论文标题
切成薄片的度量空间中的反向回归
Sliced Inverse Regression in Metric Spaces
论文作者
论文摘要
在本文中，当预测变量和响应位于某些通用度量空间中时，我们提出了一个一般的非线性降低（SDR）框架。我们构建了繁殖的内核希尔伯特空间，其内核完全由公制空间的距离函数确定，然后利用这些空间的固有结构来定义非线性SDR框架。我们在此框架内适应了\ citet {li：1991}的经典切片反向回归，以用于度量空间数据。我们基于相应的线性运算符构建估计器，并表明其无偏恢复回归信息。我们在操作员级别和坐标系下得出估计器，并确定其收敛速率。我们说明了提出的方法，其中均表现出非欧盟几何形状的合成数据集和真实数据集。
In this article, we propose a general nonlinear sufficient dimension reduction (SDR) framework when both the predictor and response lie in some general metric spaces. We construct reproducing kernel Hilbert spaces whose kernels are fully determined by the distance functions of the metric spaces, then leverage the inherent structures of these spaces to define a nonlinear SDR framework. We adapt the classical sliced inverse regression of \citet{Li:1991} within this framework for the metric space data. We build the estimator based on the corresponding linear operators, and show it recovers the regression information unbiasedly. We derive the estimator at both the operator level and under a coordinate system, and also establish its convergence rate. We illustrate the proposed method with both synthetic and real datasets exhibiting non-Euclidean geometry.
