Counterfactual Estimation under Composite Treatments via Progressive Distribution Alignment

Estimating counterfactual outcomes when multiple treatments are applied simultaneously, the composite treatment setting, is fundamentally harder than the single-cause case: the treatment space grows combinatorially, most combinations are unobserved, and confounding is entangled across dimensions. We propose PACE (Progressive Alignment for Composite Effects), which exploits a known causal DAG over treatment variables to progressively transform the observational data distribution into the target interventional distribution. PACE performs K sequential augmentation steps in reverse topological order, each isolating a single treatment component and conditioning only on its parents in the DAG. We derive the closed-form optimal augmentation density minimizing KL divergence at each step, establish finite-sample bounds prescribing the augmentation budget via DAG-aware selection bias ratios, and show that the DAG provides a deterministic processing order that eliminates the need for random permutation averaging. On semi-synthetic benchmarks with real covariates (IHDP, Twins, Hillstrom) and controlled synthetic environments, PACE substantially outperforms seven baselines on both continuous and binary outcomes, with the largest gains on rare treatment combinations where confounding is most severe. Ablations confirm consistent improvements over the closest prior method across varying DAG topologies, confounding strengths, and under DAG misspecification.