Block-Wise MAP Inference for Determinantal Point Processes with Application to Change-Point Detection

TL;DR

This paper introduces BwDPPs, a class of determinantal point processes with block diagonal kernels enabling efficient MAP inference, and applies them to improve change-point detection by selecting diverse, high-quality change-points.

Contribution

The paper proposes BwDPPs with block-wise MAP inference and develops a new change-point detection method using these processes, addressing computational challenges in DPPs.

Findings

BwDppCpd outperforms existing methods on real datasets.

Efficient block-wise inference reduces computational complexity.

DPP-based selection improves change-point detection quality.

Abstract

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.