Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes
Abstract
Strongly Rayleigh distributions are natural generalizations of product and determinantal probability distributions and satisfy strongest form of negative dependence properties. We show that the "natural" Monte Carlo Markov Chain (MCMC) is rapidly mixing in the support of a {\em homogeneous} strongly Rayleigh distribution. As a byproduct, our proof implies Markov chains can be used to efficiently generate approximate samples of a $k$-determinantal point process. This answers an open question raised by Deshpande and Rademacher.
Cite
Text
Anari et al. "Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes." Annual Conference on Computational Learning Theory, 2016.Markdown
[Anari et al. "Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes." Annual Conference on Computational Learning Theory, 2016.](https://mlanthology.org/colt/2016/anari2016colt-monte/)BibTeX
@inproceedings{anari2016colt-monte,
title = {{Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes}},
author = {Anari, Nima and Gharan, Shayan Oveis and Rezaei, Alireza},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2016},
pages = {103-115},
url = {https://mlanthology.org/colt/2016/anari2016colt-monte/}
}