B1061
Title: Sequential gradient descent and quasi-Newton's method for change-point analysis
Authors: Xianyang Zhang - Texas A\&M University (United States) [presenting]
Trisha Dawn - Texas AM University (United States)
Abstract: One common approach to detecting change points is minimizing a cost function over possible numbers and locations of change points. The framework includes several well-established procedures, such as the penalized likelihood and minimum description length. Such an approach requires finding the cost value repeatedly over different segments of the data set, which can be time-consuming when (i) the data sequence is long and (ii) obtaining the cost value involves solving a non-trivial optimization problem. A new sequential method (SE) is introduced that can be coupled with gradient descent (SeGD) and Quasi-Newton's method (SeN) to find the cost value effectively. The core idea is to update the cost value using the information from previous steps without re-optimizing the objective function. The new method is applied to change-point detection in generalized linear models and penalized regression. Numerical studies show that the new approach can be orders of magnitude faster than the Pruned exact linear time (PELT) method without sacrificing estimation accuracy.
