Moreover,the proposed multi-class kernel learning algorithms have statistical guarantees and fast convergence rates. Experimental results on lots of benchmark datasets show that our proposed methods can significantly outperform the existing multi-class classification methods. The major contributions ofthispaper include: 1)Anewlocal Rademacher complexitybased bound withfastconvergence rate for multi-class classification is established. Existing works [16,27] for multi-class classifiers with Rademacher complexity does not take into account couplings among different classes.

We study problem-dependent rates, i.e., generalization errors that scale tightly with the variance or the effectiveloss at the "besthypothesis."

Importantly, our rates are optimistic, i.e., they interpolate

The theoretical analysis motivates us to devise two effective multi-class kernel learning algorithms with statistical guarantees.

We study problem-dependent rates, i.e., generalization errors that scale tightly with the variance or the effective loss at the "best hypothesis."