Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes

TL;DR

This paper introduces scalable algorithms for learning and MAP inference in nonsymmetric determinantal point processes, enabling practical application to large datasets without sacrificing predictive accuracy.

Contribution

The authors propose a new NDPP kernel decomposition and linear-complexity algorithms for learning and MAP inference, improving scalability over prior methods.

Findings

Algorithms scale linearly with dataset size

Matching predictive performance of previous methods

Significant improvements in computational efficiency

Abstract

Determinantal point processes (DPPs) have attracted significant attention in machine learning for their ability to model subsets drawn from a large item collection. Recent work shows that nonsymmetric DPP (NDPP) kernels have significant advantages over symmetric kernels in terms of modeling power and predictive performance. However, for an item collection of size $M$, existing NDPP learning and inference algorithms require memory quadratic in $M$ and runtime cubic (for learning) or quadratic (for inference) in $M$, making them impractical for many typical subset selection tasks. In this work, we develop a learning algorithm with space and time requirements linear in $M$ by introducing a new NDPP kernel decomposition. We also derive a linear-complexity NDPP maximum a posteriori (MAP) inference algorithm that applies not only to our new kernel but also to that of prior work. Through evaluation on real-world datasets, we show that our algorithms scale significantly better, and can match the predictive performance of prior work.