Hirt, M;
Titsias, M;
Dellaportas, P;
(2021)
Gradient-based adaptive HMC.
In:
Advances in Neural Information Processing Systems 35 (NeurIPS 2021).
NeurIPS: Online.
(In press).
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Abstract
Hamiltonian Monte Carlo (HMC) is a popular Markov Chain Monte Carlo (MCMC) algorithm to sample from an unnormalized probability distribution. A leapfrog integrator is commonly used to implement HMC in practice, but its performance can be sensitive to the choice of mass matrix used therein. We develop a gradient-based algorithm that allows for the adaptation of the mass matrix by encouraging the leapfrog integrator to have high acceptance rates while also exploring all dimensions jointly. In contrast to previous work that adapt the hyperparameters of HMC using some form of expected squared jumping distance, the adaptation strategy suggested here aims to increase sampling efficiency by maximizing an approximation of the proposal entropy. We illustrate that using multiple gradients in the HMC proposal can be beneficial compared to a single gradientstep in Metropolis-adjusted Langevin proposals. Empirical evidence suggests that the adaptation method can outperform different versions of HMC schemes by adjusting the mass matrix to the geometry of the target distribution and by providing some control on the integration time.
| Type: | Proceedings paper |
|---|---|
| Title: | Gradient-based adaptive HMC |
| Event: | NeurIPS 2021 Thirty-fifth Conference on Neural Information Processing Systems |
| Dates: | 07 December 2021 - 10 December 2021 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://proceedings.neurips.cc/ |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10137053 |
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