A Unified Framework for Semiparametrically Efficient Semi-Supervised Learning
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半参数有效半监督学习的统一框架
- 研究问题
- 同时拥有带标签与不带标签样本时，哪些推断问题能从未标注数据中获得效率提升，提升幅度又如何由理论刻画？
- 方法与思路
- 作者通过半参数效率理论刻画效率下界，构造安全型与有效型估计量，并允许纳入黑箱模型预测，讨论多类参数应用。
- 材料陈述的贡献
- 摘要称，安全型估计量至少保持原监督估计量的效率，有效型在更强条件下达到效率界，并统一及扩展相关推断理论。
- 阅读关注点
- 应核对参数设定正确性的含义、两类样本的分布关系、安全性与有效性各自的条件，以及预测模型误差如何影响结论。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未获验证；摘要未给出完整假设，效率保证与对预测驱动推断的比较须核对全文。
原文摘要
We consider statistical inference under a semi-supervised setting where we have access to both a labeled dataset consisting of pairs $\{X_i, Y_i \}_{i=1}^n$ and an unlabeled dataset $\{ X_i \}_{i=n+1}^{n+N}$. We ask the question: under what circumstances, and by how much, can incorporating the unlabeled dataset improve upon inference using the labeled data? To answer this question, we investigate semi-supervised learning through the lens of semiparametric efficiency theory. We characterize the efficiency lower bound under the semi-supervised setting for an arbitrary inferential problem, and show that incorporating unlabeled data can potentially improve efficiency if the parameter is not well-specified. We then propose two types of semi-supervised estimators: a safe estimator that imposes minimal assumptions, is simple to compute, and is guaranteed to be at least as efficient as the initial supervised estimator; and an efficient estimator, which -- under stronger assumptions -- achieves the semiparametric efficiency bound. Our findings unify existing semiparametric efficiency results for particular special cases, and extend these results to a much more general class of problems. Moreover, we show that our estimators can flexibly incorporate predicted outcomes arising from ``black-box" machine learning models, and thereby achieve the same goal as prediction-powered inference (PPI), but with superior theoretical guarantees. We also provide a complete understanding of the theoretical basis for the existing set of PPI methods. Finally, we apply the theoretical framework developed to derive and analyze efficient semi-supervised estimators in a number of settings, including M-estimation, U-statistics, and average treatment effect estimation, and demonstrate the performance of the proposed estimators via simulations.