Related papers: Identifiability in Graphical Discrete Lyapunov Mod…
In his pioneering paper on matroids in 1935, Whitney obtained a characterization for binary matroids and left a comment at end of the paper that the problem of characterizing graphic matroids is the same as that of characterizing matroids…
Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…
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…
We consider a class of linear differential operators acting on vector-valued function spaces with general coupled boundary conditions. Unlike in the more usual case of so-called quantum graphs, the boundary conditions can be nonlinear.…
Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal…
A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear…
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which…
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…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
We consider a random model for directed graphs whereby an arc is placed from one vertex to another with a prescribed probability which may vary from arc to arc. Using perturbation bounds as well as Chernoff inequalities, we show that the…
We consider the following generalization of dominating sets: Let $G$ be a host graph and $P$ be a pattern graph $P$. A dominating $P$-pattern in $G$ is a subset $S$ of vertices in $G$ that (1) forms a dominating set in $G$ \emph{and} (2)…
Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from…
Directed acyclic graphs have been used fruitfully to represent causal strucures (Pearl 1988). However, in the social sciences and elsewhere models are often used which correspond both causally and statistically to directed graphs with…
We address some computational issues that may hinder the use of AMP chain graphs in practice. Specifically, we show how a discrete probability distribution that satisfies all the independencies represented by an AMP chain graph factorizes…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
Estimating the structure of directed acyclic graphs (DAGs) from observational data remains a significant challenge in machine learning. Most research in this area concentrates on learning a single DAG for the entire population. This paper…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
This paper studies cooperative tracking problem of heterogeneous Euler-Lagrange systems with an uncertain leader. Different from most existing works, system dynamic knowledge of the leader node is unaccessible to any follower node in our…