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On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models

arXiv 2609.17942 ↗First posted 16 Sep 2026cs.LG math.ST stat.MEcited by 0

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Abstract (arXiv)

The problem of identifiability in linear parametric models (LPMs) whose nodes follow either an ordered logit model or a regular one-parameter exponential family is evaluated. The results go beyond classical structural equation models as well as results for nodes with observations from a homogeneous family of distributions. The main result establishes that the orientation of every edge joining an ordinal node to an exponential-family node is identifiable from the joint distribution alone at every parameter value, provided the ordinal node has at least three categories and the exponential-family node at least three points of support, with no restriction on the sufficient statistic. Converses show that both requirements are necessary: the three-category requirement is binding only for affine sufficient statistics, and the three-point requirement is binding under the canonical link. The guarantee extends to orienting every such mixed ordinal-exponential family edge of a given d-node undirected skeleton. Numerical experiments illustrate the theoretical results by successfully separating orientations within a Markov equivalence class, which are indistinguishable by conditional independence alone.

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References · 23

  1. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  2. 2016Causal Bandits: Learning Good Interventions via Causal Inferencecited by 101
  3. 2020Causal Autoregressive Flowscited by 99
  4. 2018Characterizing and Learning Equivalence Classes of Causal DAGs under Interventionscited by 76
  5. 2022On the Identifiability and Estimation of Causal Location-Scale Noise Modelscited by 56
  6. 2013Learning Sparse Causal Models is not NP-hardcited by 49
  7. 2022Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Modelcited by 38
  8. 2017Learning Identifiable Gaussian Bayesian Networks in Polynomial Time and Sample Complexitycited by 27
  9. 2022Causal Bandits for Linear Structural Equation Modelscited by 19
  10. 2022Optimal estimation of Gaussian DAG modelscited by 17
  11. 2023Causal Reasoning: Charting a Revolutionary Course for Next-Generation AI-Native Wireless Networkscited by 16
  12. 2021Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential familiescited by 11
11 more
  1. 2017Causal Inference on Multivariate and Mixed-Type Datacited by 7
  2. 2022Ordinal Causal Discoverycited by 6
  3. 2023Identifiability of causal graphs under nonadditive conditionally parametric causal modelscited by 6
  4. 2023Structural restrictions in local causal discovery: identifying direct causes of a target variablecited by 5
  5. 2014Identifiability of an Integer Modular Acyclic Additive Noise Model and its Causal Structure Discoverycited by 3
  6. 2025Causal Link Discovery with Unequal Edge Error Tolerancecited by 3
  7. 2023Causal Discovery with Generalized Linear Models through Peeling Algorithmscited by 2
  8. 2024Asymmetric Graph Error Control with Low Complexity in Causal Banditscited by 2
  9. 2026Causal Discovery in Equal Variance Linear Gaussian DAGs via SURE-Tuned Ridge Regressioncited by 2
  10. 2025Density Ratio-based Causal Discovery from Bivariate Continuous-Discrete Datacited by 1
  11. 2025Skewness-Robust Causal Discovery in Location-Scale Noise Modelscited by 1

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