Activity Number:
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373
- Recent Advances in Complex and High-Dimensional Data
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Type:
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Topic Contributed
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Date/Time:
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Wednesday, August 10, 2022 : 8:30 AM to 10:20 AM
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Sponsor:
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IMS
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Abstract #322739
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Title:
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Leave-One-Out Singular Subspace Perturbation Analysis for Spectral Clustering
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Author(s):
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Harrison Zhou*
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Companies:
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Yale University
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Keywords:
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Spectral method;
clustering;
Leave-one-out;
minimax estimation;
Gaussian mixtures
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Abstract:
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The singular subspaces perturbation theory is of fundamental importance in probability and statistics. It has various applications across different fields. We consider two arbitrary matrices where one is a leave-one-column-out submatrix of the other one and establish a novel perturbation upper bound for the distance between two corresponding singular subspaces. It is well-suited for mixture models and results in a sharper and finer statistical analysis than classical perturbation bounds such as Wedin’sTheorem. Powered by this leave-one-out perturbation theory, we provide a deterministic entrywise analysis for the performance of the spectral clustering under mixture models. Our analysis leads to an explicit exponential error rate for the clustering of sub-Gaussian mixture models. For the mixture of isotropic Gaussians, the rate is optimal under a weaker signal-to-noise condition than that of Löffler et al. (2021).
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Authors who are presenting talks have a * after their name.
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