Hanson-Wright inequality in Hilbert spaces with application to \(K\)-means clustering for non-Euclidean data

DOI10.3150/20-BEJ1251zbMath1475.60044arXiv1810.11180WikidataQ114038756 ScholiaQ114038756MaRDI QIDQ2214261

Yun Yang, Xiaohui Chen

Publication date: 7 December 2020

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.11180

zbMATH Keywords

Hilbert space\(K\)-meanssemidefinite relaxationHanson-Wright inequality

Mathematics Subject Classification ID

Gaussian processes (60G15) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Inequalities; stochastic orderings (60E15) Probability theory on linear topological spaces (60B11)

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Cites Work

• Unnamed Item
• A mathematical introduction to compressive sensing
• Transference principles for log-Sobolev and spectral-gap with applications to conservative spin systems
• A tail inequality for quadratic forms of subgaussian random vectors
• Hanson-Wright inequality and sub-Gaussian concentration
• A note on the Hanson-Wright inequality for random vectors with dependencies
• SubGaussian random variables in Hilbert spaces
• Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications
• Clustering functional data
• Adaptive estimation of a quadratic functional by model selection.
• A bound on tail probabilities for quadratic forms in independent random variables whose distributions are not necessarily symmetric
• When do birds of a feather flock together? \(k\)-means, proximity, and conic programming
• Partial recovery bounds for clustering with the relaxed \(K\)-means
• A survey of kernel and spectral methods for clustering
• Nonparametric functional data analysis. Theory and practice.
• Random weighted projections, random quadratic forms and random eigenvectors
• Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh
• High-Dimensional Statistics
• High-Dimensional Probability
• Least squares quantization in PCM
• Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
• Advanced Lectures on Machine Learning
• Approximating K‐means‐type Clustering via Semidefinite Programming
• A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables
• Theory of Reproducing Kernels