Geodesic optimal transport regression
测地线最优传输回归AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究通用非欧氏对象回归，未明确涉及分位数或分布处理效应等所列方向。
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测地线最优传输回归
- 研究问题
- 当响应与多个预测变量都是非欧氏随机对象，并共同位于测地度量空间时，如何建立能够表达它们之间关系的多元回归模型？
- 方法与思路
- 作者定义沿测地线的最优传输，将分布空间中的传输概念推广至更一般的测地度量空间，并据此构造包含多个随机对象预测变量的回归。
- 材料陈述的贡献
- 摘要称，该方法扩展经典多元回归，覆盖分布、球面及对称正定矩阵等对象，并以夏季温度分布和人类死亡率数据说明其用途。
- 阅读关注点
- 应核对各类空间中最优传输的定义与存在条件、回归关系如何参数化和估计，以及多个对象预测变量的解释与计算方式。
- 阅读边界
- 仅据所给 Crossref 摘要；估计理论、唯一性和模型条件未说明，响应为分布对象也不能据此解释为因果分布效应研究。
原文摘要
Summary Classical regression models do not cover non-Euclidean data that reside in a general metric space, while the current literature on non-Euclidean regression has, by and large, focused on scenarios where either predictors or responses are random objects, i.e., non-Euclidean, but not both. In this paper we propose geodesic optimal transport regression models for the case where both predictors and responses lie in a common geodesic metric space, and predictors may include not only one, but also several random objects. This provides an extension of classical multiple regression to the case where both predictors and responses reside in non-Euclidean metric spaces, a scenario that has not been considered before. It is based on the concept of optimal geodesic transports, which we define as an extension of the notion of optimal transports in distribution spaces to more general geodesic metric spaces, where we characterize optimal transports as transports along geodesics. The proposed regression models cover the relation between non-Euclidean responses and vectors of non-Euclidean predictors in many spaces of practical statistical interest. These include one-dimensional distributions viewed as elements of the 2-Wasserstein space and multi-dimensional distributions with the Fisher–Rao metric that are represented as data on the Hilbert sphere. Also included are data on finite-dimensional Riemannian manifolds, with an emphasis on spheres, covering directional and compositional data, as well as data that consist of symmetric positive definite matrices. We illustrate the utility of geodesic optimal transport regression with data on summer temperature distributions and human mortality.