Learning k-Determinantal Point Processes for Personalized Ranking

TL;DR

This work presents a new optimization criterion LkP based on set probability comparison for personalized ranking that moves beyond traditional ranking-based methods and is broadly applicable, and when applied to existing recommendation models it yields strong performance improvements, suggesting that LkP holds significant value to the field of recommender systems.

Abstract

The key to personalized recommendation is to predict a personalized ranking on a catalog of items by modeling the user's preferences. There are many personalized ranking approaches for item recommendation from implicit feedback like Bayesian Personalized Ranking (BPR) and listwise ranking. Despite these methods have shown performance benefits, there are still limitations affecting recommendation performance. First, none of them directly optimize ranking of sets, causing inadequate exploitation of correlations among multiple items. Second, the diversity aspect of recommendations is insufficiently addressed compared to relevance. In this work, we present a new optimization criterion LkP based on set probability comparison for personalized ranking that moves beyond traditional ranking-based methods. It formalizes set-level relevance and diversity ranking comparisons through a Determinantal Point Process (DPP) kernel decomposition. To confer ranking interpretability to the DPP set probabilities and prioritize the practicality of LkP, we condition the standard DPP on the cardinality k of the DPP-distributed set, known as k-DPP, a less-explored extension of DPP. The generic stochastic gradient descent based technique can be directly applied to optimizing models that employ LkP. We implement LkP in the context of both Matrix Factorization (MF) and neural networks approaches, on three real-world datasets, obtaining improved relevance and diversity performances. LkP is broadly applicable, and when applied to existing recommendation models it also yields strong performance improvements, suggesting that LkP holds significant value to the field of recommender systems.

Figures (5)

• Figure 1: The diagrammatic sketch of L$k$P. Each square in the middle represents an item (denoted as $v$), with the subscript numeral indicating its index. The superscript $1$ ($0$) signifies an observed (unobserved) interaction of user $u$, while $a$, $b$, and $c$ denote three distinct categories of items. The top layer is a simple comparative illustration of different optimization methods. The layers below show our two types (set-level relevance ranking $>_u$ and diversity ranking $>_d$) of comparison, which are integrated using the $k$-DPP probability ranking. The focal comparison points are indicated by red markers.
• Figure 2: Performance trends at different $k$ on Beauty.
• Figure 3: Performance of L$k$P$_{PS}$ at different $n$.
• Figure 4: Probability distributions at different epochs on Anime.
• Figure 5: Case study of L$k$P$_{PS}$ optimization criterion.