Relative Deviation Margin Bounds
This work offers incremental theoretical improvements in statistical learning theory for researchers in that field.
The authors developed new margin-based learning guarantees that depend on empirical margin loss, providing distribution-dependent bounds using Rademacher complexity and empirical covering numbers, and extended these to unbounded loss functions under finite moment assumptions.
We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. We give two types of learning bounds, both distribution-dependent and valid for general families, in terms of the Rademacher complexity or the empirical $\ell_\infty$ covering number of the hypothesis set used. Furthermore, using our relative deviation margin bounds, we derive distribution-dependent generalization bounds for unbounded loss functions under the assumption of a finite moment. We also briefly highlight several applications of these bounds and discuss their connection with existing results.