{"ID":3004781,"CreatedAt":"2026-06-03T03:09:48.883664427Z","UpdatedAt":"2026-06-05T11:43:53.432517148Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.03719","arxiv_id":"2606.03719","title":"Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphs","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.","short_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 wor...","url_abs":"https://arxiv.org/abs/2606.03719","url_pdf":"https://arxiv.org/pdf/2606.03719v1","authors":"[\"Clément Yvernes\",\"Emilie Devijver\",\"Marianne Clausel\",\"Eric Gaussier\"]","published":"2026-06-02T14:40:39Z","proceeding":"cs.AI","tasks":"[\"cs.AI\"]","methods":"[]","has_code":false}