Related papers: Nested Markov Properties for Acyclic Directed Mixe…
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…
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…
Acyclic directed mixed graphs (ADMGs) are graphs that contain directed ($\rightarrow$) and bidirected ($\leftrightarrow$) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the…
Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a…
Real causal processes may contain feedback loops and change over time. In this paper, we model cycles and non-stationary distributions using a mixture of directed acyclic graphs (DAGs). We then study the conditional independence (CI)…
We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such…
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…
We develop the theory linking 'E-separation' in directed mixed graphs (DMGs) with conditional independence relations among coordinate processes in stochastic differential equations (SDEs), where causal relationships are determined by "which…
This paper explores the role of Directed Acyclic Graphs (DAGs) as a representation of conditional independence relationships. We show that DAGs offer polynomially sound and complete inference mechanisms for inferring conditional…
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,…
Directed acyclic graph (DAG) models have become widely studied and applied in statistics and machine learning -- indeed, their simplicity facilitates efficient procedures for learning and inference. Unfortunately, these models are not…
The local Markov condition for a DAG to be an independence map of a probability distribution is well known. For DAGs with latent variables, represented as bi-directed edges in the graph, the local Markov property may invoke exponential…
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that…
Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal…
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Chickering (1995) provided a transformational characterization of…
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…
The investigation of directed acyclic graphs (DAGs) encoding the same Markov property, that is the same conditional independence relations of multivariate observational distributions, has a long tradition; many algorithms exist for model…
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Meek (1995) characterizes Markov equivalence classes for DAGs (with no…
We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully…
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…