Polynomial-Delay MAG Listing with Novel Locally Complete Orientation Rules

Tian-Zuo Wang, Wen-Bo Du, Zhi-Hua Zhou

TL;DR: We present the first Polynomial-Delay Maximal Ancestral Graph Listing Algorithm

Abstract: A maximal ancestral graph (MAG) is widely used to characterize the causal relations among observable variables in the presence of latent variables. However, given observational data, only a partial ancestral graph representing a Markov equivalence class (MEC) of MAGs is identifiable, which generally contains uncertain causal relations. Due to the uncertainties, \emph{MAG listing}, \emph{i.e.}, listing all the MAGs in the MEC, is critical for many downstream tasks. In this paper, we present the first \emph{polynomial-delay} MAG listing method, where delay refers to the time for outputting each MAG, through introducing enumerated structural knowledge in the form of \emph{singleton background knowledge (BK)}. To incorporate such knowledge, we propose the \emph{sound} and \emph{locally complete} orientation rules. By recursively introducing singleton BK and applying the rules, our method can output all and only MAGs in the MEC with polynomial delay. Additionally, while the proposed novel rules enable more efficient MAG listing, for the goal of incorporating general BK, we present two counterexamples to imply that existing rules including ours, are not yet \emph{complete}, which motivate two more rules. Experimental results validate the efficiency of the proposed MAG listing method.

Lay Summary: Understanding cause-and-effect relations is crucial in many areas, such as medicine, biology, and economics. However, in real-world tasks, not all factors can be observed, making it difficult to reveal how each factor causally influence others. Our research tackles this challenge by developing a new method to list all possible explanations for the observed relations among the factors when some factors are unobserved. We create a faster way to generate these explanations. This helps researchers and decision-makers see every possible scenario that fits the data. By making it easier and more efficient to explore all the ways things might be connected, our work supports better, more reliable insights from data when the full picture is hidden from view.

Primary Area: Probabilistic Methods->Graphical Models

Keywords: maximal ancestral graphs, MAG listing

Submission Number: 3646