Spectral Analysis of Symmetric and Anti-Symmetric Pairwise Kernels

We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or anti-symmetrizing pairwise kernel functions. Through spectral ana...

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Bibliographic Details
Published in:arXiv.org 2015-06
Main Authors: Pahikkala, Tapio, Viljanen, Markus, Airola, Antti, Waegeman, Willem
Format: Article
Language:English
Subjects:
Bias
Kernel functions
Regression analysis
Regularization
Online Access:Get full text
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Summary:We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or anti-symmetrizing pairwise kernel functions. Through spectral analysis, we show that these transformations reduce the kernel's effective dimension. Further, we provide an analysis of the approximation properties of the resulting kernels, and bound the regularization bias of the kernels in terms of the corresponding bias of the original kernel.
ISSN:2331-8422