Related papers: Graphical lasso for extremes
Natural images follow statistics inherited by the structure of our physical (visual) environment. In particular, a prominent facet of this structure is that images can be described by a relatively sparse number of features. We designed a…
Robust Bayesian methods for high-dimensional regression problems under diverse sparse regimes are studied. Traditional shrinkage priors are primarily designed to detect a handful of signals from tens of thousands of predictors in the…
High-dimensional data analysis typically focuses on low-dimensional structure, often to aid interpretation and computational efficiency. Graphical models provide a powerful methodology for learning the conditional independence structure in…
Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally.…
We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is…
High-dimensional multivariate time series are common in many scientific and industrial applications, where the interest lies in identifying key dependence structure within the data for subsequent analysis tasks, such as forecasting. An…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
This paper introduces the Gaussian multi-Graphical Model, a model to construct sparse graph representations of matrix- and tensor-variate data. We generalize prior work in this area by simultaneously learning this representation across…
Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence…
Number counts of massive high-redshift clusters provide a window to study primordial non-Gaussianity. The current quality of data, however, forces the statistical analysis to probe a region of parameter space -- the extreme tail of the mass…
We develop a method for probabilistic prediction of extreme value hot-spots in a spatio-temporal framework, tailored to big datasets containing important gaps. In this setting, direct calculation of summaries from data, such as the minimum…
To model high dimensional data, Gaussian methods are widely used since they remain tractable and yield parsimonious models by imposing strong assumptions on the data. Vine copulas are more flexible by combining arbitrary marginal…
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…
Motivated by the problem of inferring the graph structure of functional connectivity networks from multi-level functional magnetic resonance imaging data, we develop a valid inference framework for high-dimensional graphical models that…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…
Modelling non-homogeneous and multi-component data is a problem that challenges scientific researchers in several fields. In general, it is not possible to find a simple and closed form probabilistic model to describe such data. That is why…
Despite numerous years of research into the merits and trade-offs of various model selection criteria, obtaining robust results that elucidate the behavior of cross-validation remains a challenging endeavor. In this paper, we highlight the…
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…