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Parameter and Structure Learning in Nested Markov Models
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Parameter and Structure Learning in Nested Markov Models
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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 latent variables imply independence constraints in the distribution resulting from a 'fixing' operation, in which a joint distribution is divided by a conditional. This operation generalizes marginalizing and conditioning. Some of these constraints correspond to identifiable 'dormant' independence constraints, with the well known 'Verma constraint' as one example. Recently, models defined by a set of the constraints arising after fixing from a DAG with latents, were characterized via a recursive factorization and a nested Markov property. In addition, a parameterization was given in the discrete case. In this paper we use this parameterization to describe a parameter fitting algorithm, and a search and score structure learning algorithm for these nested Markov models. We apply our algorithms to a variety of datasets.
Forward citations
Cited by 3 Pith papers
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Bounding Classical and Quantum Correlations in Bayesian Networks with Quasiprobabilities
Quasiprobability models in Bayesian networks generalize to produce all non-signalling correlations for a broad class of networks and conjecturally recover the nested Markov model.
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Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models
Introduces Generalized N Factor Model and LGES algorithm that identifies true causal structure including latents up to Markov equivalence class via score-based greedy search.
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Score-Based Causal Discovery of Latent Variable Causal Models
Introduces score-based causal discovery algorithms for latent variable models that achieve score equivalence and consistency while unifying some existing constraint-based approaches via degrees-of-freedom characterization.
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