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  Painless Embeddings of Distributions: the Function Space View

Smola, A., Gretton, A., & Fukumizu, K. (2008). Painless Embeddings of Distributions: the Function Space View. Talk presented at 25th International Conference on Machine Learning (ICML 2008). Helsinki, Finland. 2008-07-05 - 2008-07-09.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-C8A9-9 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-A7C2-5
Genre: Talk

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 Creators:
Smola, A, Author              
Gretton, A1, 2, Author              
Fukumizu, K, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: This tutorial will give an introduction to the recent understanding and methodology of the kernel method: dealing with higher order statistics by embedding painlessly random variables/probability distributions. In the early days of kernel machines research, the "kernel trick" was considered a useful way of constructing nonlinear algorithms from linear ones. More recently, however, it has become clear that a potentially more far reaching use of kernels is as a linear way of dealing with higher order statistics by embedding distributions in a suitable reproducing kernel Hilbert space (RKHS). Notably, unlike the straightforward expansion of higher order moments or conventional characteristic function approach, the use of kernels or RKHS provides a painless, tractable way of embedding distributions. This line of reasoning leads naturally to the questions: what does it mean to embed a distribution in an RKHS? when is this embedding injective (and thus, when do different distributions have unique mappings)? what implications are there for learning algorithms that make use of these embeddings? This tutorial aims at answering these questions. There are a great variety of applications in machine learning and computer science, which require distribution estimation and/or comparison.

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 Dates: 2008-07
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: BibTex Citekey: 5271
 Degree: -

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Title: 25th International Conference on Machine Learning (ICML 2008)
Place of Event: Helsinki, Finland
Start-/End Date: 2008-07-05 - 2008-07-09

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Title: ICML 2008: 25th International Conference on Machine Learning
Source Genre: Proceedings
 Creator(s):
McCallum , A, Editor
Roweis, S, Editor
Affiliations:
-
Publ. Info: Madison, WI, USA : Oregon State University
Pages: - Volume / Issue: - Sequence Number: T1 Start / End Page: XXXVII Identifier: ISBN: 978-1-60558-205-4