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  Probabilistic Solutions to Differential Equations and their Application to Riemannian Statistics

Hennig, P., & Hauberg, S. (2014). Probabilistic Solutions to Differential Equations and their Application to Riemannian Statistics. In S. Kaski, & J. Corander (Eds.), Proceedings of the 17th International Conference on Artificial Intelligence and Statistics (AISTATS) (pp. 347-355). Retrieved from http://jmlr.org/proceedings/papers/v33/hennig14.pdf.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0024-C5D0-4 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0024-E1EA-A
Genre: Conference Paper

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 Creators:
Hennig, P1, Author           
Hauberg, Soren2, Author           
Affiliations:
1Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society, ou_1497647              
2Dept. Perceiving Systems, Max Planck Institute for Intelligent Systems, Max Planck Society, ou_1497642              

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Free keywords: Abt. Schölkopf; Abt. Black
 Abstract: We study a probabilistic numerical method for the solution of both\u000A boundary and initial value problems that returns a joint Gaussian\u000A process posterior over the solution. Such methods have concrete value\u000A in the statistics on Riemannian manifolds, where non‐analytic ordinary\u000A differential equations are involved in virtually all computations. The\u000A probabilistic formulation permits marginalising the uncertainty of the\u000A numerical solution such that statistics are less sensitive to\u000A inaccuracies. This leads to new Riemannian algorithms for mean value\u000A computations and principal geodesic analysis. Marginalisation also\u000A means results can be less precise than point estimates, enabling a\u000A noticeable speed‐up over the state of the art. Our approach is an\u000A argument for a wider point that uncertainty caused by numerical\u000A calculations should be tracked throughout the pipeline of machine\u000A learning algorithms.

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Language(s): eng - English
 Dates: 2014-04
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: hennig:aistats:2014
URI: http://jmlr.org/proceedings/papers/v33/hennig14.pdf
 Degree: -

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Title: Seventeenth International Conference on Artificial Intelligence and Statistics
Place of Event: Reykjavik, Iceland
Start-/End Date: 2014-04-22 - 2014-04-25

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Title: Proceedings of the 17th International Conference on Artificial Intelligence and Statistics (AISTATS)
Source Genre: Proceedings
 Creator(s):
Kaski, Samuel, Editor
Corander, Jukka, Editor
Affiliations:
-
Publ. Info: -
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 347 - 355 Identifier: -

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Title: JMLR: Workshop and Conference Proceedings
Source Genre: Series
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Publ. Info: Brookline, MA : Microtome Publishing
Pages: - Volume / Issue: 33 Sequence Number: - Start / End Page: - Identifier: ISSN: 1938-7228