Predictive Adaptation of Hybrid Monte Carlo with Bayesian Parametric Bandits

This paper introduces a novel way of adapting the Hybrid Monte Carlo (HMC) algorithm using parametric bandits with nonlinear features. HMC is a powerful Markov chain Monte Carlo (MCMC) method, but it requires careful tuning of its hyper-parameters. We propose a Bayesian parametric bandit approach to carry out the adaptation of the hyper-parameters while the Markov chain progresses. We also introduce the use of cross-validation error measures for adaptation, which we believe are more pragmatic than many existing adaptation objectives. The new measures take the intended statistical use of the model, whose parameters are estimated by HMC, into consideration. We apply these two innovations to the adaptation of HMC for prediction and feature selection with multi-layer feedforward neural networks. The experiments with synthetic and real data show that the proposed adaptive scheme is not only automatic, but also does better tuning than human experts.