Subsampling in Smoothed Range Spaces

30 Oct 2015  ·  Jeff M. Phillips, Yan Zheng ·

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.

PDF Abstract
No code implementations yet. Submit your code now



  Add Datasets introduced or used in this paper

Results from the Paper

  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.


No methods listed for this paper. Add relevant methods here