论文标题
高维线性回归中的稀疏变化检测
Sparse change detection in high-dimensional linear regression
论文作者
论文摘要
我们引入了一种新的方法“木炭”，用于估计高维线性回归系数稀疏变化的位置，而不假设这些系数单独稀疏。该过程通过在每个时间点构造设计矩阵的不同草图（投影）来起作用，其中连续投影矩阵在一列中的符号上有所不同。然后，将草绘的设计矩阵的序列与单个草图的响应矢量进行比较，以形成一系列测试统计序列，其行为表现出与众所周知的单变量变更点分析的令人惊讶的链接。该过程在计算上具有吸引力，并且为其估计准确性而得出了强大的理论保证。仿真确认我们的方法在广泛的设置中表现良好，以及对大型单细胞RNA测序数据集的现实应用程序展示了实际相关性。
We introduce a new methodology 'charcoal' for estimating the location of sparse changes in high-dimensional linear regression coefficients, without assuming that those coefficients are individually sparse. The procedure works by constructing different sketches (projections) of the design matrix at each time point, where consecutive projection matrices differ in sign in exactly one column. The sequence of sketched design matrices is then compared against a single sketched response vector to form a sequence of test statistics whose behaviour shows a surprising link to the well-known CUSUM statistics of univariate changepoint analysis. The procedure is computationally attractive, and strong theoretical guarantees are derived for its estimation accuracy. Simulations confirm that our methods perform well in extensive settings, and a real-world application to a large single-cell RNA sequencing dataset showcases the practical relevance.
