Research map / Learning theory and algorithms / Sample complexity
Are Gaussian Data All You Need? The Extents and Limits of Universality in High-Dimensional Generalized Linear Estimation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a homoscedastic mixture rather than a single Gaussian with matching covariance | Generalized linear estimation with a teacher uncorrelated with the cluster means · Homoscedastic GMM | training error: ε_tr^GMM({μ_c}_{c=1}^K,Σ) ≃ ε_tr^GCM(θ₀,Σ,0) | No clear effect |
| Use a homoscedastic mixture rather than a single Gaussian with matching covariance | Generalized linear estimation with a teacher uncorrelated with the cluster means · Homoscedastic GMM | generalization error: ε_gen^GMM({μ_c}_{c=1}^K,Σ) ≃ ε_gen^GCM(θ₀,Σ,0) | No clear effect |
| Set regularization to zero for square-loss estimation | GMM estimation with a noisy linear teacher · Underparametrized GMM | training error: ε_tr^GMM({μ_c}_{c=1}^K,{Σ_c}_{c=1}^K) ≃ ((α -1) Δ )/α | No clear effect |
| Correlate the target weights with the cluster means | Ridge and logistic regression · Two-cluster homoscedastic GMM with finite regularization | training error | Mixed |
| Correlate the target weights with the cluster means | Ridge and logistic regression · Two-cluster homoscedastic GMM with finite regularization | generalization error | Mixed |
| Take vanishing regularization in the underparametrized regime | Ridge regression with any teacher vector · Two-cluster GMM with isotropic covariance | generalization error: ε_gen^GMM = Δ α/(α - 1) | No clear effect |
| Take vanishing regularization in the underparametrized regime | Ridge regression with any teacher vector · Two-cluster GMM with isotropic covariance | training error: ε_tr^GMM = Δ((α - 1))/α | No clear effect |
| Use non-homogenizing transforms or no transform on real data | Ridge regression with a random teacher · Grayscale CIFAR-10 | generalization error | Mixed |
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