Forster-Warmuth Counterfactual Regression: A Unified Learning Approach
Forster–Warmuth 反事实回归：统一学习方法AI 解读 ↓
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Forster–Warmuth 反事实回归：统一学习方法
- 研究问题
- 如何放宽级数回归对基函数和协变量分布的限制，并在目标响应并非对所有样本可见时，统一估计相应的反事实回归曲线？
- 方法与思路
- 作者提出基于 Forster–Warmuth 学习器的级数估计，并通过统一伪结果构造处理不可见响应，使相关偏差具有二阶性质。
- 材料陈述的贡献
- 摘要称新估计在较弱条件下达到极小极大速率，并提出通用、可构造的二阶偏差伪结果方法，覆盖缺失数据和因果推断应用。
- 阅读关注点
- 核对放宽条件的具体比较、伪结果构造与识别的关系、二阶偏差的含义，以及各应用达到极小极大速率所需的条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核验；摘要未列完整条件、速率表达式和证明，首创性及适用边界仍需核查。
原文摘要
Series or orthogonal basis regression is one of the most popular non-parametric regression techniques in practice, obtained by regressing the response on features generated by evaluating the basis functions at observed covariate values. The most routinely used series estimator is based on ordinary least squares fitting, which is known to be minimax rate optimal in various settings, albeit under stringent restrictions on the basis functions and the distribution of covariates. In this work, inspired by the recently developed Forster-Warmuth (FW) learner, we propose an alternative series regression estimator that can attain the minimax estimation rate under strictly weaker conditions imposed on the basis functions and the joint law of covariates, than existing series estimators in the literature. Moreover, a key contribution of this work generalizes the FW-learner to a so-called counterfactual regression problem, in which the response variable of interest may not be directly observed (hence, the name ``counterfactual'') on all sampled units, and therefore needs to be inferred in order to identify and estimate the regression in view from the observed data. Although counterfactual regression is not entirely a new area of inquiry, we propose the first-ever systematic study of this challenging problem from a unified pseudo-outcome perspective. In fact, we provide what appears to be the first generic and constructive approach for generating the pseudo-outcome (to substitute for the unobserved response) which leads to the estimation of the counterfactual regression curve of interest with small bias, namely bias of second order. Several applications are used to illustrate the resulting FW-learner including many nonparametric regression problems in missing data and causal inference literature, for which we establish high-level conditions for minimax rate optimality of the proposed FW-learner.