AI 中文总结
研究针对社会调查元数据不完整问题，提出上下文分布恢复（CDR）框架。通过定义可恢复性并引入自适应传输机制，在最优传输框架内调节权衡。实验表明该方法能在极小精度损失下恢复元数据，为计算社会科学提供了有效框架。
AI 中文摘要
诸如中国健康与营养调查（CHNS）、美国国家健康与营养检查调查（NHANES）和美国国家健康访问调查（BRFSS）等社会调查为人口健康和不平等研究提供支持，但关键元数据（城乡状况、性别及相关分层字段）往往不完整。外部人口统计或调查设计信息可提供元数据类别的已知先验概率P(M)。我们将此设置形式化为上下文分布恢复（CDR）：从协变量X中恢复样本级元数据分配同时遵循P(M)。核心挑战是元数据可恢复性因情况而异。我们从理论上定义可恢复性为互信息R(M|X)=I(X;M)，并通过校准预测不确定性进行操作近似。然后在最优传输框架内引入可恢复性自适应传输机制来调节个体证据与总体约束之间的权衡。在三项大规模调查（CHNS、NHANES、BRFSS；多达67k个测试样本）中，我们表明无约束分类器（XGBoost）准确率高但违反P(M)（总变差距离约0.11），而CDR将总变差距离恢复到<0.001且精度损失最小。一个CHNS案例研究说明了可解释的连续体结构。CDR为计算社会科学中与总体一致的元数据恢复提供了一个框架。
英文摘要
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.
