Block-wise map inference for determinantal point processes with application to change-point detection

Most studies of change-point detection (CPD) focus on developing similarity metrics that quantify how Likely a time-point is to be a change point. After that, the process of selecting true change points among those high-score candidates is less well-studied. This paper proposes a new CPD method that uses determinantal point processes to model the process of change-point selection. Specifically, this work explores the particular kernel structure arose in such modelling, the almost block diagonal. It shows that the maximum a posteriori task, requiring at least O(N
^2,4
) in general, can be achieved using O(N) under such structure. The resulting algorithms, BwDPP-MAP and BwDppCpd, are empirically validated through simulation and five real-world data experiments.