aiqbench analysis
This paper advances the theoretical foundations of semi-parametric inference for general Markov models, specifically addressing undirected and mixed graphical structures where influence functions were previously undefined. By deriving closed-form expressions for the orthogonal complement of the tangent space, it enables statistically efficient estimation in broader classes of empirical science applications beyond standard DAGs. The work represents a significant step forward in machine learning methodology by expanding the toolkit available for robust parameter inference in complex dependency networks.
A Characterization of the Orthocomplement of the Tangent Space of Semiparametric Markov Models
arXiv:2607.23439v1 Announce Type: cross Abstract: 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.
Abstract: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.
Methodology (stat.ME); Artificial Intelligence (cs.AI)
arXiv:2607.23439 [stat.ME]
(or arXiv:2607.23439v1 [stat.ME] for this version)
https://doi.org/10.48550/arXiv.2607.23439 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 307 words
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