# Smooth, identifiable supermodels of discrete DAG models with latent variables

arXiv: https://arxiv.org/abs/1511.06813 · HTML: https://mlsanity.com/paper/1511.06813/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2015.

## Built on by (most cited first, 8 of 8)

- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [A Free Lunch with Influence Functions? Improving Neural Network Estimates with Concepts from Semiparametric Statistics](https://mlsanity.com/paper/2202.09096/) (2022)
- [Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables](https://mlsanity.com/paper/2107.07087/) (2021)
- [Detecting and Measuring Confounding Using Causal Mechanism Shifts](https://mlsanity.com/paper/2409.17840/) (2024)
- [Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path Diagrams](https://mlsanity.com/paper/2406.09049/) (2024)
- [Identifying Structural Biases from Causal Mechanism Shifts](https://mlsanity.com/paper/2606.18834/) (2026)
- [A Characterization of the Orthocomplement of the Tangent Space of Semiparametric Markov Models](https://mlsanity.com/paper/2607.23439/) (2026)

## Abstract (arXiv)

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.