Title: Decoding Do-Calculus Reasoning Through the Lens of Derivation Graphs

Abstract:

The do-calculus provides a comprehensive framework for reasoning about interventional queries, enabling the transformation of causal quantities by sequentially applying its foundational rules. While this methodology generates a vast landscape of equivalent interventional expressions, effectively merging and sequencing these rules presents significant difficulties. To address this, we propose derivation graphs, a novel representation that maps the application and combination of do-calculus rules, thereby delineating the complete space of observational and interventional probabilities that remain equivalent under the calculus. The structural properties inherent to these graphs facilitate a streamlined procedure requiring no more than four rule applications. Furthermore, we demonstrate that applying identification algorithms to these equivalent causal queries can generate multiple valid estimands for a single causal quantity, ultimately leading to the development of more efficient estimators.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC