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One common approach to detecting change-points is minimizing a cost functionover possible numbers and locations of change-points. The framework includesseveral well-established procedures, such as the penalized likelihood andminimum description length. Such an approach requires finding the cost valuerepeatedly over different segments of the data set, which can be time-consumingwhen (i) the data sequence is long and (ii) obtaining the cost value involvessolving a non-trivial optimization problem. This paper introduces a newsequential method (SE) that can be coupled with gradient descent (SeGD) andquasi-Newton's method (SeN) to find the cost value effectively. The core ideais to update the cost value using the information from previous steps withoutre-optimizing the objective function. The new method is applied to change-pointdetection in generalized linear models and penalized regression. Numericalstudies show that the new approach can be orders of magnitude faster than thePruned Exact Linear Time (PELT) method without sacrificing estimation accuracy.

Sequential Gradient Descent and Quasi-Newton's Method for Change-Point Analysis