Variance misspecification in Gaussian mixtures creates a phase diagram: correct specification recovers true means independent of SNR, under-smoothing biases means with SNR^{-1} error in low SNR, and over-smoothing collapses clusters above an SNR-dependent threshold.
Small-variance asymptotics for exponential family Dirichlet process mixture models.Advances in Neural Information Processing Systems, 25
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The interplay of signal-to-noise ratio and variance misspecification in Gaussian mixtures
Variance misspecification in Gaussian mixtures creates a phase diagram: correct specification recovers true means independent of SNR, under-smoothing biases means with SNR^{-1} error in low SNR, and over-smoothing collapses clusters above an SNR-dependent threshold.