Sharp margin-based generalization bounds for realizable SVM
Let the exact homogeneous hard-margin support vector machine be trained on \(m\) independent observations from a Borel probability law on a real Hilbert space. We prove that, with score zero counted as an error, there is a universal numerical constant \(C\) such that \[ \Pp\left( γ_m>0,\quad \Risk(u_m)> \frac{C}{m} \left( K_m+\log\frac1δ \right) \right) \le δ. \] Here \(γ_m\) is the empirical homogeneous margin, \(u_m\) is the exact minimum-norm unit-margin separator, \(r_m\) is the largest training radius, and \(K_m:=r_m^2\norm{u_m}^2=r_m^2/γ_m^2\) on \(\{γ_m>0\}\). The proof is driven by a deterministic deletion problem. Given vectors \(x_1,\ldots,x_n\) in the unit ball, delete a set \(...
| Authors | Steve Hanneke, Aryeh Kontorovich |
|---|---|
| Primary category | stat.ML |
| Published | 15 September 2026 |
| Last updated at source | 15 September 2026 |
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