Influential observations detection by random projection in high-dimensional multivariate response linear model

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.

本文聚焦带多变量响应的高维线性回归中的影响点检测这一富有挑战性的研究问题。本文提出一种基于新型随机投影方法的多变量响应影响点（Multivariate Response Influential Point, MRIP）检测算法，该方法充分考量了响应变量间的相关性。当投影方向数趋于无穷大时，本文推导得到极限统计量，可大幅简化计算流程。所提MRIP算法可有效缓解掩蔽（masking）与淹没（swamping）两类负面影响。在模拟数据集与真实数据集上开展的实验结果显示，本文所提方法的性能优于当前主流的前沿检测方法。该方法计算效率优异且可良好扩展至大规模数据集，具备实际应用的可行性。