Variational MCMC
This addresses the issue of efficient Bayesian parameter estimation for models like logistic belief networks, offering incremental improvements in accuracy and convergence speed.
The paper tackles the problem of poor performance in naive algorithms combining variational approximation and MCMC by proposing a new algorithm that mixes a random walk Metropolis kernel and a block Metropolis-Hastings kernel with variational approximation, resulting in slightly better mean estimates and considerably better higher moment estimates like covariances, while speeding up convergence compared to standard MCMC.
We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly because this approximation tends to underestimate the true variance and other features of the data. We solve this problem by introducing more sophisticated MCMC algorithms. One of these algorithms is a mixture of two MCMC kernels: a random walk Metropolis kernel and a blockMetropolis-Hastings (MH) kernel with a variational approximation as proposaldistribution. The MH kernel allows one to locate regions of high probability efficiently. The Metropolis kernel allows us to explore the vicinity of these regions. This algorithm outperforms variationalapproximations because it yields slightly better estimates of the mean and considerably better estimates of higher moments, such as covariances. It also outperforms standard MCMC algorithms because it locates theregions of high probability quickly, thus speeding up convergence. We demonstrate this algorithm on the problem of Bayesian parameter estimation for logistic (sigmoid) belief networks.