New Rules for Causal Identification with Background Knowledge

TL;DR

This work tackles the problem of identifying causal relations from observational data when background knowledge (BK) and latent confounders are present. It introduces two novel BK-incorporation rules, $\\mathcal{R}_{12}$ and $\\mathcal{R}_{13}$, grounded in unbridged-path structure, which generalize existing rules and are backed by soundness proofs. The rules are integrated into a BK-enhanced PAGcauses framework to develop a set-determination method that avoids exponential block-set enumeration, achieving polynomial-time subroutines and enabling complete identification of causal effects estimable by covariate adjustment within the MEC represented by a PAG. The approach improves efficiency while preserving theoretical guarantees, enabling practical BK-based causal effect estimation in the presence of latent confounders. Overall, the paper advances the foundational rules for BK incorporation and delivers a scalable algorithm for determining the set of possible causal effects from observational data augmented with BK.

Abstract

Identifying causal relations is crucial for a variety of downstream tasks. In additional to observational data, background knowledge (BK), which could be attained from human expertise or experiments, is usually introduced for uncovering causal relations. This raises an open problem that in the presence of latent variables, what causal relations are identifiable from observational data and BK. In this paper, we propose two novel rules for incorporating BK, which offer a new perspective to the open problem. In addition, we show that these rules are applicable in some typical causality tasks, such as determining the set of possible causal effects with observational data. Our rule-based approach enhances the state-of-the-art method by circumventing a process of enumerating block sets that would otherwise take exponential complexity.

Figures (2)

• Figure 1: Two examples for $\mathcal{R}_{12}$ and $\mathcal{R}_{13}$. Two PAGs are shown in Fig. \ref{['figure:11']} and \ref{['figure:13']}. Blue lines denote the edges transformed according to BK, red lines denote the edges transformed by $\mathcal{R}_{12}$ and $\mathcal{R}_{13}$. Fig. \ref{['figure:12']} shows a PMG transformed from Fig. \ref{['figure:11']} with additional BK and $\mathcal{R}_{12}$. Fig. \ref{['figure:14']} shows a PMG transformed from Fig. \ref{['figure:13']} with additional BK and $\mathcal{R}_{13}$.
• Figure 2: Fig. \ref{['figure:21']} shows a PAG $\mathcal{P}$. In the first step of PAGcauses, they obtain the maximal local MAG by introducing the local transformation of $X$ and updating the graph with their proposed orientation rules. $\mathbb{M}_1$ and $\mathbb{M}_2$ in Fig. \ref{['figure:22']} and \ref{['figure:23']} are two examples of the maximal local MAG obtained after different local transformations of $X$. Fig. \ref{['figure:23']} and \ref{['figure:24']} show two examples for implementing Alg. \ref{['alg:get S']} given $\mathbf{W}=\emptyset$, where $\mathbf{S}=\{E\}$ and $\mathbf{S}=\{C_1,C_2,B\}$ are returned, respectively.

Theorems & Definitions (35)

• Definition 1: Unbridged path relative to $\mathbf{V}'$
• Remark 1
• Theorem 1
• Proposition 1
• Definition 2
• Definition 3
• Proposition 2
• Definition 4
• Theorem 2
• Theorem 3