Seeded binary segmentation: a general methodology for fast and optimal changepoint detection

In recent years, there has been an increasing demand on efficient algorithms for large scale change point detection problems. To this end, we propose seeded binary segmentation, approach relying a deterministic construction of background intervals, called in which single points are searched. The final selection based the candidates from intervals can be done various ways, adapted to problem at hand. Thus, segmentation is easy adapt wide range problems, let that univariate, multivariate or even high-dimensional. We consider univariate Gaussian mean setup detail. For specific case show leads near-linear time (i.e. linear up logarithmic factor) independent underlying number points. Furthermore, using appropriate methods, methodology shown asymptotically minimax optimal. While computationally more efficient, finite sample estimation performance remains competitive compared state art procedures. Moreover, illustrate high-dimensional settings with inverse covariance where our proposal massive computational gains while still exhibiting good statistical performance.