The Bayesian Low-Rank Determinantal Point Process Mixture Model

TL;DR

This paper introduces a scalable low-rank DPP mixture model for subset probability modeling, improving recommendation accuracy and scalability over traditional DPPs by capturing latent structures with a mixture approach.

Contribution

It proposes a novel low-rank DPP mixture model with an efficient MCMC learning algorithm, enhancing modeling capacity and predictive performance for large-scale recommendation tasks.

Findings

Outperforms single low-rank and full-rank DPPs in predictive accuracy.

Achieves significant scalability improvements for large datasets.

Provides better recommendations compared to competing methods.

Abstract

Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix. Recent work has shown that using a low-rank factorization of this kernel provides remarkable scalability improvements that open the door to training on large-scale datasets and computing online recommendations, both of which are infeasible with standard DPP models that use a full-rank kernel. In this paper we present a low-rank DPP mixture model that allows us to represent the latent structure present in observed subsets as a mixture of a number of component low-rank DPPs, where each component DPP is responsible for representing a portion of the observed data. The mixture model allows us to effectively address the capacity constraints of the low-rank DPP model. We present an efficient and scalable Markov Chain Monte Carlo (MCMC) learning algorithm for our model that uses Gibbs sampling and stochastic gradient Hamiltonian Monte Carlo (SGHMC). Using an evaluation on several real-world product recommendation datasets, we show that our low-rank DPP mixture model provides substantially better predictive performance than is possible with a single low-rank or full-rank DPP, and significantly better performance than several other competing recommendation methods in many cases.