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Learning Gaussian Mixtures with Generalized Linear Models: Precise Asymptotics in High-dimensions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use an ℓ1 penalty instead of an ℓ2 penalty | Binary classification with correlated sparse means · Correlated sparse Gaussian mixture, Δ1/Δ2 ≲ 1 | generalisation error | Helped |
| Use an ℓ1 penalty instead of an ℓ2 penalty | Binary classification with correlated sparse means · Correlated sparse Gaussian mixture, Δ1/Δ2 ≳ 1 | generalisation error | No clear effect |
| Use an ℓ1 penalty instead of an ℓ2 penalty | Binary classification with correlated sparse means · Correlated sparse Gaussian mixture, Δ1/Δ2 ≲ 1 | training loss | Hurt |
| Use an ℓ1 penalty instead of an ℓ2 penalty | Binary classification with correlated sparse means · Correlated sparse Gaussian mixture, Δ1/Δ2 ≳ 1 | training loss | Helped |
| Increase the number of clusters | Cross-entropy classification with ridge · K Gaussian clusters | separability threshold α*K | Helped |
| Increase covariance scale Δ | Cross-entropy classification with ridge · K Gaussian clusters | separability threshold α*K | Hurt |
| Increase ridge regularization toward λ → +∞ | Cross-entropy classification with identical covariances and balanced clusters · K Gaussian clusters | generalisation error | Helped |
| Tune ridge regularization to a finite strength | Ridge regression with different cluster covariances · Two balanced Gaussian clusters | generalisation error | Helped |
| Use a Gaussian-mixture surrogate matched to empirical means and covariances | Binary logistic classification · MNIST and Fashion-MNIST | generalisation error | No clear effect |
| Use a Gaussian-mixture surrogate after a nonlinear random feature map | Binary logistic classification · MNIST and Fashion-MNIST random features | generalisation error | No clear effect |
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