解决结构化缺失数据的贝叶斯推理，实现高精度且可信的预测。
Nearly Optimal Bayesian Inference for Structural Missingness
- 分离缺失值后验与标签预测，用贝叶斯后验积分实现不确定性传播
- 在43个分类和15个插补任务上达到顶尖性能，有限样本下接近贝叶斯最优
- 适合处理因果或逻辑约束导致的缺失（MNAR），避免单一填充带来的偏差
结构化缺失数据使传统‘填补后训练’方法失效：缺失值可能因因果或逻辑约束而无定义，掩码依赖于观测变量、未观测变量（即MNAR）及其他缺失指示。这带来三重挑战：(i) 因果循环困境——预测需缺失特征，但推断又依赖缺失机制；(ii) MNAR下未见数据分布偏移；(iii) 单一填充会固化不确定性，导致过度自信与偏差决策。本文采用贝叶斯视角，通过后验预测分布整合模型后验不确定性，将‘学习缺失值后验’与‘标签预测’解耦，实现后验积分。该框架可实现‘近似零成本’预测：一旦后验学习完成，预测即可直接使用并保持不确定性传播。在43个分类与15个插补基准上均达当前最优表现，并在结构因果模型（SCM）先验下具备有限样本近贝叶斯最优性保证。
原文摘要 · Abstract (English)
Structural missingness breaks 'just impute and train': values can be undefined by causal or logical constraints, and the mask may depend on observed variables, unobserved variables (MNAR), and other missingness indicators. It simultaneously brings (i) a catch-22 situation with causal loop, prediction needs the missing features, yet inferring them depends on the missingness mechanism, (ii) under MNAR, the unseen are different, the missing part can come from a shifted distribution, and (iii) plug-in imputation, a single fill-in can lock in uncertainty and yield overconfident, biased decisions. In the Bayesian view, prediction via the posterior predictive distribution integrates over the full model posterior uncertainty, rather than relying on a single point estimate. This framework decouples (i) learning an in-model missing-value posterior from (ii) label prediction by optimizing the predictive posterior distribution, enabling posterior integration. This decoupling yields an in-model almost-free-lunch: once the posterior is learned, prediction is plug-and-play while preserving uncertainty propagation. It achieves SOTA on 43 classification and 15 imputation benchmarks, with finite-sample near Bayes-optimality guarantees under our SCM prior.
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