Asymptotically Exact, Embarrassingly Parallel MCMC

Communication costs, resulting from synchronization requirements during learning, can greatly slow down many parallel machine learning algorithms. In this paper, we present a parallel Markov chain Monte Carlo (MCMC) algorithm in which subsets of data are processed independently, with very little communication. First, we arbitrarily partition data onto multiple machines. Then, on each machine, any classical MCMC method (e.g., Gibbs sampling) may be used to draw samples from a posterior distribution given the data subset. Finally, the samples from each machine are combined to form samples from the full posterior. This embarrassingly parallel algorithm allows each machine to act independently on a subset of the data (without communication) until the final combination stage. We prove that our algorithm generates asymptotically exact samples and empirically demonstrate its ability to parallelize burn-in and sampling in several models

Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an observed response, a Gaussian process model can easily be implemented using matrix computations that are feasible for datasets of up to about a thousand cases. Hyperparameters that define the covariance function of the Gaussian process can be sampled using Markov chain methods. Regression models where the noise has a t distribution and logistic or probit models for classification applications can be implemented by sampling as well for latent values underlying the observations. Software is now available that implements these methods using covariance functions with hierarchical parameterizations. Models defined in this way can discover high-level properties of the data, such as which inputs are relevant to predicting the response