Testing Determinantal Point Processes

Determinantal point processes (DPPs) are a rich class of discrete probability distributions that were first studied in the context of quantum physics [54] and random matrix theory [30]. Initiated by the seminal work of Kulesza and Taskar [46], DPPs have gained a lot of attention in machine learning, due to their ability to naturally capture notions of diversity and repulsion. Moreover, they are easy to define via a similarity (kernel) matrix, and, as opposed to many other probabilistic models, offer tractable exact algorithms for marginalization, conditioning and sampling [5, 42, 46, 51]. Therefore, DPPs have been explored in a wide range of applications, including video summarization [38, 39], image search [2, 45], document and timeline summarization [53], recommendation [69], feature selection in bioinformatics [9], modeling neurons [63], and matrix approximation [22, 23, 50]. A Determinantal Point Process is a distribution over the subsets of a ground set [n] {1,2,...n}, and parameterized by a marginal kernel matrix K R