提出适用于非欧随机对象的随机效应算法，突破传统方法局限。
Random-Effects Algorithm for Random Objects in Metric Spaces
- 基于弗雷歇均值的非线性算法，处理任意度量空间中的随机对象。
- 在合成数据与数字健康数据上表现优于基于希尔伯特空间的方法。
- 适合需要分析概率分布、随机图等非欧数据的研究者使用。
在多个科学领域中，同一实验单元会产生多个观测值，而现代数据中的这些观测常表现为非欧随机对象。在此类场景下，引入随机效应是高效估计和个性化预测的关键建模步骤。尽管混合效应模型在标量结果和希尔伯特空间中的函数数据中已有成熟应用，但针对度量空间中随机对象的通用随机效应框架仍不完善。本文提出一种基于弗雷歇均值的非线性算法，用于对任意定义在度量空间中的随机对象进行随机效应建模。通过M-估计理论，我们建立了在工作随机效应设定下，所提度量空间预测目标一致估计的条件。随后，我们在合成数据和数字健康数据集上评估了该方法的实证性能，这些数据集需要实际工具来分析如多变量概率分布、随机图等度量空间中的随机对象。结果显示，尽管本方法超越希尔伯特空间限制，却能优于现有基于希尔伯特空间的方法。
原文摘要 · Abstract (English)
Across many scientific disciplines, multiple observations are collected from the same experimental units, and in modern datasets these observations often arise as non-Euclidean random objects. In such settings, the incorporation of random effects is a critical modeling step for efficient estimation and personalized prediction. Although mixed-effects models are well established for scalar outcomes and, more recently, for functional data in Hilbert spaces, general random-effects frameworks for objects in metric spaces remain underdeveloped. In this paper, we propose a nonlinear Fréchet-based algorithm for random-effects modeling of arbitrary random objects defined on a metric space. Using M-estimation theory, we establish conditions under which the proposed metric-space prediction target is consistently estimated under a working random-effects formulation. We then evaluate the empirical performance of the proposed method using both synthetic data and digital health datasets that require practical tools for analyzing random objects in metric spaces, such as multivariate probability distributions and random graphs. We show that, although our method is developed beyond Hilbert spaces, it can outperform existing Hilbert space-based methods.
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