Related papers: Robust sparse Gaussian graphical modeling
Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
We introduce a novel edge tracing algorithm using Gaussian process regression. Our edge-based segmentation algorithm models an edge of interest using Gaussian process regression and iteratively searches the image for edge pixels in a…
Gaussian processes (GPs) are popular as nonlinear regression models for expensive computer simulations, yet GP performance relies heavily on estimation of unknown covariance parameters. Maximum likelihood estimation (MLE) is common, but it…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…
Statistical inference using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this paper, we propose a general framework to model the mutual interactions in a network, which enjoys ample…
We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…
In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty…
In the context of undirected Gaussian graphical models, we introduce three estimators based on elastic net penalty for the underlying dependence graph. Our goal is to estimate the sparse precision matrix, from which to retrieve both the…
Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint…
In this article, we consider the problem of reconstructing networks for continuous, binary, count and discrete ordinal variables by estimating sparse precision matrix in Gaussian copula graphical models. We propose two approaches: $\ell_1$…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…
Probabilistic graphical models (PGMs) provide a compact and flexible framework to model very complex real-life phenomena. They combine the probability theory which deals with uncertainty and logical structure represented by a graph which…
Inferring relations from correlational data allows researchers across the sciences to uncover complex connections between variables for insights into the underlying mechanisms. The researchers often represent inferred relations using…
Gaussian Process (GP) regression is a flexible modeling technique used to predict outputs and to capture uncertainty in the predictions. However, the GP regression process becomes computationally intensive when the training spatial dataset…
We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…
Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…
We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…