A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a 
Noisy Function

Ortega, PA; Grau-Moya, J; Genewein, T; Balduzzi, D; Braun, DA

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A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function

Ortega, P., Grau-Moya, J., Genewein, T., Balduzzi, D., & Braun, D. (2013). A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function. In P. Bartlett (Ed.), Advances in Neural Information Processing Systems 25 (pp. 3014-3022). Red Hook, NY, USA: Curran.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-B548-F Version Permalink: https://hdl.handle.net/21.11116/0000-0004-C38F-F

Genre: Conference Paper

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https://papers.nips.cc/paper/4536-a-nonparametric-conjugate-prior-distribution-for-the-maximizing-argument-of-a-noisy-function.pdf (Publisher version) Open Access status unknown

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Creators:
Ortega, PA^{1, 2}, Author
Grau-Moya, J^{1, 2}, Author
Genewein, T^{1, 2}, Author
Balduzzi, D³, Author
Braun, DA^{1, 2}, Author

Affiliations:
1Research Group Sensorimotor Learning and Decision-Making, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497809
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794
3Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society, DE, ou_1497647

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Abstract: We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the distribution over extrema. To this end, we devise a non-parametric conjugate prior where the natural parameter corresponds to a given kernel function and the sufficient statistic is composed of the observed function values. The resulting posterior distribution directly captures the uncertainty over the maximum of the unknown function.

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Dates: Date issued: 2013-04

Publication Status: Issued

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Identifiers: URI: http://nips.cc/Conferences/2012/
BibTex Citekey: OrtegaGGBB2012

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Title: Twenty-Sixth Annual Conference on Neural Information Processing Systems (NIPS 2012)

Place of Event: Lake Tahoe, NV, USA

Start-/End Date: 2012-12-03 - 2012-12-06

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Title: Advances in Neural Information Processing Systems 25

Source Genre: Proceedings

Creator(s):
Bartlett, P, Editor
Pereira, FCN, Author
Bottou, L, Author
Burges, CJC, Author
Weinberger, KQ, Author

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Publ. Info: Red Hook, NY, USA : Curran

Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 3014 - 3022 Identifier: ISBN: 978-1-62748-003-1