线性参数模型下混合有序与指数族因果有向无环图的可识别性
On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models
浏览论文内容
中文总结 AI 辅助
本文研究线性参数模型中混合有序与指数族节点间因果边的方向可识别性，证明在有序节点至少三类别且指数族节点至少三支撑点条件下，边方向可由联合分布唯一识别，并通过实验验证了理论。
中文摘要 AI 辅助
本文评估了线性参数模型（LPMs）中节点遵循有序Logit模型或正则单参数指数族分布时的可识别性问题。研究结果超越了经典的结构方程模型，也超越了节点观测来自同质分布族的结果。主要结果证明，在有序节点至少有三个类别且指数族节点至少有三个支撑点（对充分统计量无限制）的条件下，连接有序节点与指数族节点的每条边的方向仅从联合分布即可在每个参数值处被识别。逆命题表明这两个要求都是必要的：三类别要求仅对仿射充分统计量具有约束力，而三支撑点要求在规范连接函数下具有约束力。该保证可扩展到给定$d$节点无向骨架中所有此类混合有序-指数族边的定向。数值实验通过成功区分马尔可夫等价类内的方向（这些方向仅靠条件独立性无法区分）验证了理论结果。
英文摘要
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.
发表机构
- University of Southern California（南加州大学）
机构由 AI 辅助整理，请以论文原文为准。
