A Polynomial Time MCMC Method for Sampling from Continuous DPPs

We study the Gibbs sampling algorithm for continuous determinantal point processes. We show that, given a warm start, the Gibbs sampler generates a random sample from a continuous k-DPP defined on a d-dimensional domain by only taking poly(k) number of steps. As an application, we design an algorithm to generate random samples from k-DPPs defined by a spherical Gaussian kernel on a unit sphere in d-dimensions, mathbbSd-1 in time polynomial in k,d.