Sampling Graphical Networks via Conditional Independence Coupling of Markov Chains

Markov Chain Monte Carlo (MCMC) methods have been used for sampling Online SNs. The main drawbacks are that traditional MCMC techniques such as the Metropolis-Hastings Random Walk (MHRW) suffer from slow mixing rates, and the resulting sample is usually approximate. An appealing solution is to adapt the MHRW sampler to probability coupling techniques for perfect sampling. While this MHRW coupler is theoretically advanced, it is inapplicable for sampling large SNs in practice. We develop a new coupling algorithm, called Conditional Independence Coupler (CIC), which improves existing coupling techniques by adopting a new coalescence condition, called Conditional Independence (CI), for efficient coalescence detection. The proposed CIC algorithm is outstandingly scalable for sampling large SNs without any bias as compared to previous traditional MCMC sampling algorithms.