| 1. |
- Dang, Khue-Dung, et al.
(author)
-
Hamiltonian Monte Carlo with Energy Conserving Subsampling
- 2019
-
In: Journal of machine learning research. - : MIT Press. - 1532-4435 .- 1533-7928. ; 20, s. 1-31
-
Journal article (peer-reviewed)abstract
- Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC computationally costly, especially in problems with large data sets, since it is necessary to compute posterior densities and their derivatives with respect to the parameters. Naively computing the Hamiltonian dynamics on a subset of the data causes HMC to lose its key ability to generate distant parameter proposals with high acceptance probability. The key insight in our article is that efficient subsampling HMC for the parameters is possible if both the dynamics and the acceptance probability are computed from the same data subsample in each complete HMC iteration. We show that this is possible to do in a principled way in a HMC-within-Gibbs framework where the subsample is updated using a pseudo marginal MH step and the parameters are then updated using an HMC step, based on the current subsample. We show that our subsampling methods are fast and compare favorably to two popular sampling algorithms that use gradient estimates from data subsampling. We also explore the current limitations of subsampling HMC algorithms by varying the quality of the variance reducing control variates used in the estimators of the posterior density and its gradients.
|
|
| 2. |
- Quiroz, Matias, et al.
(author)
-
The Block-Poisson Estimator for Optimally Tuned Exact Subsampling MCMC
- 2021
-
In: Journal of Computational And Graphical Statistics. - : Informa UK Limited. - 1061-8600 .- 1537-2715. ; 30:4, s. 877-888
-
Journal article (peer-reviewed)abstract
- Speeding up Markov chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators, allowing us to update a single block of subsample indicators in each MCMC iteration so that a desired correlation is achieved between the logs of successive likelihood estimates. This is important since pseudo-marginal MCMC with positively correlated likelihood estimates can use substantially smaller subsamples without adversely affecting the sampling efficiency. The block-Poisson estimator is unbiased but not necessarily positive, so the algorithm runs the MCMC on the absolute value of the likelihood estimator and uses an importance sampling correction to obtain consistent estimates of the posterior mean of any function of the parameters. Our article derives guidelines to select the optimal tuning parameters for our method and shows that it compares very favorably to regular MCMC without subsampling, and to two other recently proposed exact subsampling approaches in the literature. Supplementary materials for this article are available online.
|
|
