We develop a novel, general and computationally efficient framework, called Divide and Conquer Dynamic Programming (DCDP), for localizing change points in time series data with high-dimensional features. DCDP deploys a class of greedy algorithms that are applicable to a broad variety of high-dimensional statistical models and can enjoy almost linear computational complexity. We investigate the performance of DCDP in three commonly studied change point settings in high dimensions: the mean model, the Gaussian graphical model, and the linear regression model. In all three cases, we derive non-asymptotic bounds for the accuracy of the DCDP change point estimators. We demonstrate that the DCDP procedures consistently estimate the change points with sharp, and in some cases, optimal rates while incurring significantly smaller computational costs than the best available algorithms. Our findings are supported by extensive numerical experiments on both synthetic and real data.

翻译：我们提出了一种新颖、通用且计算高效的框架，称为分治动态规划（DCDP），用于定位具有高维特征的时间序列数据中的变化点。DCDP采用了一类贪心算法，这些算法适用于多种高维统计模型，并且能够实现近似线性的计算复杂度。我们研究了DCDP在三种常见的高维变化点设置中的性能：均值模型、高斯图模型和线性回归模型。在所有三种情况下，我们推导了DCDP变化点估计量准确性的非渐近界。我们证明，DCDP程序能够以尖锐、在某些情况下最优的速率一致地估计变化点，同时其计算成本显著低于现有最佳算法。我们的发现得到了对合成数据和真实数据的大量数值实验的支持。