Subsampling in Smoothed Range Spaces

  • Jeff M. Phillips
  • Yan Zheng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9355)


We consider smoothed versions of geometric range spaces, so an element of the ground set (e.g. a point) can be contained in a range with a non-binary value in [0, 1]. Similar notions have been considered for kernels; we extend them to more general types of ranges. We then consider approximations of these range spaces through \(\varepsilon \)-nets and \(\varepsilon \)-samples (aka \(\varepsilon \)-approximations). We characterize when size bounds for \(\varepsilon \)-samples on kernels can be extended to these more general smoothed range spaces. We also describe new generalizations for \(\varepsilon \)-nets to these range spaces and show when results from binary range spaces can carry over to these smoothed ones.


Kernel Density Estimate Generalization Error Range Space Polynomial Surface Ball Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of UtahSalt Lake CityUSA

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