Markov Determinantal Point Process for Dynamic Random Sets

The Law of Determinantal Point Process (LDPP) is a flexible parametric family of distributions over random sets defined on a finite state space, or equivalently over multivariate binary variables. The aim of this paper is to introduce Markov processes of random sets within the LDPP framework. We show that, when the pairwise distribution of two neighboring terms follows the LDPP, both the transition distribution and the stationary distribution belong to the LDPP family as well. We explore how their parameterizations are related. We investigate various constrained model specifications, develop procedures for exploratory analysis of a series of sets, and discuss model estimation on both simulated data and topics published in National Geographic.