Epidemiological Causal Graph Identification: Challenges, Identifiability and Algorithms
Abstract
Causal discovery from observational data is fundamental to statistics and machine learning, yet determining causal direction without interventions necessitates structural assumptions. Existing identifiability research primarily focuses on continuous variables under additive noise models, often neglecting mixed datasets containing ordinal scales, counts, and continuous measurements. This paper investigates causal discovery in Directed Acyclic Graphs (DAGs) where nodes follow either an ordinal distribution (via an ordered logit model) or a regular one-parameter exponential family distribution. We prove that the edge direction between an ordinal and an exponential family node is distributionally identifiable for generic parameter values. Our findings generalize previous Ordinal-Poisson results to the broader exponential family. Computationally, we introduce a score-based exhaustive search and a masked continuous optimization framework using DAGMA for larger graphs. Numerical results validate the theory, recovering edge orientations within a Markov equivalence class that are unidentifiable under classical structural equation models.
Related
- Causal Discovery beyond Conditional Independence: Identifiability, Algorithms, and Statistical Inference for Directed Acyclic and Cyclic Graphs
- Generalizing Identifiability Results in Causal Discovery from Complete Data to Missing Data Settings
- On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models
- On the bias distribution of pseudo-linear regression algorithms for recursive identification
- Hazard ratios and their causal interpretation: challenges and guidance.
BibTeX
@misc{mishra2026epidemiological,
title = {{Epidemiological Causal Graph Identification: Challenges, Identifiability and Algorithms}},
author = {Sambit Mishra and Yingying Wang and Christine K. Johnson and Urbashi Mitra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20676},
eprint = {2609.20676},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20676},
}
RIS
TY - UNPB
TI - Epidemiological Causal Graph Identification: Challenges, Identifiability and Algorithms
AU - Sambit Mishra
AU - Yingying Wang
AU - Christine K. Johnson
AU - Urbashi Mitra
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20676
UR - https://arxiv.org/abs/2609.20676
AB - Causal discovery from observational data is fundamental to statistics and machine learning, yet determining causal direction without interventions necessitates structural assumptions. Existing identifiability research primarily focuses on continuous variables under additive noise models, often neglecting mixed datasets containing ordinal scales, counts, and continuous measurements. This paper investigates causal discovery in Directed Acyclic Graphs (DAGs) where nodes follow either an ordinal distribution (via an ordered logit model) or a regular one-parameter exponential family distribution. We prove that the edge direction between an ordinal and an exponential family node is distributionally identifiable for generic parameter values. Our findings generalize previous Ordinal-Poisson results to the broader exponential family. Computationally, we introduce a score-based exhaustive search and a masked continuous optimization framework using DAGMA for larger graphs. Numerical results validate the theory, recovering edge orientations within a Markov equivalence class that are unidentifiable under classical structural equation models.
ER -