Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by matrix determinants. In this paper, we develop fast algorithms to find the most likely configuration (MAP) of large-scale DPPs, which is NP-hard in general. Due to the submodular nature of the MAP objective, greedy algorithms have been used with empirical success. Greedy implementations require computation of log-determinants, matrix inverses or solving linear systems at each iteration. We present faster implementations of the greedy algorithms by utilizing the complementary benefits of two log-determinant approximation schemes: (a) first-order expansions to the matrix log-determinant function and (b) high-order expansions to the scalar log function with stochastic trace estimators. In our experiments, our algorithms are orders of magnitude faster than their competitors, while sacrificing marginal accuracy.

本文提出了使用log-determinants和stochastic trace estimators的两种逼近方案来使得贪心算法更快速，从而解决大规模determinantal point processes的MAP问题。实验表明，该算法在不牺牲较少精度的情况下比其竞争对手快数个数量级。

用于行列式点过程的更快贪婪MAP推断