多源共形预测：通过局部化利用异质性
Multi-source conformal prediction: leveraging heterogeneity via localization
- Stanford University（斯坦福大学）
- Boston University（波士顿大学）
- MBZUAI（穆罕默德·本·扎耶德人工智能大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对多源异质数据下的预测问题，提出多源随机局部化共形预测（MS-RLCP），通过数据自适应源选择扩展RLCP，在共享条件响应分布假设下建立有限样本覆盖界，并验证其有效性。
AI中文摘要：
许多现代预测任务涉及来自多个异质来源的数据，而测试分布可能与任何单个来源都有显著差异。尽管异质性带来了挑战，但也提供了机会：不同来源可能提供互补信息，特征空间的某些区域在一个来源中的表示可能优于另一个来源。我们提出了多源随机局部化共形预测（MS-RLCP），该方法基于随机局部化共形预测（RLCP）（Hore 和 Barber，2025）的局部覆盖性质，并通过数据自适应源选择将其扩展到多个来源。在广泛采用的假设下，即各来源和测试总体中给定特征时响应分布相同，我们利用可解释的包络分布概念建立了有限样本覆盖界，该分布捕捉了它们在特征空间中的聚合表示。我们的分析允许测试特征分布相对于包络分布是绝对连续的，从而超越了源分布的混合。在额外的正则性条件下，我们还建立了渐近测试条件覆盖。模拟和真实世界实验证明了MS-RLCP在不同数据异质性水平下的有效性。
英文摘要：
Many modern prediction tasks involve data from multiple heterogeneous sources, while the test distribution may differ substantially from any individual source. Although heterogeneity poses challenges, it also offers an opportunity: different sources may provide complementary information, with some regions of the feature space better represented in one source than another. We propose Multi-Source Randomly Localized Conformal Prediction (MS-RLCP), which builds on the local coverage properties of randomly localized conformal prediction (RLCP) (Hore and Barber, 2025) and extends it to multiple sources through data-adaptive source selection. Under the widely adopted assumption of a shared response distribution conditional on the features across sources and the test population, we establish finite-sample coverage bounds using an interpretable notion of envelope distribution that captures their aggregate feature-space representation. Our analysis allows the test feature distribution to be absolutely continuous with respect to the envelope, extending beyond mixtures of source distributions. Under additional regularity conditions, we also establish asymptotic test-conditional coverage. Simulations and real-world experiments demonstrate the effectiveness of MS-RLCP across varying levels of data heterogeneity.
