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Faster Greedy MAP Inference for Determinantal Point Processes
Insu Han · Prabhanjan Kambadur · Kyoungsoo Park · Jinwoo Shin

Tue Aug 08 01:30 AM -- 05:00 AM (PDT) @ Gallery #73

Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by determinants of their features. 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 orthogonal 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.

Author Information

Insu Han (Korea Advanced Institute of Science and Technology)
Prabhanjan Kambadur (Bloomberg)
Kyoungsoo Park (KAIST)
Jinwoo Shin (KAIST)

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