Stochastic gradient annealed importance sampling for efficient online marginal likelihood estimation
Date
2019-11-12
Journal Title
Journal ISSN
Volume Title
Publisher
MDPI
Abstract
We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such settings by using stochastic gradient Markov Chain Monte Carlo techniques. This approach is far more efficient than traditional marginal likelihood estimation techniques such as nested sampling and annealed importance sampling due to its use of mini-batches to approximate the likelihood. Stability of the estimates is provided by an adaptive annealing schedule. The resulting stochastic gradient annealed importance sampling (SGAIS) technique, which is the key contribution of our paper, enables us to estimate the marginal likelihood of a number of models considerably faster than traditional approaches, with no noticeable loss of accuracy. An important benefit of our approach is that the marginal likelihood is calculated in an online fashion as data becomes available, allowing the estimates to be used for applications such as online weighted model combination.
Description
CITATION: Cameron, S. A.; Eggers, H. C. & Kroon, S. 2019. Stochastic gradient annealed importance sampling for efficient online marginal likelihood estimation. Entropy, 21(11). doi:10.3390/e21111109
The original publication is available at https://www.mdpi.com/journal/entropy
The original publication is available at https://www.mdpi.com/journal/entropy
Keywords
Marginal distributions, Estimation theory, Nested sampling, Annealed importance sampling, Monte Carlo method, Simulated annealing (Mathematics), Conjugate gradient methods
Citation
Cameron, S. A.; Eggers, H. C. & Kroon, S. 2019. Stochastic gradient annealed importance sampling for efficient online marginal likelihood estimation. Entropy, 21(11). doi:10.3390/e21111109