Doubly Robust Calibration of Prediction Sets under Covariate Shift
协变量漂移下预测集的双重稳健校准AI 解读 ↓
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协变量漂移下预测集的双重稳健校准
- 研究问题
- 当训练与测试总体的协变量分布发生漂移时，如何构造具有可靠平均覆盖率的预测集，并分析潜在不可观测漂移的影响？
- 方法与思路
- 作者将测试总体结局分位数的有效影响函数与机器学习预测结合，提出三种构造方案，并扩展至半参数敏感性分析。
- 材料陈述的贡献
- 摘要称乘积偏差结构支持双重稳健的大样本平均覆盖保证，并扩展到个体处理效应预测集及不同算法预测集的聚合。
- 阅读关注点
- 应核对可解释协变量漂移假设、辅助估计误差要求，以及平均与条件覆盖的区别、潜在漂移参数和处理效应预测集定义。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审或期刊接收未经核实；摘要给出的是大样本平均覆盖，不能据此声称有限样本或个体条件覆盖。
原文摘要
Conformal prediction has received tremendous attention in recent years and has offered new solutions to problems in missing data and causal inference; yet these advances have not leveraged modern semiparametric efficiency theory for more robust and efficient uncertainty quantification. In this paper, we consider the problem of obtaining distribution-free prediction regions accounting for a shift in the distribution of the covariates between the training and test data. Under an explainable covariate shift assumption analogous to the standard missing at random assumption, we propose three variants of a general framework to construct well-calibrated prediction regions for the unobserved outcome in the test sample. Our approach is based on the efficient influence function for the quantile of the unobserved outcome in the test population combined with an arbitrary machine learning prediction algorithm, without compromising asymptotic coverage. Next, we extend our approach to account for departure from the explainable covariate shift assumption in a semiparametric sensitivity analysis for potential latent covariate shift. In all cases, we establish that the resulting prediction sets eventually attain nominal average coverage in large samples. This guarantee is a consequence of the product bias form of our proposal which implies correct coverage if either the propensity score or the conditional distribution of the response is estimated sufficiently well. Our results also provide a framework for construction of doubly robust prediction sets of individual treatment effects, under both unconfoundedness and allowing for some degree of unmeasured confounding. Finally, we discuss aggregation of prediction sets from different machine learning algorithms for optimal prediction and illustrate the performance of our methods in both synthetic and real data.