dorsal/arxiv
View SchemaAnnealed Importance Sampling
| Authors | Radford M. Neal |
|---|---|
| Categories | |
| ArXiv ID | physics/9803008 |
| URL | https://arxiv.org/abs/physics/9803008 |
Abstract
Simulated annealing - moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions - has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers. Here, it is shown how one can use the Markov chain transitions for such an annealing sequence to define an importance sampler. The Markov chain aspect allows this method to perform acceptably even for high-dimensional problems, where finding good importance sampling distributions would otherwise be very difficult, while the use of importance weights ensures that the estimates found converge to the correct values as the number of annealing runs increases. This annealed importance sampling procedure resembles the second half of the previously-studied tempered transitions, and can be seen as a generalization of a recently-proposed variant of sequential importance sampling. It is also related to thermodynamic integration methods for estimating ratios of normalizing constants. Annealed importance sampling is most attractive when isolated modes are present, or when estimates of normalizing constants are required, but it may also be more generally useful, since its independent sampling allows one to bypass some of the problems of assessing convergence and autocorrelation in Markov chain samplers.
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"abstract": "Simulated annealing - moving from a tractable distribution to a distribution\nof interest via a sequence of intermediate distributions - has traditionally\nbeen used as an inexact method of handling isolated modes in Markov chain\nsamplers. Here, it is shown how one can use the Markov chain transitions for\nsuch an annealing sequence to define an importance sampler. The Markov chain\naspect allows this method to perform acceptably even for high-dimensional\nproblems, where finding good importance sampling distributions would otherwise\nbe very difficult, while the use of importance weights ensures that the\nestimates found converge to the correct values as the number of annealing runs\nincreases. This annealed importance sampling procedure resembles the second\nhalf of the previously-studied tempered transitions, and can be seen as a\ngeneralization of a recently-proposed variant of sequential importance\nsampling. It is also related to thermodynamic integration methods for\nestimating ratios of normalizing constants. Annealed importance sampling is\nmost attractive when isolated modes are present, or when estimates of\nnormalizing constants are required, but it may also be more generally useful,\nsince its independent sampling allows one to bypass some of the problems of\nassessing convergence and autocorrelation in Markov chain samplers.",
"arxiv_id": "physics/9803008",
"authors": [
"Radford M. Neal"
],
"categories": [
"physics.comp-ph",
"physics.data-an"
],
"title": "Annealed Importance Sampling",
"url": "https://arxiv.org/abs/physics/9803008"
},
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