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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Bibliographic Details
Published in:Theoretical computer science Vol. 558; pp. 159 - 178
Main Authors: Warmuth, Manfred K., Kotłowski, Wojciech, Zhou, Shuisheng
Format: Journal Article
Language:English
Published: Elsevier B.V 13.11.2014
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2014.09.031