Posterior distributions are computable from predictive distributions

Cameron Freer, Daniel Roy
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:233-240, 2010.

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 this Paper

BibTeX
@InProceedings{pmlr-v9-freer10a, 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}, pages = {233--240}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/freer10a/freer10a.pdf}, url = {https://proceedings.mlr.press/v9/freer10a.html}, 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.} }
Endnote
%0 Conference Paper %T Posterior distributions are computable from predictive distributions %A Cameron Freer %A Daniel Roy %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-freer10a %I PMLR %P 233--240 %U https://proceedings.mlr.press/v9/freer10a.html %V 9 %X 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.
RIS
TY - CPAPER TI - Posterior distributions are computable from predictive distributions AU - Cameron Freer AU - Daniel Roy BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-freer10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 233 EP - 240 L1 - http://proceedings.mlr.press/v9/freer10a/freer10a.pdf UR - https://proceedings.mlr.press/v9/freer10a.html AB - 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. ER -
APA
Freer, C. & Roy, D.. (2010). Posterior distributions are computable from predictive distributions. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:233-240 Available from https://proceedings.mlr.press/v9/freer10a.html.

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