The m-connecting imset and factorization for ADMG models
Directed acyclic graph (DAG) models have become widely studied and applied in statistics and machine learning -- indeed, their simplicity facilitates efficient procedures for learning and inference. Unfortunately, these models are not closed under marginalization, making them poorly equipped to handle systems with latent confounding. Acyclic directed mixed graph (ADMG) models characterize margins of DAG models, making them far better suited to handle such systems. However, ADMG models have not seen wide-spread use due to their complexity and a shortage of statistical tools for their analysis. In this paper, we introduce the m-connecting imset which provides an alternative representation for the independence models induced by ADMGs. Furthermore, we define the m-connecting factorization criterion for ADMG models, characterized by a single equation, and prove its equivalence to the global Markov property. The m-connecting imset and factorization criterion provide two new statistical tools for learning and inference with ADMG models. We demonstrate the usefulness of these tools by formulating and evaluating a consistent scoring criterion with a closed form solution.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
RimSet: Quantitatively Identifying and Characterizing Chronic Active Multiple Sclerosis Lesion on Quantitative Susceptibility Maps
Background: Rim+ lesions in multiple sclerosis (MS), detectable via Quantitative Susceptibility Mapping (QSM), correlate with increased disability. Existing literature lacks quantitative analysis of these lesions. We int…
Differentiable Causal Discovery Under Unmeasured Confounding
The data drawn from biological, economic, and social systems are often confounded due to the presence of unmeasured variables. Prior work in causal discovery has focused on discrete search procedures for selecting acycli…
Causal DiscoveryCausal Reasoning in the Presence of Latent Confounders via Neural ADMG Learning
Latent confounding has been a long-standing obstacle for causal reasoning from observational data. One popular approach is to model the data using acyclic directed mixed graphs (ADMGs), which describe ancestral relations…
Identifying Macro Causal Effects in C-DMGs over DMGs
The do-calculus is a sound and complete tool for identifying causal effects in acyclic directed mixed graphs (ADMGs) induced by structural causal models (SCMs). However, in many real-world applications, especially in hig…
Integer Programming for Causal Structure Learning in the Presence of Latent Variables
The problem of finding an ancestral acyclic directed mixed graph (ADMG) that represents the causal relationships between a set of variables is an important area of research on causal inference. Most existing score-based …
Causal Inferencevalid