Posterior Distributions Are Computable from Predictive Distributions
Abstract
As we devise more complicated prior distributions, will inference algorithms keep up? We highlight a negative result in computable probability theory by Ackerman, Freer, and Roy (2010) that shows that there exist computable priors with noncomputable posteriors. In addition to providing a brief survey of computable probability theory geared towards the A.I. and statistics community, we give a new result characterizing when conditioning is computable in the setting of exchangeable sequences, and provide a computational perspective on work by Orbanz (2010) on conjugate nonparametric models. In particular, using a computable extension of de Finetti’s theorem (Freer and Roy 2009), we describe how to transform a posterior predictive rule for generating an exchangeable sequence into an algorithm for computing the posterior distribution of the directing random measure.
Cite
Text
Freer and Roy. "Posterior Distributions Are Computable from Predictive Distributions." Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 2010.Markdown
[Freer and Roy. "Posterior Distributions Are Computable from Predictive Distributions." Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 2010.](https://mlanthology.org/aistats/2010/freer2010aistats-posterior/)BibTeX
@inproceedings{freer2010aistats-posterior,
title = {{Posterior Distributions Are Computable from Predictive Distributions}},
author = {Freer, Cameron and Roy, Daniel},
booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics},
year = {2010},
pages = {233-240},
volume = {9},
url = {https://mlanthology.org/aistats/2010/freer2010aistats-posterior/}
}