Conformal inference for random objects
随机对象的共形推断AI 解读 ↓
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随机对象的共形推断
- 研究问题
- 研究当响应位于一般度量空间、预测变量为欧氏向量时，如何构造预测集合并获得渐近条件有效性。
- 方法与思路
- 作者利用距离剖面间的最优传输定义条件平均传输成本，以相关分布构造共形分数并实施拆分共形算法。
- 材料陈述的贡献
- 摘要称给出分数估计的一致收敛速率及预测集合的渐近条件有效性，并在模拟与网络、组成数据中展示表现。
- 阅读关注点
- 应核对条件分数的定义与估计、度量空间及预测变量条件，并区分渐近条件有效性与有限样本比较结果。
- 阅读边界
- 仅据OpenAlex索引摘要，稿件版本未注明；具体条件与数值未提供，模拟中的覆盖率和集合大小优势不能视为普遍保证。
原文摘要
We develop an inferential tool kit for analyzing object-valued responses, which correspond to data situated in general metric spaces, paired with Euclidean predictors within the conformal framework. To this end, we introduce conditional profile average transport costs, where we compare distance profiles that correspond to one-dimensional distributions of probability mass falling into balls of increasing radius through the optimal transport cost when moving from one distance profile to another. The average transport cost to transport a given distance profile to all others is crucial for statistical inference in metric spaces and underpins the proposed conditional profile scores. A key feature of the proposed approach is to utilize the distribution of conditional profile average transport costs as conformity score for general metric space-valued responses, which facilitates the construction of prediction sets by the split conformal algorithm. We derive the uniform convergence rate of the proposed conformity score estimators and establish asymptotic conditional validity for the prediction sets. The finite sample performance for synthetic data in various metric spaces demonstrates that the proposed conditional profile score outperforms existing methods in terms of both coverage level and size of the resulting prediction sets, even in the special case of scalar Euclidean responses. We also demonstrate the practical utility of conditional profile scores for network data from New York taxi trips and for compositional data reflecting energy sourcing of U.S. states.