何处胜出？用于局部优势的共形模型比较

中文摘要 AI 辅助

标准模型比较是全局的，它会聚合协变量空间上的损失以宣布单一胜出者，这可能掩盖异质性性能，即不同区域中不同模型更具优势。我们提出共形化局部模型比较，这是一种用于构建校准局部最佳模型图的拆分样本框架。给定模型比较得分（例如两个平方损失的差值），该方法使用三个不相交的拆分来拟合竞争模型，从样本外得分估计局部中心和尺度，并共形校准残差不确定性。在目标点处，该过程仅当单侧共形界限排除平局时才宣布局部胜出者，且得分的符号决定受青睐的模型。我们证明了在实现的未来比较得分上单侧错误声明的有限样本边际控制，建立了远离平局边界时局部均值得分估计量的逐点一致性，表明全局比较可能与局部优势的普遍性存在显著分歧，并推导了平方损失的偏差-方差分解，以阐明模型结构如何影响局部胜出。合成数据和真实数据实验表明，该方法能恢复异质性胜出区域，在不确定性下弃权（不执行），且比全局选择产生更高的条件增益。

英文摘要

Standard model comparison is global, aggregating losses across the covariate space to declare a single winner. This can obscure heterogeneous performance, where different models are preferable in different regions. We introduce conformalized local model comparison, a split-sample framework for constructing calibrated local best-model maps. Given a model comparison score, such as the difference between two squared losses, the method uses three disjoint splits to fit competing models, estimate local centers and scales from out-of-sample scores, and conformally calibrate residual uncertainty. At a target point, the procedure declares a local winner only when a one-sided conformal bound excludes a tie, with the score's sign determining the favored model. We prove finite-sample marginal control for one-sided erroneous declarations on the realized future comparison score, establish pointwise consistency of the localized mean-score estimator away from tie boundaries, show that aggregate comparison can disagree sharply with the prevalence of local superiority, and derive a squared-loss bias--variance decomposition that clarifies how model structure affects local wins. Synthetic and real-data experiments show that the method recovers heterogeneous winner regions, abstains under uncertainty, and yields higher conditional gain than global selection.

发表机构

• Asian Institute of Digital Finance, National University of Singapore（新加坡国立大学亚洲数字金融研究院）

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