Research map / Learning theory and algorithms / Kernels and regression theory
Near-Tight Margin-Based Generalization Bounds for Support Vector Machines
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a margin bound with a linear complexity term and a square-root term weighted by empirical margin error | SVM margin-based generalization analysis · Binary classification with inputs in a radius-R ball | generalization error upper bound: \mathcal{L}_S^\theta(w) + O\left(\frac{(R/\theta)^2\ln m + \ln(1/\delta)}{m} + \sqrt{\frac{(R/\theta)^2\ln m + \ln(1/\de | Helped |
| Establish a matching existential lower bound for margin-based generalization | SVM margin-based generalization analysis · Binary classification with inputs in a radius-R ball | generalization error lower bound: \Omega\left(\frac{R^2 \ln m}{\theta^2 m}+ \sqrt{\frac{R^2\ln(\tau^{-1})\tau}{\theta^2 m}} \right) | Mixed |
| Use a dimension-reducing random projection followed by a finite grid of classifiers | Proof of the proposed SVM generalization bound · Dimension-independent margin generalization | generalization error upper bound | Helped |
| Apply the upper bound to infinite-dimensional feature spaces using Johnson-Lindenstrauss transforms | Proposed margin generalization bound · Hilbert spaces | applicability | Helped |
| Use an algorithmic lower-bound construction against any learning algorithm | SVM learning algorithms · Binary classification with margin at least \theta on a fraction of training data | out-of-sample error lower bound: \tau + \Omega\left(\frac{R^2}{m \theta^2} + \sqrt{\tau \cdot \frac{R^2}{m \theta^2}}\right) | Hurt |
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