Continuous Optimization for Offline Change Point Detection and Estimation

Change point detection and estimation are an incredibly diverse and widely scattered field in applied and mathematical statistics, with a large variety of applications. To provide a high-level intuition, change point detection may be understood as a signal processing tool for identifying abrupt changes in the generative parameters of a data sequence. While a strong line of work in change point detection is well established with Page's pioneering work (see Page [1954]) and rigorous results by Chernoff and Zacks [1964], Lorden [1971] and Sen and Srivastava [1975], many aspects of this problem are open and the general understanding of good solutions depends strongly on the problem at hand Niu et al. [2016], Truong et al. [2020], and Ma et al. [2020]. Among the open research questions, the simultaneous detection of multiple change points in large data sets is of major interest. Taking a machine learning and data scientific motivated approach, in this paper, we explore the applicability of recent advances in best subset selection of covariates in linear regression proposed by Moka et al. [2024]. This method, a continuous optimization approach for best subset selection, claims to offer faster performance compared to existing exhaustive search methods, while maintaining comparable accuracy.