  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 $\text{poly}(k)$ 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, $\mathbb{S}^{d-1}$ in time
polynomial in $k,d$.

Machine Learning;Data Structures and Algorithms;Machine Learning