发表机构
Johns Hopkins University（约翰斯·霍普金斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究不等价于DAG模型的马尔可夫模型切线空间正交补的刻画问题，通过推导闭式表达式，为这些模型的半参数推断提供支持，并以几个图形模型中条件均值参数的影响函数类为例进行说明
AI 中文摘要
图形模型在社会和实证科学中无处不在，因其直观易用。这些模型属于更广泛的马尔可夫模型类别，仅通过条件独立性（CI）限制来定义。为了有效估计此类模型中的有限维目标参数，半参数理论提供了一个原则框架，通过影响函数（IFs）构建正则且渐近线性的估计量。这些估计量是渐近正态且根\(n\)一致的。对于相对于有向无环图（DAG）的马尔可夫模型，切线空间的正交补是已知的。然而，对于不等价于DAG模型的马尔可夫模型，如与无向图、链图或无环有向混合图相关的普通马尔可夫模型，其正交补尚未被刻画，这阻碍了这些模型中的半参数推断。我们推导了一般马尔可夫模型切线空间正交补的闭式表达式，并通过刻画几个图形模型中条件均值参数的影响函数类来说明我们的结果。
英文摘要
Graphical models are ubiquitous in social and empirical science as they are intuitive and easy to use. These models belong to the broader class of Markov models, defined using solely conditional independence (CI) restrictions. In order to estimate finite-dimensional target parameters in such models efficiently, semi-parametric theory provides a principled framework for constructing regular and asymptotically linear estimators via influence functions (IFs). These estimators are asymptotically normal and root-$n$ consistent. Characterizing the class of all influence functions for a target parameter is crucial for statistically efficient inference in these models. For models that are Markov relative to directed acyclic graphs (DAGs), the orthogonal complement of the tangent space is known, implying that for any target the class of all influence functions can be derived once an influence function is obtained. On the other hand, for Markov models not equivalent to a DAG model -- such as ordinary Markov models associated with undirected graphs, chain graphs, or acyclic directed mixed graphs -- the orthogonal complement has not been characterized, impeding semi-parametric inference in these models. We derive closed form expressions for the orthogonal complement of the tangent space for general Markov models and illustrate our results by characterizing the class of influence functions for the conditional mean parameter in several graphical models.
Comments23 pages, 2 figures, accepted for the 42nd Conference on Uncertainty in Artificial Intelligence (UAI 2026)
