Abstract: Although change-point detection for high-dimensional data has become increasingly important in many scientific fields, most existing methods are designed for specific models (e.g., mean shift model, vector auto-regressive model, graphical model). Here, we provide a unified framework for structural break detection that is suitable for a large class of models. Moreover, we propose a three-step algorithm that automatically achieves consistent parameter estimates during the change-point detection process, without needing to refit the model. The first step combines the block segmentation strategy and a fused lasso-based estimation criterion, leading to significant computational gains, without compromising the statistical accuracy of identifying the number and location of the structural breaks. Then, we use hard-thresholding and exhaustive search steps to consistently estimate the number and location of the break points. We prove strong guarantees on both the number of estimated change points and the rates of convergence of their locations, and provide consistent estimates of the model parameters. The findings of our numerical studies support the theory and validate the competitive performance of the algorithm for a wide range of models. The proposed algorithm is implemented in the R package LinearDetect.

Key words and phrases: Block segmentation, fused Lasso, high-dimensional data, linear model, piecewise stationarity, structural breaks.