A Polynomial Time MCMC Method for Sampling from Continuous Determinantal Point Processes
Abstract
We study the Gibbs sampling algorithm for discrete and continuous $k$-determinantal point processes. We show that in both cases, the spectral gap of the chain is bounded by a polynomial of $k$ and it is independent of the size of the domain. As an immediate corollary, we obtain sublinear time algorithms for sampling from discrete $k$-DPPs given access to polynomially many processors. In the continuous setting, our result leads to the first class of rigorously analyzed efficient algorithms to generate random samples of continuous $k$-DPPs. We achieve this by showing that the Gibbs sampler for a large family of continuous $k$-DPPs can be simulated efficiently when the spectrum is not concentrated on the top $k$ eigenvalues.
Cite
Text
Rezaei and Gharan. "A Polynomial Time MCMC Method for Sampling from Continuous Determinantal Point Processes." International Conference on Machine Learning, 2019.Markdown
[Rezaei and Gharan. "A Polynomial Time MCMC Method for Sampling from Continuous Determinantal Point Processes." International Conference on Machine Learning, 2019.](https://mlanthology.org/icml/2019/rezaei2019icml-polynomial/)BibTeX
@inproceedings{rezaei2019icml-polynomial,
title = {{A Polynomial Time MCMC Method for Sampling from Continuous Determinantal Point Processes}},
author = {Rezaei, Alireza and Gharan, Shayan Oveis},
booktitle = {International Conference on Machine Learning},
year = {2019},
pages = {5438-5447},
volume = {97},
url = {https://mlanthology.org/icml/2019/rezaei2019icml-polynomial/}
}