[1912.01937] Quantum-Inspired Hamiltonian Monte Carlo for Bayesian Samplingopen searchopen navigation menucontact arXivsubscribe to arXiv mailings

Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is inefficient to sample from spiky and multimodal distributions. Motivated by the energy-time uncertainty relation from quantum mechanics, we propose a Quantum-Inspired Hamiltonian Monte Carlo algorithm (QHMC). This algorithm allows a particle to have a random mass with a probability distribution rather than a fixed mass. We prove the convergence property of QHMC in the spatial domain and in the time sequence. We further show why such a random mass can improve the performance when we sample a broad class of distributions. In order to handle the big training data sets in large-scale machine learning, we develop a stochastic gradient version of QHMC using Nosé-Hoover thermostat called QSGNHT, and we also provide theoretical justifications about its stead

1 mentions: @_stakaya
Keywords: bayesian
Date: 2020/06/29 02:21

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