Research map / Learning theory and algorithms / Kernels and regression theory
Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| optimize L2 strength for logistic regression | logistic regression · Sign-teacher perceptron | generalization error vs Bayes: gap to Bayes of order 10^-5 | Helped |
| use logistic/hinge max-margin instead of ridge regression | linear classifier · Sign-teacher perceptron, large alpha | error decay rate: 0.500 alpha^-1 vs 0.2405 alpha^-1/2 | Helped |
| keep lambda finite instead of lambda->0 as alpha grows (ablation) | logistic/hinge · Sign-teacher perceptron, large alpha | error decay rate | Hurt |
| lambda->0 (pseudo-inverse) for ridge (ablation) | ridge regression · Sign-teacher perceptron, alpha=1 | generalization error: e_g = 0.5 at peak | Hurt |
| use custom non-convex optimal loss and regularizer instead of logistic | ERM · Sign-teacher perceptron | generalization error | Helped |
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