On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approach
This work addresses computational bottlenecks in Gaussian process models for machine learning and statistics, offering a scalable and flexible inference method, though it is incremental as it builds on prior variational sparse GP approaches.
The paper tackles the problem of intractable likelihood evaluations in variationally sparse Gaussian processes combined with MCMC by proposing a pseudo-marginal scheme, achieving asymptotically exact inference and computational gains, as demonstrated on a two-level GP regression model with non-stationary covariance.
Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden, approximation of the posterior, choice of the covariance function and inference of its hyperparmeters. To address these issues, Hensman et al. (2015) combine variationally sparse GPs with Markov chain Monte Carlo (MCMC) to derive a scalable, flexible and general framework for GP models. Nevertheless, the resulting approach requires intractable likelihood evaluations for many observation models. To bypass this problem, we propose a pseudo-marginal (PM) scheme that offers asymptotically exact inference as well as computational gains through doubly stochastic estimators for the intractable likelihood and large datasets. In complex models, the advantages of the PM scheme are particularly evident, and we demonstrate this on a two-level GP regression model with a nonparametric covariance function to capture non-stationarity.