论文标题
高维数据的最佳多个更改点检测
Optimal multiple change-point detection for high-dimensional data
论文作者
论文摘要
该手稿对更改点检测的领域有两个贡献。在GeneralChange点设置中，我们提供了一种通用算法，用于汇总局部均匀性测试，一个时间序列中变更点的估计器。有趣的是，我们确定测试收集的错误将直接转化为更改点估计器的检测属性。然后将此通用方案应用于各种问题，包括协方差更改点检测，非参数更改点检测和稀疏的多元平均变更点检测。对于后者，我们得出了适应于未知的稀疏性以及噪声为高斯时变化点之间的距离的最小最佳速率。 Forsub-Gaussian噪音，我们引入了一种在几乎所有稀疏方案中都是最佳的变体。
This manuscript makes two contributions to the field of change-point detection. In a generalchange-point setting, we provide a generic algorithm for aggregating local homogeneity testsinto an estimator of change-points in a time series. Interestingly, we establish that the errorrates of the collection of tests directly translate into detection properties of the change-pointestimator. This generic scheme is then applied to various problems including covariance change-point detection, nonparametric change-point detection and sparse multivariate mean change-point detection. For the latter, we derive minimax optimal rates that are adaptive to theunknown sparsity and to the distance between change-points when the noise is Gaussian. Forsub-Gaussian noise, we introduce a variant that is optimal in almost all sparsity regimes.
