Optimal Covariance Change Point Detection in High Dimension
Optimal Covariance Change Point Detection in High Dimension
复制标题
高维最优协方差变点检测
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Rinaldo
中科院分区：
文献类型：
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作者：
Daren Wang;Yi Yu;A. Rinaldo
我们研究高维协方差矩阵的变点检测问题。我们假设 {Xi}i=1,...,n 是观察到的独立的、居中的 p 维亚高斯随机向量序列，其协方差矩阵是分段常数。我们的任务是高精度地恢复未知的变化点的数量和位置。我们的通用模型设置允许所有模型参数随 n 变化，包括维度 p、连续变化点之间的最小间距、最小变化的幅度以及样本点协方差矩阵的最大算子范数。我们介绍了两种程序，一种基于二进制分割算法（例如 Vostrikova，1981），另一种基于其扩展，称为 Fryzlewicz（2014）的野生二进制分割，并证明，在适当的条件下，两者都能够一致地估计变化点的数量和位置。我们的第二种算法，称为通过独立投影进行野生二值分割（WBSIP），在所有相关参数方面被证明是极小极大最优。我们的极小极大分析还揭示了基于我们的通用模型设置的相变效应。据我们所知，这种类型的结果尚未在变点检测文献的其他地方建立。
We study the problem of change point detection for covariance matrices in high dimensions. We assume that {Xi}i=1,...,n is a sequence of independent, centered p-dimensional sub-Gaussian random vectors is observed whose covariance matrices are piece-wise constant. Our task is to recover with high accuracy the number and locations the of change points, which are unknown. Our generic model setting allows for all the model parameters to change with n, including the dimension p, the minimal spacing between consecutive change points, the magnitude of smallest change and the maximal operator norm of the covariance matrices of the sample points. We introduce two procedures, one based on the binary segmentation algorithm (e.g. Vostrikova, 1981) and the other on its extension known as wild binary segmentation of Fryzlewicz (2014), and demonstrate that, under suitable conditions, both are able to consistently estimate the number and locations of change points. Our second algorithm, called Wild Binary Segmentation through Independent Projection (WBSIP) is shown to be minimax optimal in the in terms of all the relevant parameters. Our minimax analysis also reveals a phase transition effect based on our generic model setting. To the best of our knowledge, this type of results has not been established elsewhere in the change point detection literature.
DOI：
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发表时间：
2017
期刊：
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影响因子：
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作者：
Kevin Lin;J. Sharpnack;A. Rinaldo;R. Tibshirani
通讯作者：
Kevin Lin;J. Sharpnack;A. Rinaldo;R. Tibshirani
影响因子：
2.1
作者：
Olshen, AB;Venkatraman, ES;Wigler, M
通讯作者：
Wigler, M