Research map / Learning theory and algorithms / Kernels and regression theory
Max-Margin Works while Large Margin Fails: Generalization without Uniform Convergence
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a near-max-margin classifier | Linear classification · Linear problem class | 0/1 test loss: e^{-\frac{n}{36d\sigma^4}} + e^{-n/8} | Helped |
| Use a near-max-margin classifier with relu^h, h in (1, 2) | Two-layer neural network · Quadratic XOR problem | 0/1 test loss: e^{-\frac{1}{c\sigma^2}} | Helped |
| Use a near-max-margin classifier below the generalization threshold | Two-layer neural network · Quadratic XOR problem, κ < κ_gen^X | 0/1 test loss: \frac{1}{2} | Hurt |
| Use a classifier achieving a constant fraction of maximum margin rather than near-maximal margin | Linear and nonlinear classifiers · Linear and quadratic XOR problems | 0/1 test loss: half the max-margin | Mixed |
| Apply uniform-convergence bounds to useful hypothesis classes in the intermediate signal-to-noise regime | Near-max-margin classifiers · Linear and quadratic XOR problems, κ_gen < κ < κ_phen | uniform-convergence guarantee: 1 - δ | Hurt |
| Apply polynomial margin bounds | Max-margin classifiers · Linear and quadratic XOR problems, κ_gen < κ < κ_phen | test-loss guarantee: no better than an absolute constant | Hurt |
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