Causal Density Functions

arXiv:2606.00754v1 Announce Type: cross 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 [ E_{do}[f(Y)] = E_{obs}!left[f(Y)rho(X,Y)right] ] makes causal density directly testable: if the estimated density ratio is correct, observational expectations reweighted by rho 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.

Source: arXiv cs.AI | 2026-06-02