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——分治动态规划（Divide and Conquer Dynamic Programming, DCDP），用于在高维特征时间序列数据中定位变点。DCDP部署了一类适用于多种高维统计模型的贪心算法，并能够实现近乎线性的计算复杂度。我们研究了DCDP在三种常见的高维变点设定中的表现：均值模型、高斯图模型和线性回归模型。在这三种情况下，我们推导了DCDP变点估计器精度的非渐近界。实验证明，DCDP过程能以尖锐（某些情况下甚至最优）的速率一致地估计变点，同时计算成本显著低于现有最佳算法。基于合成数据与真实数据的大量数值实验进一步支持了我们的结论。