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We develop a novel, general and computationally efficient framework, calledDivide and Conquer Dynamic Programming (DCDP), for localizing change points intime series data with high-dimensional features. DCDP deploys a class of greedyalgorithms that are applicable to a broad variety of high-dimensionalstatistical models and can enjoy almost linear computational complexity. Weinvestigate the performance of DCDP in three commonly studied change pointsettings in high dimensions: the mean model, the Gaussian graphical model, andthe linear regression model. In all three cases, we derive non-asymptoticbounds for the accuracy of the DCDP change point estimators. We demonstratethat the DCDP procedures consistently estimate the change points with sharp,and in some cases, optimal rates while incurring significantly smallercomputational costs than the best available algorithms. Our findings aresupported by extensive numerical experiments on both synthetic and real data.

Divide and Conquer Dynamic Programming: An Almost Linear Time Change Point Detection Methodology in High Dimensions