Kernelization of matrix updates, when and how?

We define what it means for a learning algorithm to be kernelizable in the case when the instances are vectors, asymmetric matrices and symmetric matrices, respectively. We can characterize kernelizability in terms of an invariance of the algorithm to certain orthogonal transformations. If we assume...

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Vydáno v:Theoretical computer science Ročník 558; s. 159 - 178
Hlavní autoři: Warmuth, Manfred K., Kotłowski, Wojciech, Zhou, Shuisheng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 13.11.2014
Témata:
Algorithms
Asymmetry
Exponentiated Gradient algorithm
Gradient Descent algorithm
Invariance
Kernelization
Learning
Linear prediction
Mathematical analysis
Multiplicative updates
Rotational invariance
Transformations
Vectors (mathematics)
Multiplicative updates
Exponentiated Gradient algorithm
Gradient Descent algorithm
Rotational invariance
Kernelization
ISSN:0304-3975, 1879-2294
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Shrnutí:We define what it means for a learning algorithm to be kernelizable in the case when the instances are vectors, asymmetric matrices and symmetric matrices, respectively. We can characterize kernelizability in terms of an invariance of the algorithm to certain orthogonal transformations. If we assume that the algorithm's action relies on a linear prediction, then we can show that in each case, the linear parameter vector must be a certain linear combination of the instances. We give a number of examples of how to apply our methods. In particular we show how to kernelize multiplicative updates for symmetric instance matrices.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2014.09.031