2013/01/10 by Nando de Freitas, de Freitas, Nando, Pedro Højen-Sørensen +5
Computer Science · #Bayesian Methods and Mixture Models #Computation (stat.CO) #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms
paper · pdf · doi:10.48550/arxiv.1301.2266
openalex publication_date 2013/01/10 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
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.