Multi-environment Invariance Learning with Missing Data
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结果缺失下的多环境不变性学习
- 研究问题
- 多个环境的结果变量存在缺失时，如何利用环境间异质性学习稳定关系，并兼顾变量选择、稳健预测与可能的因果解释？
- 方法与思路
- 作者从结果缺失下的不变性目标推导估计量，建立变量选择与二范数误差的非渐近保证，并分析缺失比例及插补质量的影响。
- 材料陈述的贡献
- 摘要称，新估计量在模拟与自行车租赁预测中表现良好；当插补偏差处于一定范围内时，仍可获得较低预测误差。
- 阅读关注点
- 应核对缺失机制、环境间不变性条件、插补误差限制，以及结构方程模型的模块性如何支持因果解释和理论保证。
- 阅读边界
- 这是 arXiv 预印本，不能据此声称已获同行评审或接收；摘要未说明缺失机制和可容许偏差范围，因果解释也有条件。
原文摘要
Learning models that can handle distribution shifts is a key challenge in domain generalization. Invariance learning, an approach that focuses on identifying features invariant across environments, improves model generalization by capturing stable relationships, which may represent causal effects when the data distribution is encoded within a structural equation model (SEM) and satisfies modularity conditions. This has led to a growing body of work that builds on invariance learning, leveraging the inherent heterogeneity across environments to develop methods that provide causal explanations while enhancing robust prediction. However, in many practical scenarios, obtaining complete outcome data from each environment is challenging due to the high cost or complexity of data collection. This limitation in available data hinders the development of models that fully leverage environmental heterogeneity, making it crucial to address missing outcomes to improve both causal insights and robust prediction. In this work, we derive an estimator from the invariance objective under missing outcomes. We establish non-asymptotic guarantees on variable selection property and $\ell_2$ error convergence rates, which are influenced by the proportion of missing data and the quality of imputation models across environments. We evaluate the performance of the new estimator through extensive simulations and demonstrate its application using the UCI Bike Sharing dataset to predict the count of bike rentals. The results show that despite relying on a biased imputation model, the estimator is efficient and achieves lower prediction error, provided the bias is within a reasonable range.