aiqbench analysis
This paper introduces the Poisson thinning structural equation model (PT-SEM), a novel framework that achieves full causal DAG identification for count-valued observational data, addressing a significant limitation in existing branching models. By replacing binomial thinning with Poisson thinning and leveraging diverse exogenous distributions, the authors establish rigorous identifiability conditions and develop a consistent structure learning algorithm optimized via dynamic programming. The work advances structural causal modeling by providing a robust method for recovering causal graphs in settings involving discrete count variables, which are common in fields like epidemiology and ecology.
Causal DAG Identification for Count Data via Poisson Thinning Structural Equation Models
arXiv:2609.06098v1 Announce Type: cross Abstract: Count-valued variables arise in many scientific and applied settings, yet explicit structural models that allow full identification of causal DAGs from observational data remain limited. The Poisson branching structural causal model (PB-SCM) provides a count-valued analogue of linear structural equation models using binomial thinning and independent Poisson exogenous variables, but its causal DAG is generally only partially identifiable. Building on this framework, we propose the Poisson thinning structural equation model (PT-SEM), which replaces binomial thinning in PB-SCM with Poisson thinning and allows node-wise exogenous distributions from diverse count-distribution families. Under node-wise regularity conditions, we establish identifiability of the causal DAG, the thinning coefficients, and the node-wise exogenous distributions. The same identification analysis extends to binomial thinning, yielding full identifiability whenever every nonsink has non-Poisson exogenous noise. We further develop a structure learning algorithm that optimizes, via dynamic programming, a BIC score based on local likelihoods evaluated at plug-in moment estimates, and establish its consistency for DAG selection. Simulations demonstrate favorable performance in DAG recovery and thinning-coefficient estimation, and a real-data application illustrates the practical utility of PT-SEM.
Abstract:Count-valued variables arise in many scientific and applied settings, yet explicit structural models that allow full identification of causal DAGs from observational data remain limited. The Poisson branching structural causal model (PB-SCM) provides a count-valued analogue of linear structural equation models using binomial thinning and independent Poisson exogenous variables, but its causal DAG is generally only partially identifiable. Building on this framework, we propose the Poisson thinning structural equation model (PT-SEM), which replaces binomial thinning in PB-SCM with Poisson thinning and allows node-wise exogenous distributions from diverse count-distribution families. Under node-wise regularity conditions, we establish identifiability of the causal DAG, the thinning coefficients, and the node-wise exogenous distributions. The same identification analysis extends to binomial thinning, yielding full identifiability whenever every nonsink has non-Poisson exogenous noise. We further develop a structure learning algorithm that optimizes, via dynamic programming, a BIC score based on local likelihoods evaluated at plug-in moment estimates, and establish its consistency for DAG selection. Simulations demonstrate favorable performance in DAG recovery and thinning-coefficient estimation, and a real-data application illustrates the practical utility of PT-SEM.
Methodology (stat.ME); Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2609.06098 [stat.ME]
(or arXiv:2609.06098v1 [stat.ME] for this version)
https://doi.org/10.48550/arXiv.2609.06098 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 276 words
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