Gaussian Approximation of Besov Functions for Logistic Classification on Manifolds
We study Gaussian kernel approximation and regularized logistic classification on a connected compact smooth embedded manifold $X\subset\mathbb R^d$ without boundary and of intrinsic dimension $\varrho$. Two main challenges are to derive a fast oracle inequality without assuming a bounded Bayes function and to construct Gaussian approximants that exploit both the intrinsic dimension and the target's regularity without saturation. We address the first challenge through a Bernstein-type inequality whose constant depends linearly on the supremum norm of the predictor. Combined with localized complexity estimates, this yields an oracle inequality over separable normed function spaces. To addr...
| Authors | Guanhang Lei, Lei Shi, Xiaoming Yuan |
|---|---|
| Primary category | stat.ML |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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