Related papers: Learning High-dimensional Gaussian Graphical Model…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…
Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the…
This paper considers learning of the graphical structure of a $p$-dimensional random vector $X \in R^p$ using both parametric and non-parametric methods. Unlike the previous works which observe $x$ directly, we consider the indirect…
Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or…
We propose a new procedure for estimating high dimensional Gaussian graphical models. Our approach is asymptotically tuning-free and non-asymptotically tuning-insensitive: it requires very few efforts to choose the tuning parameter in…
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple…
This paper studies the estimation of high dimensional Gaussian graphical model (GGM). Typically, the existing methods depend on regularization techniques. As a result, it is necessary to choose the regularized parameter. However, the…
Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables. Knowing the sparsity of such a graphical model is valuable for modeling multivariate distributions…
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…
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…
We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary…
In undirected graphical models, learning the graph structure and learning the functions that relate the predictive variables (features) to the responses given the structure are two topics that have been widely investigated in machine…
Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…
Motivated by the need to study the molecular mechanism underlying Type 1 Diabetes (T1D) with the gene expression data collected from both the patients and healthy controls at multiple time points, we propose an innovative method for jointly…
Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation…
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
A general theory for Gaussian mean estimation that automatically adapts to unknown sparsity under arbitrary norms is proposed. The theory is applied to produce adaptively minimax rate-optimal estimators in high dimensional regression and…
The edge structure of the graph defining an undirected graphical model describes precisely the structure of dependence between the variables in the graph. In many applications, the dependence structure is unknown and it is desirable to…
Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…