Baseline-Calibrated Adaptive Gaussian Processes for Conditional Dose-Response Estimation

Estimating conditional dose–response functions from observational data requires capturing heterogeneous treatment responses while accounting for covariate-driven outcome variation. We propose Baseline-Calibrated Adaptive Gaussian Processes (BCA-GP), a structured Gaussian process estimator that combines an unpenalized covariate baseline with an adaptive dose kernel. The method learns dose directions from baseline-residualized outcomes and retains a common baseline space throughout direction learning, hyperparameter selection, and prediction. This construction prevents additive signals within the baseline space from altering dose adaptation. We establish exact baseline reproduction and equivariance of the complete fitting procedure: adding a baseline-space function to the outcomes produces the corresponding shift in predictions while preserving response-surface estimation error. We further characterize prediction as constrained kernel approximation and derive a deterministic error bound that separates function approximation, representation error, and adaptive noise propagation. Under standard causal identification assumptions, BCA-GP directly estimates conditional intervention responses. Experiments on semi-synthetic benchmarks show improved estimation of both conditional and average dose–response functions relative to the evaluated GP and neural baselines.