Moment-based Uniform Deviation Bounds for k-means and Friends

Suppose $k$ centers are fit to $m$ points by heuristically minimizing the $k$-means cost; what is the corresponding fit over the source distribution? This question is resolved here for distributions with $p\geq 4$ bounded moments; in particular, the difference between the sample cost and distribution cost decays with $m$ and $p$ as $m^{\min\{-1/4, -1/2+2/p\}}$... (read more)

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