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The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…
Learning a Gaussian Mixture Model (GMM) is hard when the number of parameters is too large given the amount of available data. As a remedy, we propose restricting the GMM to a Gaussian Markov Random Field Mixture Model (GMRF-MM), as well as…
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}…
Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…
Estimation of Gaussian graphical models is important in natural science when modeling the statistical relationships between variables in the form of a graph. The sparsity and clustering structure of the concentration matrix is enforced to…
We propose Nodewise Loreg, a nodewise $L_0$-penalized regression method for estimating high-dimensional sparse precision matrices. We establish its asymptotic properties, including convergence rates, support recovery, and asymptotic…
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…
This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…
Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…
The multivariate regression interpretation of the Gaussian chain graph model simultaneously parametrizes (i) the direct effects of $p$ predictors on $q$ outcomes and (ii) the residual partial covariances between pairs of outcomes. We…
We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…
The precision matrix that encodes conditional linear dependency relations among a set of variables forms an important object of interest in multivariate analysis. Sparse estimation procedures for precision matrices such as the graphical…
We consider the problem of automatic variable selection in a linear model with asymmetric or heavy-tailed errors when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
Anomalies and outliers are common in real-world data, and they can arise from many sources, such as sensor faults. Accordingly, anomaly detection is important both for analyzing the anomalies themselves and for cleaning the data for further…
In recent years, network models have gained prominence for their ability to capture complex associations. In statistical omics, networks can be used to model and study the functional relationships between genes, proteins, and other types of…
We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two…
In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…
We introduce GGLasso, a Python package for solving General Graphical Lasso problems. The Graphical Lasso scheme, introduced by (Friedman 2007) (see also (Yuan 2007; Banerjee 2008)), estimates a sparse inverse covariance matrix $\Theta$ from…