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

2026-09-15

AI Summary

研究解决了混合有序和指数族因果DAG在参数线性模型下的可识别性问题，通过联合分布确定节点间边的方向。

Abstract

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.

Problem

• Identifiability
• Linear Parametric Models
• Causal DAGs
• Ordinal Nodes
• Exponential Family

Innovation

• Identifiability
• Mixed Ordinal and Exponential Family Causal DAGs
• Linear Parametric Models
• Ordered Logit Model
• Exponential Family