Related papers: Markov Equivalence Classes for Maximal Ancestral G…
The use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways. Recursive structural equation models are one kind of DAG model. However,…
Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive…
Max-linear Bayesian networks have emerged as highly applicable models for causal inference via extreme value data. However, conditional independence (CI) for max-linear Bayesian networks behaves differently than for classical Gaussian…
We describe structural properties of strongly connected finite directed graphs, that are invariants of the topological conjugacy of their Markov-Dyck shifts. For strongly connected finite directed graphs with these properties topological…
It is our view that the state of the art in constructing a large collection of graph algorithms in terms of linear algebraic operations is mature enough to support the emergence of a standard set of primitive building blocks. This paper is…
Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond…
We give characterizations of the structure and degree sequences of hereditary unigraphs, those graphs for which every induced subgraph is the unique realization of its degree sequence. The class of hereditary unigraphs properly contains the…
Directed acyclic graph models with hidden variables have been much studied, particularly in view of their computational efficiency and connection with causal methods. In this paper we provide the circumstances under which it is possible for…
Most causal discovery procedures assume that there are no latent confounders in the system, which is often violated in real-world problems. In this paper, we consider a challenging scenario for causal structure identification, where some…
We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of a discrete model is always restricted…
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of…
Assuming a directed acyclic graph (DAG) that represents prior knowledge of causal relationships between variables is a common starting point for cause-effect estimation. Existing literature typically invokes hypothetical domain expert…
Two different Markov jump processes driven out of equilibrium by constant thermodynamic forces may have identical current fluctuations in the stationary state. The concept of dynamical equivalence classes emerges from this statement as…
For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types…
Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest…
Given a graph $G$, a vertex switch of $v \in V(G)$ results in a new graph where neighbors of $v$ become nonneighbors and vice versa. This operation gives rise to an equivalence relation over the set of labeled digraphs on $n$ vertices. The…
Identifying controlled direct effects (CDEs) is crucial across numerous scientific domains. While existing methods can identify these effects from causal directed acyclic graphs (DAGs), the true DAG is often unknown in practice. Essential…
Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…
Graphs can have different properties that lead to several graph types and may allow for a varying representation of diverse information. In order to clarify the modeling power of graphs, we introduce a partial order on the most common graph…
Graphical Markov models use graphs, either undirected, directed, or mixed, to represent possible dependences among statistical variables. Applications of undirected graphs (UDGs) include models for spatial dependence and image analysis,…