Related papers: Learning extremal graphical structures in high dim…
Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information,…
In this paper we investigate the computational complexity of learning the graph structure underlying a discrete undirected graphical model from i.i.d. samples. We first observe that the notoriously difficult problem of learning parities…
Conditionally specified models are often used to describe complex multivariate data. Such models assume implicit structures on the extremes. So far, no methodology exists for calculating extremal characteristics of conditional models since…
Regarding the analysis of Web communication, social and complex networks the fast finding of most influential nodes in a network graph constitutes an important research problem. We use two indices of the influence of those nodes, namely,…
In this paper we consider a natural extremal graph theoretic problem of topological sort, concerning the minimization of the (topological) connectedness of the independence complex of graphs in terms of its dimension. We observe that the…
Let $X = \{X_{u}\}_{u \in U}$ be a real-valued Gaussian process indexed by a set $U$. It can be thought of as an undirected graphical model with every random variable $X_{u}$ serving as a vertex. We characterize this graph in terms of the…
We study the problem of recovering the structure underlying large Gaussian graphical models or, more generally, partial correlation graphs. In high-dimensional problems it is often too costly to store the entire sample covariance matrix. We…
Recently, there has been great success in applying deep neural networks on graph structured data. Most work, however, focuses on either node- or graph-level supervised learning, such as node, link or graph classification or node-level…
In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can…
Causality is essential for understanding complex systems, such as the economy, the brain, and the climate. Constructing causal graphs often relies on either data-driven or expert-driven approaches, both fraught with challenges. The former…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…
Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on…
The exponential random graph model (ERGM) is a central object in the study of clustering properties in social networks as well as canonical ensembles in statistical physics. Despite some breakthrough works in the mathematical understanding…
A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their…
We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that…
We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is…
Inferring the underlying graph topology that characterizes structured data is pivotal to many graph-based models when pre-defined graphs are not available. This paper focuses on learning graphs in the case of sequential data in dynamic…
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…