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We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex}…
We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated…
We study the problem of sampling and reconstructing spectrally sparse graph signals where the objective is to select a subset of nodes of prespecified cardinality that ensures interpolation of the original signal with the lowest possible…
Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an…
We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal…
In multivariate statistics, the question of finding direct interactions can be formulated as a problem of network inference - or network reconstruction - for which the Gaussian graphical model (GGM) provides a canonical framework.…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
Various $\ell_1$-penalised estimation methods such as graphical lasso and CLIME are widely used for sparse precision matrix estimation. Many of these methods have been shown to be consistent under various quantitative assumptions about the…
We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
We propose a new 2-stage procedure that relies on the elastic net penalty to estimate a network based on partial correlations when data are heavy-tailed. The new estimator allows to consider the lasso penalty as a special case. Using Monte…
We consider penalized estimation in hidden Markov models (HMMs) with multivariate Normal observations. In the moderate-to-large dimensional setting, estimation for HMMs remains challenging in practice, due to several concerns arising from…
The exponential family random graph modeling (ERGM) framework provides a flexible approach for the statistical analysis of networks. As ERGMs typically involve normalizing factors that are costly to compute, practical inference relies on a…
Deep networks are increasingly applied to a wide variety of data, including data with high-dimensional predictors. In such analysis, variable selection can be needed along with estimation/model building. Many of the existing deep network…
Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested…
We propose maximum likelihood estimation for learning Gaussian graphical models with a Gaussian (ell_2^2) prior on the parameters. This is in contrast to the commonly used Laplace (ell_1) prior for encouraging sparseness. We show that our…
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…
Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this…
We propose an L1-penalized algorithm for fitting high-dimensional generalized linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as an extension of generalized linear models for clustered observations. This…
We consider both $\ell _{0}$-penalized and $\ell _{0}$-constrained quantile regression estimators. For the $\ell _{0}$-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and…