Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributions
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We obtain several quantitative bounds on the mixing properties of the Hamiltonian Monte Carlo (HMC) algorithm for a strongly log-concave target distribution π on R^d, showing that HMC mixes quickly in this setting. One of our main results is a dimension-free bound on the mixing of an "ideal" HMC chain, which is used to show that the usual leapfrog implementation of HMC can sample from π using only O(d^1/4) gradient evaluations. This dependence on dimension is sharp, and our results significantly extend and improve previous quantitative bounds on the mixing of HMC.
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