Learning Nonsymmetric Determinantal Point Processes

Abstract

Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPPs are conventionally parameterized by a positive semi-definite kernel matrix, and this symmetric kernel encodes only repulsive interactions between items. These so-called symmetric DPPs have significant expressive power, and have been successfully applied to a variety of machine learning tasks, including recommendation systems, information retrieval, and automatic summarization, among many others. Efficient algorithms for learning symmetric DPPs and sampling from these models have been reasonably well studied. However, relatively little attention has been given to nonsymmetric DPPs, which relax the symmetric constraint on the kernel. Nonsymmetric DPPs allow for both repulsive and attractive item interactions, which can significantly improve modeling power, resulting in a model that may better fit for some applications. We present a method that enables a tractable algorithm, based on maximum likelihood estimation, for learning nonsymmetric DPPs from data composed of observed subsets. Our method imposes a particular decomposition of the nonsymmetric kernel that enables such tractable learning algorithms, which we analyze both theoretically and experimentally. We evaluate our model on synthetic and real-world datasets, demonstrating improved predictive performance compared to symmetric DPPs, which have previously shown strong performance on modeling tasks associated with these datasets.

arXiv commentNeurIPS 2019

Cited by in corpus (8)

• Probabilistic Generating Circuits
• Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes
• DPPy: Sampling DPPs with Python
• Wasserstein Learning of Determinantal Point Processes
• Entropic Independence I: Modified Log-Sobolev Inequalities for Fractionally Log-Concave Distributions and High-Temperature Ising Models
• Nonparametric estimation of continuous DPPs with kernel methods
• Online MAP Inference and Learning for Nonsymmetric Determinantal Point Processes
• Learning from DPPs via Sampling: Beyond HKPV and symmetry