Continuous Optimization for Offline Change Point Detection and Estimation

This work explores use of novel advances in best subset selection for regression modelling via continuous optimization for offline change point detection and estimation in univariate Gaussian data sequences. The approach exploits reformulating the normal mean multiple change point model into a regularized statistical inverse problem enforcing sparsity. After introducing the problem statement, criteria and previous investigations via Lasso-regularization, the recently developed framework of continuous optimization for best subset selection (COMBSS) is briefly introduced and related to the problem at hand. Supervised and unsupervised perspectives are explored with the latter testing different approaches for the choice of regularization penalty parameters via the discrepancy principle and a confidence bound. The main result is an adaptation and evaluation of the COMBSS approach for offline normal mean multiple change-point detection via experimental results on simulated data for different choices of regularisation parameters. Results and future directions are discussed.