Abstract
We derive a dimension-free Hanson–Wright inequality for quadratic forms of independent sub-gaussian random variables in a separable Hilbert space. Our inequality is an infinite-dimensional generalization of the classical Hanson–Wright inequality for finite-dimensional Euclidean random vectors. We illustrate an application to the generalized K-means clustering problem for non-Euclidean data. Specifically, we establish the exponential rate of convergence for a semidefinite relaxation of the generalized K-means, which together with a simple rounding algorithm imply the exact recovery of the true clustering structure.
Original language | English (US) |
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Pages (from-to) | 586-614 |
Number of pages | 29 |
Journal | Bernoulli |
Volume | 27 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2021 |
Keywords
- Hanson–Wright inequality
- Hilbert space
- K-means
- Semidefinite relaxation
ASJC Scopus subject areas
- Statistics and Probability