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Variational Inference with Hamiltonian Monte Carlo
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Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we explore this idea using steps of the Hamiltonian Monte Carlo (HMC) algorithm, an efficient MCMC method. In particular, we incorporate the acceptance step of the HMC algorithm, guaranteeing asymptotic convergence to the true posterior. Additionally, we introduce some extensions to the HMC algorithm geared towards faster convergence. The theoretical advantages of these modifications are reflected by performance improvements in our experimental results.
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Cited by 1 Pith paper
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Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators
A hybrid VI-HMC method runs expensive Hamiltonian Monte Carlo only on the neural network parameters most responsible for predictive uncertainty, cutting sampling cost while approximating full HMC posteriors.
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