Kronecker Determinantal Point Processes

Determinantal Point Processes (DPPs) are discrete probability models over the subsets of a ground set of N items. They provide an elegant model to assign probabilities to an exponentially large sample, while permitting tractable (polynomial time) sampling and marginalization. They are often used to provide models that balance "diversity" and quality, characteristics valuable to numerous problems in machine learning and related areas [17]. The antecedents of DPPs lie in statistical mechanics [24], but since the seminal work of [15] they have made inroads into machine learning. By now they have been applied to a variety of problems such as document and video summarization [6, 21], sensor placement [14], recommender systems [31], and object retrieval [2]. More recently, they have been used to compress fully-connected layers in neural networks [26] and to provide optimal sampling procedures for the Nyström method [20]. The more general study of DPP properties has also garnered a significant amount of interest, see e.g., [1, 5, 7, 12, 16-18, 23].