Related papers: Graphical models for multivariate extremes
Conditional independence, graphical models and sparsity are key notions for parsimonious statistical models and for understanding the structural relationships in the data. The theory of multivariate and spatial extremes describes the risk…
Colored graphical models provide a parsimonious approach to modeling high-dimensional data by exploiting symmetries in the model parameters. In this work, we introduce the notion of coloring for extremal graphical models on multivariate…
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
Extremal graphical models encode the conditional independence structure of multivariate extremes. Key statistics for learning extremal graphical structures are empirical extremal variograms, for which we prove non-asymptotic concentration…
The field of extreme value statistics is concerned with modeling and predicting rare events. In a H\"usler-Reiss graphical model, a graph represents extremal conditional independence (CI) relations between random variables. These models are…
Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the…
Extremal graphical models encode the conditional independence structure of multivariate extremes and provide a powerful tool for quantifying the risk of rare events. Prior work on learning these graphs from data has focused on the setting…
The severity of multivariate extreme events is driven by the dependence between the largest marginal observations. The H\"usler-Reiss distribution is a versatile model for this extremal dependence, and it is usually parameterized by a…
A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts.…
The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modelling the extremes of multivariate data. These shapes,…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…
Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models…
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…
Modelling multivariate extreme events is essential when extrapolating beyond the range of observed data. Parametric models that are suitable for real-world extremes must be flexible -- particularly in their ability to capture asymmetric…
We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite…
Detecting anomalies in a temporal sequence of graphs can be applied is areas such as the detection of accidents in transport networks and cyber attacks in computer networks. Existing methods for detecting abnormal graphs can suffer from…
The behavior of extreme observations is well-understood for time series or spatial data, but little is known if the data generating process is a structural causal model (SCM). We study the behavior of extremes in this model class, both for…
In this paper, we estimate the sparse dependence structure in the tail region of a multivariate random vector, potentially of high dimension. The tail dependence is modeled via a graphical model for extremes embedded in the H\"usler-Reiss…
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…