Shift-aware score transport for privacy auditing without retraining

Privacy auditing empirically assesses privacy leakage by using membership inference attacks to establish lower bounds on privacy loss. We consider an observational auditing setting in which the auditor cannot insert canaries, control data inclusion, or retrain the target model, and must instead rely on fixed sets of known members and non-members. This setting is relevant for large deployed models or when retraining is restricted by computational or access constraints. In this case, non-members available for auditing may differ in distribution from the training data, causing membership-inference scores to be skewed due to the distribution shift. We address this problem by estimating the counterfactual in-distribution non-member score distribution using the available out-of-distribution (OOD) non-members. Our proposed method learns the relationship between data representations and membership-inference scores from OOD non-members and transports it to the target covariate distribution. Because this transport may become unreliable under extrapolation or imperfect conditional invariance, we further introduce a conservative correction calibrated directly to the nominal transported privacy level. We construct controlled calibration tasks from the available non-member data to estimate how representation-space displacement inflates the audit, and use this estimate to correct the transport-induced audit error. Across multiple datasets with distribution shifts, our method yields substantially more stable privacy estimates while retaining tighter lower bounds than baselines.