Research map / Learning theory and algorithms / Sample complexity
Benefits of over-parameterization with EM
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Estimate mixture weights along with component means instead of fixing known weights | EM on two-Gaussian mixtures · Separation 2, n=1000, w1*=0.52 | success probability: 0.799 -> 0.500 | Hurt |
| Estimate mixture weights along with component means instead of fixing known weights | EM on two-Gaussian mixtures · Separation 2, n=1000, w1*=0.7 | success probability: 0.497 -> 0.800 | Helped |
| Estimate mixture weights along with component means instead of fixing known weights | EM on two-Gaussian mixtures · Separation 2, n=1000, w1*=0.9 | success probability: 0.499 -> 0.899 | Helped |
| Estimate mixture weights along with component means instead of fixing known weights | Population EM on two-Gaussian mixtures · Separation 2, n=∞, w1*=0.52 | success probability: 0.504 -> 1.000 | Helped |
| Estimate mixture weights along with component means instead of fixing known weights | Population EM on two-Gaussian mixtures · Separation 2, n=∞, w1*=0.7 | success probability: 0.514 -> 1.000 | Helped |
| Estimate mixture weights along with component means instead of fixing known weights | Population EM on two-Gaussian mixtures · Separation 2, n=∞, w1*=0.9 | success probability: 0.506 -> 1.000 | Helped |
| Estimate mixture weights along with component means instead of fixing known weights | EM on three-Gaussian mixtures · Three components on a line, n=2000 | success probability: 0.164 -> 0.900 | Helped |
| Estimate mixture weights along with component means instead of fixing known weights | EM on three-Gaussian mixtures · Three components on a triangle, n=2000 | success probability: 0.167 -> 1.000 | Helped |
| Estimate mixture weights along with component means instead of fixing known weights | EM on four-Gaussian mixtures · Four components on a line, n=2000 | success probability: 0.145 -> 0.956 | Helped |
| Estimate mixture weights along with component means instead of fixing known weights | EM on four-Gaussian mixtures · Four components on a trapezoid, n=2000 | success probability: 0.159 -> 0.861 | Helped |
| Estimate mixture weights rather than fixing them to known values | Population EM for symmetric two-Gaussian mixtures · Any w1* in [0.5,1), except initial means on the hyperplane orthogonal to the true mean | convergence to a global maximizer | Helped |
| Estimate mixture weights rather than fixing them to known values | Population EM for symmetric two-Gaussian mixtures · Unequal mixture weights and initial mean at or below -θ* | convergence to a wrong fixed point | Helped |
Closest papers by meaning
- Global Analysis of Expectation Maximization for Mixtures of Two Gaussians (NeurIPS 2016 · similarity 0.91)
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- Is $\sqrt{d}$ Separation Necessary for Gradient EM to Learn Gaussian Mixtures in High Dimensions? (NeurIPS 2026 · similarity 0.85)
- Unveiling the Cycloid Trajectory of EM Iterations in Mixed Linear Regression (ICML 2024 · similarity 0.84)
- Minimax Optimal Early-Stopped Gradient Descent for Gaussian Mixture Classification (NeurIPS 2026 · similarity 0.83)
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