Fixed-point algorithms for learning determinantal point processes

TL;DR

This paper introduces a simple, efficient fixed-point algorithm for learning the kernel of determinantal point processes, outperforming previous methods in speed and sometimes in accuracy on real and simulated data.

Contribution

The paper proposes a novel fixed-point algorithm for DPP kernel estimation that is simpler, faster, and often more effective than existing approaches.

Findings

Algorithm is significantly faster on large datasets.

Achieves comparable or better local maxima.

Performs well on both real and simulated data.

Abstract

Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key to learning DPPs from observed data. We consider the task of learning the DPP kernel, and develop for it a surprisingly simple yet effective new algorithm. Our algorithm offers the following benefits over previous approaches: (a) it is much simpler; (b) it yields equally good and sometimes even better local maxima; and (c) it runs an order of magnitude faster on large problems. We present experimental results on both real and simulated data to illustrate the numerical performance of our technique.