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We propose a new modeling framework for highly-multivariate spatial processes that synthesizes ideas from recent multiscale and spectral approaches with graphical models. The basis graphical lasso writes a univariate Gaussian process as a…
Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point…
This work proposes an adaptive trace lasso regularized L1-norm based graph cut method for dimensionality reduction of Hyperspectral images, called as `Trace Lasso-L1 Graph Cut' (TL-L1GC). The underlying idea of this method is to generate…
This paper addresses learning of sparse structural changes or differential network between two classes of non-paranormal graphical models. We assume a multi-source and heterogeneous dataset is available for each class, where the covariance…
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…
The partial correlation graphical LASSO (PCGLASSO) is a penalised likelihood method for Gaussian graphical models which provides scale invariant sparse estimation of the precision matrix and improves upon the popular graphical LASSO method.…
We consider structure discovery of undirected graphical models from observational data. Inferring likely structures from few examples is a complex task often requiring the formulation of priors and sophisticated inference procedures.…
We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of…
We study ridge estimation of the precision matrix in the high-dimensional setting where the number of variables is large relative to the sample size. We first review two archetypal ridge estimators and note that their utilized penalties do…
Our concern is selecting the concentration matrix's nonzero coefficients for a sparse Gaussian graphical model in a high-dimensional setting. This corresponds to estimating the graph of conditional dependencies between the variables. We…
Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…
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: $\ell_1$…
Many Machine Learning algorithms are formulated as regularized optimization problems, but their performance hinges on a regularization parameter that needs to be calibrated to each application at hand. In this paper, we propose a general…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
This paper develops a new statistical inference theory for the precision matrix of high-frequency data in a high-dimensional setting. The focus is not only on point estimation but also on interval estimation and hypothesis testing for…
We consider the consistency properties of a regularised estimator for the simultaneous identification of both changepoints and graphical dependency structure in multivariate time-series. Traditionally, estimation of Gaussian Graphical…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
We model time-varying network data as realizations from multivariate Gaussian distributions with precision matrices that change over time. To facilitate parameter estimation, we require not only that each precision matrix at any given time…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…