A Polynomial Time MCMC Method for Sampling from Continuous DPPs

The notion of DPP was first introduced by [Mac75] to model fermions. Since then, They have been extensively studied, and efficient algorithms have been discovered for tasks like sampling from DPPs [LJS15, DR10, AGR16], marginalization [BR05], and learning [GKFT14, UBMR17] them (in the discrete domain). In machine learning they are mainly used to solve problems where selecting a diverse set of objects is preferred since they offer negative correlation. To get intuition about why they are good models to capture diversity, suppose each row of the gram matrix associated with the kernel is a feature vector representing an item. It means the probability of a set of items is proportional to the square of the volume of the space spanned the vectors representing items. Therefore, larger volume shows those items are more spread which resembles diversity.