  In recent years, change point detection for high dimensional data has become
increasingly important in many scientific fields. Most literature develop a
variety of separate methods designed for specified models (e.g. mean shift
model, vector auto-regressive model, graphical model). In this paper, we
provide a unified framework for structural break detection which is suitable
for a large class of models. Moreover, the proposed algorithm automatically
achieves consistent parameter estimates during the change point detection
process, without the need for refitting the model. Specifically, we introduce a
three-step procedure. The first step utilizes the block segmentation strategy
combined with a fused lasso based estimation criterion, leads to significant
computational gains without compromising the statistical accuracy in
identifying the number and location of the structural breaks. This procedure is
further coupled with hard-thresholding and exhaustive search steps to
consistently estimate the number and location of the break points. The strong
guarantees are proved on both the number of estimated change points and the
rates of convergence of their locations. The consistent estimates of model
parameters are also provided. The numerical studies provide further support of
the theory and validate its competitive performance for a wide range of models.
The developed algorithm is implemented in the R package LinearDetect.
