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State space models (SSM) have been widely applied for the analysis andvisualization of large sequential datasets. Sequential Monte Carlo (SMC) is avery popular particle-based method to sample latent states from intractableposteriors. However, SSM is significantly influenced by the choice of theproposal. Recently Hamiltonian Monte Carlo (HMC) sampling has shown success inmany practical problems. In this paper, we propose an SMC augmented by HMC(HSMC) for inference and model learning of nonlinear SSM, which can exempt usfrom learning proposals and reduce the model complexity significantly. Based onthe measure preserving property of HMC, the particles directly generated bytransition function can approximate the posterior of latent states arbitrarilywell. In order to better adapt to the local geometry of latent space, the HMCis conducted on Riemannian manifold defined by a positive definite metric. Inaddition, we show that the proposed HSMC method can improve SSMs realized byboth Gaussian Processes (GP) and Neural Network (NN).

Learning Nonlinear State Space Models with Hamiltonian Sequential Monte Carlo Sampler