Research map / Learning theory and algorithms / Sample complexity
Refined Convergence Rates for Maximum Likelihood Estimation under Finite Mixture Models
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Measure component error with the Voronoi-based loss D rather than only W_2 | MLE for strongly identifiable mixtures · Strongly identifiable mixtures, pointwise | component convergence rate: (\log n/ n)^{1/4} -> \left(\frac{\log n}{n}\right)^{\frac 1 2} | Helped |
| Measure component error with D-bar rather than only the Wasserstein loss | Penalized MLE for location-scale Gaussian mixtures · Location-scale Gaussian mixtures, pointwise | component convergence rate: n^{-1/8}; ... n^{-1/4}; ... \log n/ \sqrt n | Mixed |
| Use W-tilde to distinguish component rates in uniform estimation | Penalized MLE for strongly identifiable mixtures · Strongly identifiable mixtures, uniform | component convergence rate: n^{-\frac{1}{2r}} -> n^{-1/2} | Helped |
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