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For big data analysis, high computational cost for Bayesian methods oftenlimits their applications in practice. In recent years, there have been manyattempts to improve computational efficiency of Bayesian inference. Here wepropose an efficient and scalable computational technique for astate-of-the-art Markov Chain Monte Carlo (MCMC) methods, namely, HamiltonianMonte Carlo (HMC). The key idea is to explore and exploit the structure andregularity in parameter space for the underlying probabilistic model toconstruct an effective approximation of its geometric properties. To this end,we build a surrogate function to approximate the target distribution usingproperly chosen random bases and an efficient optimization process. Theresulting method provides a flexible, scalable, and efficient samplingalgorithm, which converges to the correct target distribution. We show that bychoosing the basis functions and optimization process differently, our methodcan be related to other approaches for the construction of surrogate functionssuch as generalized additive models or Gaussian process models. Experimentsbased on simulated and real data show that our approach leads to substantiallymore efficient sampling algorithms compared to existing state-of-the artmethods.

Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases