Influential Observations Detection by Random Projection in High-Dimensional Multivariate Response Linear Model
针对高维多元响应线性回归中的影响点检测难题，提出一种基于随机投影的算法，利用响应变量间的相关性，有效缓解掩蔽和淹没效应，计算高效且可扩展。
In this paper, we consider the challenging problem of influential point detection in high-dimensional linear regressions with multivariate responses. A Multivariate Response Influential Point (MRIP) detection algorithm is proposed based on a novel random projection method, which takes into account the dependence among the responses. When the number of projected directions tends to infinity, the limit statistic is derived, which simplifies the computations greatly. The proposed MRIP algorithm can mitigate the adverse effects of masking and swamping effectively. The experimental results on both simulated and real datasets demonstrate that the proposed method outperforms existing state-of-the-art methods. The proposed method is computationally efficient and scalable to large datasets, making it practical for real-world applications.