Existing MAP inference algorithms for determinantal point processes (DPPs) need to calculate determinants or conduct eigenvalue decomposition generally at the scale of the full kernel, which presents a great challenge for real-world applications. In this paper, we introduce a class of DPPs, called BwDPPs, that are characterized by an almost block diagonal kernel matrix and thus can allow efficient block-wise MAP inference. Furthermore, BwDPPs are successfully applied to address the difficulty of selecting change-points in the problem of change-point detection (CPD), which results in a new BwDPP-based CPD method, named BwDppCpd. In BwDppCpd, a preliminary set of change-point candidates is first created based on existing well-studied metrics. Then, these change-point candidates are treated as DPP items, and DPP-based subset selection is conducted to give the final estimate of the change-points that favours both quality and diversity. The effectiveness of BwDppCpd is demonstrated through extensive experiments on five real-world datasets.

本文介绍了一种新的DPP类别，即几乎分块对角线协方差矩阵的BwDPP，该DPP类别允许高效的分块MAP推断，并成功应用于解决变点检测问题（CPD），即BwDppCpd方法，通过DPP集合选择估计最终的变点，这种方法在五个真实的数据集上进行了广泛实验，显示出高效性。

应用于变点检测的行列式点过程块状MAP推断