Segmented multiple-Lasso and peak recognition algorithm for change-point detection

Change-point detection which originated from the field of quality control has become an important area of research. The Lasso method provides a novel framework for change-point detection through specialized design matrices. However, a substantial amount of data may increase dimensions of the matrix and slow computational speed. The use of Lasso to detect change-points based on the first-order difference of two adjacent points lacks stability and ignores time series information of data. This paper first proposes a Segmented Multiple-Lasso and Peak Recognition Algorithm for change-point detection. To reduce dimension of the matrix and hence improve computational efficiency, the algorithm partitions data into segments using cut-off points, then discards segments unlikely to contain change-points through screening. Subsequently, the proposed algorithm introduces a multiple difference to detect change-points with enough information in a local region. Notably, by combining a novel statistic and PULSE pattern, a generalized change point selection criterion is established. It takes order into account by using a peak detection method, which enhances robustness of the method. Our theoretical results imply asymptotic property of this algorithm. Comparative simulations reveal this algorithm’s enhanced performance metrics, surpassing other methods in both accuracy and computational efficiency, especially when a long data sequence is studied.