Research map / Learning theory and algorithms / Kernels and regression theory
Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use simplicial interpolation instead of nearest-neighbor classification | Classification · High-dimensional classification with hard margin | excess classification risk: 2 \mathcal{R}_{0/1}(f^*) -> \mathcal{R}_{0/1}(f^*) \cdot (1 + c_1 e^{-c_2d}) | Helped |
| Use simplicial interpolation in regression | Regression · Uniform distribution on a simple polytope | MSE excess over conditional mean: \limsup_{n\to\infty} \mathbb{E}[ (\hat\eta(X) - \eta(X))^2 ] \leq \frac{2}{d+2} \mathbb{E}[ (Y - \eta(X))^2 ] | Helped |
| Use singularly weighted, interpolating k-nearest neighbors | Regression · Smooth regression with regular marginal distribution | mean squared error convergence rate: n^{-2\alpha/(2\alpha+d)} | Helped |
| Use singularly weighted, interpolating k-nearest neighbors | Classification · Smooth classification with a margin condition | classification error convergence rate: n^{-\alpha\beta/(\alpha(2+\beta)+d)} | Helped |
| Interpolate the training labels | Consistent interpolating classifier · Classification with non-zero label noise | density of adversarial examples: every point in \Omega is within distance 2\epsilon | Mixed |
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