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Statistics > Machine Learning

arXiv:2302.00242 (stat)
[Submitted on 1 Feb 2023]

Title:The Parametric Stability of Well-separated Spherical Gaussian Mixtures

Authors:Hanyu Zhang, Marina Meila
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Abstract:We quantify the parameter stability of a spherical Gaussian Mixture Model (sGMM) under small perturbations in distribution space. Namely, we derive the first explicit bound to show that for a mixture of spherical Gaussian $P$ (sGMM) in a pre-defined model class, all other sGMM close to $P$ in this model class in total variation distance has a small parameter distance to $P$. Further, this upper bound only depends on $P$. The motivation for this work lies in providing guarantees for fitting Gaussian mixtures; with this aim in mind, all the constants involved are well defined and distribution free conditions for fitting mixtures of spherical Gaussians. Our results tighten considerably the existing computable bounds, and asymptotically match the known sharp thresholds for this problem.
Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG)
Cite as: arXiv:2302.00242 [stat.ML]
  (or arXiv:2302.00242v1 [stat.ML] for this version)
  https://doi.org/10.48550/arXiv.2302.00242

Submission history

From: Hanyu Zhang [view email]
[v1] Wed, 1 Feb 2023 04:52:13 UTC (2,126 KB)
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