Related papers: Enumerating Markov Equivalence Classes of Acyclic …
Although the concept of d-separation was originally defined for directed acyclic graphs (see Pearl 1988), there is a natural extension of he concept to directed cyclic graphs. When exactly the same set of d-separation relations hold in two…
The invariance properties of interventional distributions relative to the observational distribution, and how these properties allow us to refine Markov equivalence classes (MECs) of DAGs, is central to causal DAG discovery algorithms that…
In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and…
Causal discovery aims to recover graphs that represent causal relations among given variables from observations, and new methods are constantly being proposed. Increasingly, the community raises questions about how much progress is made,…
The constraints arising from DAG models with latent variables can be naturally represented by means of acyclic directed mixed graphs (ADMGs). Such graphs contain directed and bidirected arrows, and contain no directed cycles. DAGs with…
Some temporal networks, most notably citation networks, are naturally represented as directed acyclic graphs (DAGs). To detect communities in DAGs, we propose a modularity for DAGs by defining an appropriate null model (i.e., randomized…
Due to its human-interpretability and invariance properties, Directed Acyclic Graph (DAG) has been a foundational tool across various areas of AI research, leading to significant advancements. However, DAG learning remains highly…
We consider a a collection of categorical random variables. Of special interest is the causal effect on an outcome variable following an intervention on another variable. Conditionally on a Directed Acyclic Graph (DAG), we assume that the…
Acyclic directed mixed graphs, also known as semi-Markov models represent the conditional independence structure induced on an observed margin by a DAG model with latent variables. In this paper we present a factorization criterion for…
Learning the structure of causal directed acyclic graphs (DAGs) is useful in many areas of machine learning and artificial intelligence, with wide applications. However, in the high-dimensional setting, it is challenging to obtain good…
We introduce a new class of identifiable DAG models where the conditional distribution of each node given its parents belongs to a family of generalized hypergeometric distributions (GHD). A family of generalized hypergeometric…
A well-studied challenge that arises in the structure learning problem of causal directed acyclic graphs (DAG) is that using observational data, one can only learn the graph up to a "Markov equivalence class" (MEC). The remaining undirected…
Comparing directed acyclic graphs is essential in various fields such as healthcare, social media, finance, biology, and marketing. DAGs often result from contagion processes over networks, including information spreading, retweet activity,…
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…
The main approach to defining equivalence among acyclic directed causal graphical models is based on the conditional independence relationships in the distributions that the causal models can generate, in terms of the Markov equivalence.…
We analyze the identifiability of directed acyclic graphs in the case of partial excitation and measurement. We consider an additive model where the nonlinear functions located in the edges depend only on a past input, and we analyze the…
There has been a growing interest in causal learning in recent years. Commonly used representations of causal structures, including Bayesian networks and structural equation models (SEM), take the form of directed acyclic graphs (DAGs). We…
In this paper, we consider Gaussian models Markov with respect to an arbitrary DAG. We first construct a family of conjugate priors for the Cholesky parametrization of the covariance matrix of such models. This family has as many shape…
Statistical relationships in observed data can arise for several different reasons: the observed variables may be causally related, they may share a latent common cause, or there may be selection bias. Each of these scenarios can be…
Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high dimensional settings when the graphs to be learned are not sparse. In this paper, we…