Related papers: Partial correlation hypersurfaces in Gaussian grap…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
We establish finite-sample guarantees for a polynomial-time algorithm for learning a nonlinear, nonparametric directed acyclic graphical (DAG) model from data. The analysis is model-free and does not assume linearity, additivity,…
We consider a bipartite version of the color degree matrix problem. A bipartite graph $G(U,V,E)$ is half-regular if all vertices in $U$ have the same degree. We give necessary and sufficient conditions for a bipartite degree matrix (also…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
Weak convergence of joint distributions generally does not imply convergence of conditional distributions. In particular, conditional distributions need not converge when joint Gaussian distributions converge to a singular Gaussian limit.…
Haxell's condition is a natural hypergraph analog of Hall's condition, which is a well-known necessary and sufficient condition for a bipartite graph to admit a perfect matching. That is, when Haxell's condition holds it forces the…
The dual normal factor graph and the factor graph duality theorem have been considered for discrete graphical models. In this paper, we show an application of the factor graph duality theorem to continuous graphical models. Specifically, we…
We introduce a new class of graphical models that generalizes Lauritzen-Wermuth-Frydenberg chain graphs by relaxing the semi-directed acyclity constraint so that only directed cycles are forbidden. Moreover, up to two edges are allowed…
This paper considers a challenging problem of identifying a causal graphical model under the presence of latent variables. While various identifiability conditions have been proposed in the literature, they often require multiple pure…
Structural learning of directed acyclic graphs (DAGs) or Bayesian networks has been studied extensively under the assumption that data are independent. We propose a new Gaussian DAG model for dependent data which assumes the observations…
Directed Acyclic Graphs (DAGs) are a standard tool in causal modeling, but their suitability for capturing the complexity of large-scale multimodal data is questionable. In practice, real-world multimodal datasets are often collected from…
Graph-based causal discovery methods aim to capture conditional independencies consistent with the observed data and differentiate causal relationships from indirect or induced ones. Successful construction of graphical models of data…
We prove that a general determinantal hypersurface of dimension 3 is nodal. Moreover, in terms of Chern classes associated with bundle morphisms, we derive a formula for the intersection homology Euler characteristic of a general…
We study parameter identifiability of directed Gaussian graphical models with one latent variable. In the scenario we consider, the latent variable is a confounder that forms a source node of the graph and is a parent to all other nodes,…
This paper addresses the problem of learning an undirected graph from data gathered at each nodes. Within the graph signal processing framework, the topology of such graph can be linked to the support of the conditional correlation matrix…
We study imbedded hypersurfaces in spacetime whose causal character is allowed to change from point to point. Inherited geometrical structures on these hypersurfaces are defined by two methods: first, the standard rigged connection induced…
A proof of the Generalized Road Coloring Problem, independent of the recent work by Beal and Perrin, is presented, using both semigroup methods and Trakhtman's algorithm. Algebraic properties of periodic, strongly connected digraphs are…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to a fully continuous program for score-based learning of DAG…