{"ID":2922112,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-02T14:26:00.610495116Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.00754","arxiv_id":"2606.00754","title":"Causal Density Functions","abstract":"We introduce causal density functions: Radon-Nikodym derivatives that compare interventional laws to observational laws and therefore act as local density ratios for causal effects. Whereas many causal-strength measures compare whole distributions after graph surgery, causal density functions provide a pointwise change-of-measure object that can be estimated, calibrated, and used to score directed influence. The basic identity \\[ \\mathbb{E}_{\\mathrm{do}}[f(Y)] = \\mathbb{E}_{\\mathrm{obs}}\\!\\left[f(Y)ρ(X,Y)\\right] \\] makes causal density directly testable: if the estimated density ratio is correct, observational expectations reweighted by $ρ$ reproduce interventional expectations. We derive practical estimators for do-curves and directed edge scores, relate the construction to Radon-Nikodym/Kan semantics for conditioning and intervention, and evaluate the resulting estimators on synthetic and real perturbation benchmarks.","short_abstract":"We introduce causal density functions: Radon-Nikodym derivatives that compare interventional laws to observational laws and therefore act as local density ratios for causal effects. Whereas many causal-strength measures compare whole distributions after graph surgery, causal density functions provide a pointwise change...","url_abs":"https://arxiv.org/abs/2606.00754","url_pdf":"https://arxiv.org/pdf/2606.00754v1","authors":"[\"Sridhar Mahadevan\"]","published":"2026-05-30T14:41:25Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"cs.AI\",\"cs.LG\"]","methods":"[]","has_code":false}