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# MAP Inference for Customized Determinantal Point Processes via Maximum Inner Product Search

*Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics*, PMLR 108:2797-2807, 2020.

#### Abstract

Determinantal point processes (DPPs) are a good fit for modeling diversity in many machine learning applications. For instance, in recommender systems, one might have a basic DPP defined by item features, and a customized version of this DPP for each user with features re-weighted according to user preferences. While such models perform well, they are typically applied only to relatively small datasets, because existing maximum a posteriori (MAP) approximation algorithms are expensive. In this work, we propose a new MAP algorithm: we show that, by performing a one-time preprocessing step on a basic DPP, it is possible to run an approximate version of the standard greedy MAP approximation algorithm on any customized version of the DPP in time sublinear in the number of items. Our key observation is that the core computation can be written as a maximum inner product search (MIPS), which allows us to accelerate inference via approximate MIPS structures, e.g., trees or hash tables. We provide a theoretical analysis of the algorithm’s approximation quality, as well as empirical results on real-world datasets demonstrating that it is often orders of magnitude faster while sacrificing little accuracy.