行列式点过程的懒惰与快速贪婪MAP推理
Lazy and Fast Greedy MAP Inference for Determinantal Point Process
摘要：
在许多机器学习应用中，决定性点过程（DPP）的最大后验（MAP）推断对于选择不同的项目是至关重要的。虽然DPP MAP推理是NP难的，但贪心算法往往能找到高质量的解，许多研究人员研究了其高效实现。一个经典和实用的方法是懒惰的贪心算法，这是适用于一般的子模函数最大化，而最近的快速贪心算法的基础上的Cholesky分解是更有效的DPP MAP推理。本文介绍了如何结合的想法“懒惰”和“快”，这一直被认为是不相容的文献。我们的懒惰和快速的贪心算法实现了几乎相同的时间复杂度作为目前最好的一个，并在实践中运行更快。“懒惰+快速”的思想可以扩展到其他贪婪类型的算法。我们还给出了一个快速版本的双贪心算法无约束DPP MAP推理。实验验证了我们的加速思想的有效性。
英文摘要：
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.
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