Related papers: Markov equivalence for ancestral graphs
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed…
Causal processes in biomedicine may contain cycles, evolve over time or differ between populations. However, many graphical models cannot accommodate these conditions. We propose to model causation using a mixture of directed cyclic graphs…
In graphical modelling, a bi-directed graph encodes marginal independences among random variables that are identified with the vertices of the graph. We show how to transform a bi-directed graph into a maximal ancestral graph that (i)…
Many methods for causal inference generate directed acyclic graphs (DAGs) that formalize causal relations between $n$ variables. Given the joint distribution on all these variables, the DAG contains all information about how intervening on…
Directed Acyclic Graphical (DAG) models efficiently formulate causal relationships in complex systems. Traditional DAGs assume nodes to be scalar variables, characterizing complex systems under a facile and oversimplified form. This paper…
Causal models in statistics are often described using acyclic directed mixed graphs (ADMGs), which contain directed and bidirected edges and no directed cycles. This article surveys various interpretations of ADMGs, discusses their…
We develop a necessary and sufficient causal identification criterion for maximally oriented partially directed acyclic graphs (MPDAGs). MPDAGs as a class of graphs include directed acyclic graphs (DAGs), completed partially directed…
Directed acyclic graphs (DAGs) and associated probability models are widely used to model neural connectivity and communication channels. In many experiments, data are collected from multiple subjects whose connectivities may differ but are…
We consider the problem of learning causal Directed Acyclic Graphs (DAGs) using combinations of observational and interventional experimental data. Current methods tailored to this setting assume that interventions either destroy…
The essential graph is a distinguished member of a Markov equivalence class of AMP chain graphs. However, the directed edges in the essential graph are not necessarily strong or invariant, i.e. they may not be shared by every member of the…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
Directed acyclic graphs (DAGs) are used for modeling causal relationships, dependencies, and flows in various systems. However, spectral analysis becomes impractical in this setting because the eigendecomposition of the adjacency matrix…
We claimed that there is a polynomial algorithm to test if two graphs are isomorphic. But the algorithm is wrong. It only tests if the adjacency matrices of two graphs have the same eigenvalues. There is a counterexample of two…
In Pe\~na (2007), MCMC sampling is applied to approximately calculate the ratio of essential graphs (EGs) to directed acyclic graphs (DAGs) for up to 20 nodes. In the present paper, we extend that work from 20 to 31 nodes. We also extend…
We present a new, efficient procedure to establish Markov equivalence between directed graphs that may or may not contain cycles under the \textit{d}-separation criterion. It is based on the Cyclic Equivalence Theorem (CET) in the seminal…
We consider a random walk on a discrete connected graph having some infinite branches plus finitely many vertices with finite degrees. We find the generator of a strong stationary dual in the sense of Fill, and use it to find some…
We extend to infinite graphs the matroidal characterization of finite graph duality, that two graphs are dual iff they have complementary spanning trees in some common edge set. The naive infinite analogue of this fails. The key in an…
In observational studies, the true causal model is typically unknown and needs to be estimated from available observational and limited experimental data. In such cases, the learned causal model is commonly represented as a partially…
Causal effect identification typically requires a fully specified causal graph, which can be difficult to obtain in practice. We provide a sufficient criterion for identifying causal effects from a candidate set of Markov equivalence…
We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non…