Faster Greedy MAP Inference for Determinantal Point Processes
This work addresses computational bottlenecks in DPP inference for machine learning tasks involving diverse set selection, but it is incremental as it improves existing greedy methods.
The paper tackles the NP-hard problem of finding the most likely configuration (MAP) for large-scale determinantal point processes (DPPs) by developing faster greedy algorithms using log-determinant approximations, resulting in orders of magnitude speed improvements with marginal accuracy loss.
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.