Stochastic Approximation Hamiltonian Monte Carlo
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Recently, the Hamilton Monte Carlo (HMC) has become widespread as one of the more reliable approaches to efficient sample generation processes. However, HMC is difficult to sample in a multimodal posterior distribution because the HMC chain cannot cross energy barrier between modes due to the energy conservation property. In this paper, we propose a Stochastic Approximate Hamilton Monte Carlo (SAHMC) algorithm for generating samples from multimodal density under the HMC framework. SAHMC can adaptively lower the energy barrier to move the Hamiltonian trajectory more frequently and more easily between modes. The convergence of the algorithm is established under mild conditions. Gaussian mixture model and neural network model show that SAHMC is superior to HMC when target posterior density has multiple modes.
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