Fixed-point algorithms for learning determinantal point processes

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.

ICML, 2015

References in corpus (3)

• Learning Determinantal Point Processes
• Learning the Parameters of Determinantal Point Process Kernels
• Expectation-Maximization for Learning Determinantal Point Processes

Cited by in corpus (9)

• Diversity in Machine Learning
• Gaussian Determinantal Processes: a new model for directionality in data
• Probabilistic Generating Circuits
• Deep Determinantal Point Processes
• Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes
• Flexible Modeling of Diversity with Strongly Log-Concave Distributions
• Wasserstein Learning of Determinantal Point Processes
• Nonparametric estimation of continuous DPPs with kernel methods
• Testing Determinantal Point Processes