Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphs
2026-06-02 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors study do-calculus, a method used to answer 'what if' questions in cause-and-effect problems. They introduce derivation graphs to show how do-calculus rules can be combined and applied, helping to find all possible ways to rewrite causal queries into equivalent forms. Their approach simplifies the process to at most four steps. They also demonstrate that by exploring these equivalent forms, one can find multiple ways to estimate causal effects, potentially improving accuracy.
do-calculuscausal inferenceinterventional queriesderivation graphsidentification algorithmsestimandscausal effectscausal modelsobservational probabilitiesinterventional probabilities
Authors
Clément Yvernes, Emilie Devijver, Marianne Clausel, Eric Gaussier
Abstract
The do-calculus defines a general system of inference for interventional queries, allowing causal quantities to be transformed through successive applications of its rules. This process induces a rich space of equivalent interventional expressions, but combining and ordering these rules remains challenging. In this work, we introduce derivation graphs, which represent how do-calculus rules are applied and combined, and characterize the full space of observational and interventional probabilities which are equivalent under the do-calculus. The structure of these graphs yields a simple procedure that uses at most four applications of do-calculus rules. Finally, we show how applying identification algorithms to equivalent causal queries produces multiple valid estimands for the same causal quantity, eventually yielding more efficient estimators.