Lazy and Fast Greedy MAP Inference for Determinantal Point Process

TL;DR

This paper introduces a novel combination of lazy and fast greedy algorithms for DPP MAP inference, achieving near state-of-the-art efficiency and faster practical performance, with extensions to other greedy algorithms.

Contribution

It presents a new lazy and fast greedy algorithm for DPP MAP inference that is both theoretically efficient and practically faster, extending to other greedy methods.

Findings

Achieves similar time complexity to the best existing algorithms.

Runs faster in practice on real datasets.

Effective acceleration demonstrated through experiments.

Abstract

The maximum a posteriori (MAP) inference for determinantal point processes (DPPs) is crucial for selecting diverse items in many machine learning applications. Although DPP MAP inference is NP-hard, the greedy algorithm often finds high-quality solutions, and many researchers have studied its efficient implementation. One classical and practical method is the lazy greedy algorithm, which is applicable to general submodular function maximization, while a recent fast greedy algorithm based on the Cholesky factorization is more efficient for DPP MAP inference. This paper presents how to combine the ideas of "lazy" and "fast", which have been considered incompatible in the literature. Our lazy and fast greedy algorithm achieves almost the same time complexity as the current best one and runs faster in practice. The idea of "lazy + fast" is extendable to other greedy-type algorithms. We also give a fast version of the double greedy algorithm for unconstrained DPP MAP inference. Experiments validate the effectiveness of our acceleration ideas.