Stochastic Variance-Reduced Hamilton Monte Carlo Methods
This addresses the computational bottleneck of sampling in machine learning and statistics, offering improved efficiency for tasks like Bayesian inference, but it is incremental as it builds on existing HMC and stochastic optimization techniques.
The paper tackles the problem of sampling from smooth and strongly log-concave distributions by proposing a fast stochastic Hamilton Monte Carlo method with variance reduction, achieving a gradient complexity of $ ilde O(n+κ^{2}d^{1/2}/ε+κ^{4/3}d^{1/3}n^{2/3}/ε^{2/3})$ for $ε$ accuracy in 2-Wasserstein distance, which outperforms state-of-the-art methods in many cases.
We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution. At the core of our proposed method is a variance reduction technique inspired by the recent advance in stochastic optimization. We show that, to achieve $ε$ accuracy in 2-Wasserstein distance, our algorithm achieves $\tilde O(n+κ^{2}d^{1/2}/ε+κ^{4/3}d^{1/3}n^{2/3}/ε^{2/3})$ gradient complexity (i.e., number of component gradient evaluations), which outperforms the state-of-the-art HMC and stochastic gradient HMC methods in a wide regime. We also extend our algorithm for sampling from smooth and general log-concave distributions, and prove the corresponding gradient complexity as well. Experiments on both synthetic and real data demonstrate the superior performance of our algorithm.