Estimation of high-dimensional change-points under a group sparsity structure
Estimation of high-dimensional change-points under a group sparsity structure
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DOI：
10.1214/23-ejs2116
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发表时间：
2021-07
影响因子：
1.1
通讯作者：
HanQin Cai;Tengyao Wang
中科院分区：
文献类型：
--
作者：
HanQin Cai;Tengyao Wang
变化点是以高维数据流的形式观察到的“大数据”的常规特征。在许多这样的数据流中，组件系列具有组结构，并且很自然地假设仅在所有组中的一小部分中发生更改。我们提出了一种新的变化点过程，称为“groupInspect”，该过程利用群稀疏性结构来估计投影方向，从而聚合跨组件序列的信息，从而成功估计序列平均结构中的变化点。我们证明了估计的投影方向是最小最大最优的，直到对数因子，当所有的群体规模是相当的顺序。此外，我们的理论对变点位置估计器的收敛速度提供了强有力的保证。数值研究证明了groupInspect在广泛设置下的竞争性能，并通过实际数据示例证实了我们的程序的实用性。
Change-points are a routine feature of 'big data' observed in the form of high-dimensional data streams. In many such data streams, the component series possess group structures and it is natural to assume that changes only occur in a small number of all groups. We propose a new change point procedure, called 'groupInspect', that exploits the group sparsity structure to estimate a projection direction so as to aggregate information across the component series to successfully estimate the change-point in the mean structure of the series. We prove that the estimated projection direction is minimax optimal, up to logarithmic factors, when all group sizes are of comparable order. Moreover, our theory provide strong guarantees on the rate of convergence of the change-point location estimator. Numerical studies demonstrates the competitive performance of groupInspect in a wide range of settings and a real data example confirms the practical usefulness of our procedure.