The Recycling Gibbs Sampler for Efficient Learning
This work addresses a bottleneck in MCMC methods for researchers in signal processing, machine learning, and statistics, offering an incremental improvement to existing Gibbs sampling techniques.
The paper tackles the inefficiency of Gibbs sampling in Bayesian inference by proposing a method to recycle auxiliary samples, improving estimator efficiency without extra computational cost. Numerical simulations show enhanced accuracy and computational efficiency in tasks like Gaussian process hyperparameter inference and learning dependence graphs.
Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from complicated high-dimensional posterior distributions. The key point for the successful application of the Gibbs sampler is the ability to draw efficiently samples from the full-conditional probability density functions. Since in the general case this is not possible, in order to speed up the convergence of the chain, it is required to generate auxiliary samples whose information is eventually disregarded. In this work, we show that these auxiliary samples can be recycled within the Gibbs estimators, improving their efficiency with no extra cost. This novel scheme arises naturally after pointing out the relationship between the standard Gibbs sampler and the chain rule used for sampling purposes. Numerical simulations involving simple and real inference problems confirm the excellent performance of the proposed scheme in terms of accuracy and computational efficiency. In particular we give empirical evidence of performance in a toy example, inference of Gaussian processes hyperparameters, and learning dependence graphs through regression.