Context Distribution Restoration for Social Surveys: A Recoverability-Adaptive Transport Framework

Social surveys such as CHNS, NHANES, and BRFSS underpin population health and inequality research, yet critical metadata--urban/rural status, gender, and related stratification fields--are often incomplete. External population statistics or survey design information can provide a known prior P(M) over metadata categories. We formalize this setting as Context Distribution Restoration (CDR): recovering sample-level metadata assignments from covariates X while respecting P(M). The core challenge is that metadata recoverability varies by case: some respondents carry strong signals in X, others do not. We define recoverability theoretically as mutual information R(M|X) = I(X; M) and approximate it operationally via calibrated predictive uncertainty. We then introduce a recoverability-adaptive transport mechanism within an optimal transport framework to regulate the trade-off between individual evidence and population constraints. Across three large-scale surveys (CHNS, NHANES, BRFSS; up to 67k test samples), we show that unconstrained classifiers (XGBoost) achieve high accuracy but violate P(M) (TVD approximately 0.11), while CDR restores TVD < 0.001 with minimal accuracy loss. A CHNS case study illustrates interpretable continuum structure. CDR offers a framework for population-consistent metadata restoration in computational social science.