Gaussian Processes to speed up MCMC with automatic exploratory-exploitation effect
This method addresses computational bottlenecks in inference for Probabilistic Programming Languages, though it appears incremental as it builds on existing GP-based MCMC approaches.
The paper tackles the problem of sampling from probabilistic models with expensive log-likelihood evaluations by introducing a two-stage Metropolis-Hastings algorithm that uses a surrogate Gaussian Process (GP) model, achieving automatic learning without pre-training and extending it to MALA.
We present a two-stage Metropolis-Hastings algorithm for sampling probabilistic models, whose log-likelihood is computationally expensive to evaluate, by using a surrogate Gaussian Process (GP) model. The key feature of the approach, and the difference w.r.t. previous works, is the ability to learn the target distribution from scratch (while sampling), and so without the need of pre-training the GP. This is fundamental for automatic and inference in Probabilistic Programming Languages In particular, we present an alternative first stage acceptance scheme by marginalising out the GP distributed function, which makes the acceptance ratio explicitly dependent on the variance of the GP. This approach is extended to Metropolis-Adjusted Langevin algorithm (MALA).