2017/10/24 by Patrick Forré, Joris M. Mooij, Forré, Patrick +1 · 6 citations
Computer Science · #AI-based Problem Solving and Planning #Bayesian Modeling and Causal Inference #Data Management and Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Methodology (stat.ME) #Other Statistics (stat.OT) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1710.08775
openalex publication_date 2017/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 can model latent (dependent) variables, and directed mixed graphs (DMGs) that can model cycles. We define and analyse several different Markov properties that relate the graphical structure of a HEDG with a probability distribution on a corresponding product space over the set of nodes, for example factorization properties, structural equations properties, ordered/local/global Markov properties, and marginal versions of these. The various Markov properties for HEDGes are in general not equivalent to each other when cycles or hyperedges are present, in contrast with the simpler case of directed acyclic graphical (DAG) models (also known as Bayesian networks). We show how the Markov properties for HEDGes - and thus the corresponding graphical Markov models - are logically related to each other.