Smooth, identifiable supermodels of discrete DAG models with latent variables

Abstract

We provide a parameterization of the discrete nested Markov model, which is a supermodel that approximates DAG models (Bayesian network models) with latent variables. Such models are widely used in causal inference and machine learning. We explicitly evaluate their dimension, show that they are curved exponential families of distributions, and fit them to data. The parameterization avoids the irregularities and unidentifiability of latent variable models. The parameters used are all fully identifiable and causally-interpretable quantities.

30 pages

References in corpus (9)

• Likelihood ratio tests and singularities
• Discrete chain graph models
• Nested Markov Properties for Acyclic Directed Mixed Graphs
• Margins of discrete Bayesian networks
• Probability distributions with summary graph structure
• On the Testable Implications of Causal Models with Hidden Variables
• Cumulative distribution networks and the derivative-sum-product algorithm
• Maximum likelihood fitting of acyclic directed mixed graphs to binary data
• Mixed Cumulative Distribution Networks

Cited by in corpus (1)

• Margins of discrete Bayesian networks