On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approach

• DOI: 10.48550/arxiv.2103.03321
• Publication Date: 2021-01-01
• Authors: Karla Monterrubio...; Sara Wade
• Keywords: Marginal likelihood

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