are marginally dependent in $p$. In this paper, we present a…
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.…
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…
Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the…
We propose {graphical sure screening}, or GRASS, a very simple and computationally-efficient screening procedure for recovering the structure of a Gaussian graphical model in the high-dimensional setting. The GRASS estimate of the…
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. For decomposable…
The dual normal factor graph and the factor graph duality theorem have been considered for discrete graphical models. In this paper, we show an application of the factor graph duality theorem to continuous graphical models. Specifically, we…
This paper is devoted to the estimation of a partial graphical model with a structural Bayesian penalization. Precisely, we are interested in the linear regression setting where the estimation is made through the direct links between…
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…
Finding the parameters of a latent variable causal model is central to causal inference and causal identification. In this article, we show that existing graphical structures that are used in causal inference are not stable under…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
Undirected graphical models are widely used to model the conditional independence structure of vector-valued data. However, in many modern applications, for example those involving EEG and fMRI data, observations are more appropriately…
Conditional independence, graphical models and sparsity are key notions for parsimonious statistical models and for understanding the structural relationships in the data. The theory of multivariate and spatial extremes describes the risk…