Localizing Changes in High-Dimensional Regression Models
Localizing Changes in High-Dimensional Regression Models
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发表时间：
2020-10
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通讯作者：
A. Rinaldo;Daren Wang;Qin Wen;R. Willett;Yi Yu
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作者：
A. Rinaldo;Daren Wang;Qin Wen;R. Willett;Yi Yu
本文解决了在具有分段常数回归系数的高维线性回归模型中定位变化点的问题。我们开发了一种动态规划方法来估计变化点的位置，即使维度、回归系数的稀疏性、两个连续变化点之间的时间间隔以及两个连续回归系数向量的差异大小允许随样本大小变化，其性能也优于当前最先进的技术。此外，我们设计了一种计算效率高的细化程序，可以证明减少了变化点初步估计的定位误差。我们证明了定位误差的极小极大下界，几乎与我们方法的定位误差上限相匹配，并表明我们施加的信噪比条件本质上是基于信息论论证的最弱的可能条件。大量的数值结果支持我们的理论发现，而真实空气质量数据的实验揭示了算法未使用的历史信息支持的变化点。
This paper addresses the problem of localizing change points in high-dimensional linear regression models with piecewise constant regression coefficients. We develop a dynamic programming approach to estimate the locations of the change points whose performance improves upon the current state-of-the-art, even as the dimensionality, the sparsity of the regression coefficients, the temporal spacing between two consecutive change points, and the magnitude of the difference of two consecutive regression coefficient vectors are allowed to vary with the sample size. Furthermore, we devise a computationally-efficient refinement procedure that provably reduces the localization error of preliminary estimates of the change points. We demonstrate minimax lower bounds on the localization error that nearly match the upper bound on the localization error of our methodology and show that the signal-to-noise condition we impose is essentially the weakest possible based on information-theoretic arguments. Extensive numerical results support our theoretical findings, and experiments on real air quality data reveal change points supported by historical information not used by the algorithm.