Smooth, identifiable supermodels of discrete DAG models with latent variables

TL;DR

This paper introduces a new parameterization for discrete nested Markov models, which are supermodels of DAG models with latent variables, providing identifiable and interpretable parameters for causal inference.

Contribution

It offers an explicit, regular parameterization of the model that avoids unidentifiability and irregularities, enabling better fitting and interpretation.

Findings

The models are curved exponential families.

Parameters are fully identifiable and causally interpretable.

The approach improves model fitting and interpretability.

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.