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Subsampling in Smoothed Range Spaces

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Algorithmic Learning Theory (ALT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9355))

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Abstract

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.

Thanks to supported by NSF CCF-1350888, IIS-1251019, and ACI-1443046.

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Authors and Affiliations

  1. University of Utah, Salt Lake City, UT, USA

    Jeff M. Phillips & Yan Zheng

Authors
  1. Jeff M. Phillips
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  2. Yan Zheng
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Corresponding author

Correspondence to Yan Zheng .

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Editors and Affiliations

  1. University of California, La Jolla, California, USA

    Kamalika Chaudhuri

  2. UNIV DEL INSUBRIA, 21100 VARESE, Italy

    CLAUDIO GENTILE

  3. REGINA, Saskatchewan, Canada

    Sandra Zilles

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Phillips, J.M., Zheng, Y. (2015). Subsampling in Smoothed Range Spaces. In: Chaudhuri, K., GENTILE, C., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2015. Lecture Notes in Computer Science(), vol 9355. Springer, Cham. https://doi.org/10.1007/978-3-319-24486-0_15

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  • DOI: https://doi.org/10.1007/978-3-319-24486-0_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24485-3

  • Online ISBN: 978-3-319-24486-0

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