A Geometric View of Conjugate Priors

Agarwal, Arvind; III, Hal Daumé

doi:10.5591/978-1-57735-516-8/IJCAI11-426

A Geometric View of Conjugate Priors

Arvind Agarwal, Hal Daumé III

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Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence. Pages 2558-2562.

https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-426

Abstract

In Bayesian machine learning, conjugate priors are popular, mostly due to mathematical convenience. In this paper, we show that there are deeper reasons for choosing a conjugate prior. Specically, we formulate the conjugate prior in the form of Bregman divergence and show that it is the inherent geometry of conjugate priors that makes them appropriate and intuitive. This geometric interpretation allows one to view the hyperparameters of conjugate priors as the eective sample points, thus providing additional intuition. We use this geometric understanding of conjugate priors to derive the hyperparameters and expression of the prior used to couple the generative and discriminative components of a hybrid model for semi-supervised learning.

Arvind Agarwal, and Hal Daumé III. 2011. A Geometric View of Conjugate Priors. In Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI-11. IJCAI, 2558–2562. https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-426

@inproceedings{ijcai2011p426,
  title     = {A Geometric View of Conjugate Priors},
  author    = {Agarwal, Arvind and III, Hal Daumé},
  booktitle = {Proceedings of the Twenty-Second International Joint Conference on
               Artificial Intelligence, {IJCAI-11}},
  publisher = {AAAI Press/International Joint Conferences on Artificial Intelligence},
  editor    = {Toby Walsh},
  pages     = {2558--2562},
  year      = {2011},
  month     = {7},
  doi       = {10.5591/978-1-57735-516-8/IJCAI11-426},
  url       = {https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-426},
}

TY  - CPAPER
TI  - A Geometric View of Conjugate Priors
AU  - Agarwal, Arvind
AU  - III, Hal Daumé
T2  - Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI-11
PB  - AAAI Press/International Joint Conferences on Artificial Intelligence
PY  - 2011
SP  - 2558
EP  - 2562
DO  - 10.5591/978-1-57735-516-8/IJCAI11-426
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