Learning from a Biased Sample
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从有偏样本中学习
- 研究问题
- 当训练样本中可观测或不可观测群体的代表性不同于部署人口时，如何学习对这类选择偏差具有稳健性的决策规则？
- 方法与思路
- 作者以条件 Γ 偏差抽样限制未解释的选择概率变化，通过分布稳健优化最小化最坏风险，并转化为增广凸风险问题。
- 材料陈述的贡献
- 摘要称给出筛估计的统计保证与匹配稳健目标的深度学习算法，并在心理健康评分及重症监护住院时长预测中验证方法。
- 阅读关注点
- 应核对 Γ 的含义与可解释范围、目标分布集合的构造，以及凸等价结果、筛估计保证与深度学习实现之间的联系。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审与期刊接收状态未核实；摘要未说明 Γ 的选择方法、保证所需条件或应用结果数值。
原文摘要
The empirical risk minimization approach to data-driven decision making requires access to training data drawn under the same conditions as those that will be faced when the decision rule is deployed. However, in a number of settings, we may be concerned that our training sample is biased in the sense that some groups (characterized by either observable or unobservable attributes) may be under- or over-represented relative to the general population; and in this setting empirical risk minimization over the training set may fail to yield rules that perform well at deployment. We propose a model of sampling bias called conditional $Γ$-biased sampling, where observed covariates can affect the probability of sample selection arbitrarily much but the amount of unexplained variation in the probability of sample selection is bounded by a constant factor. Applying the distributionally robust optimization framework, we propose a method for learning a decision rule that minimizes the worst-case risk incurred under a family of test distributions that can generate the training distribution under $Γ$-biased sampling. We apply a result of Rockafellar and Uryasev to show that this problem is equivalent to an augmented convex risk minimization problem. We give statistical guarantees for learning a model that is robust to sampling bias via the method of sieves, and propose a deep learning algorithm whose loss function captures our robust learning target. We empirically validate our proposed method in a case study on prediction of mental health scores from health survey data and a case study on ICU length of stay prediction.