The Parametric Stability of Well-separated Spherical Gaussian Mixtures
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Abstract (arXiv)
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.
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References · 7
- 2016Statistical Query Lower Bounds for Robust Estimation of High-dimensional Gaussians and Gaussian Mixturescited by 114
- 2016Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequencescited by 34
- 2020Settling the Robust Learnability of Mixtures of Gaussianscited by 32
- 2017On Learning Mixtures of Well-Separated Gaussianscited by 30
- 2013A Bayesian information criterion for singular modelscited by 22
- 2013The More, the Merrier: the Blessing of Dimensionality for Learning Large Gaussian Mixturescited by 18
- 2013Model Selection for Gaussian Mixture Modelscited by 6
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