Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes
This provides a theoretical foundation for efficient sampling in machine learning and statistics, addressing a specific bottleneck in probabilistic modeling.
The paper tackled the problem of efficiently sampling from strongly Rayleigh distributions and determinantal point processes by proving that a natural Monte Carlo Markov Chain (MCMC) algorithm is rapidly mixing for homogeneous cases, enabling approximate sample generation and answering an open question in the field.
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.