Rademacher and gaussian complexities: risk bounds and structural results
The Journal of Machine Learning Research
Support Vector Machine Soft Margin Classifiers: Error Analysis
The Journal of Machine Learning Research
Statistical Analysis of Some Multi-Category Large Margin Classification Methods
The Journal of Machine Learning Research
On the consistency of multiclass classification methods
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Semisupervised multicategory classification with imperfect model
IEEE Transactions on Neural Networks
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The consistency of classification algorithm plays a central role in statistical learning theory. A consistent algorithm guarantees us that taking more samples essentially suffices to roughly reconstruct the unknown distribution. We consider the consistency of ERM scheme over classes of combinations of very simple rules (base classifiers) in multiclass classification. Our approach is, under some mild conditions, to establish a quantitative relationship between classification errors and convex risks. In comparison with the related previous work, the feature of our result is that the conditions are mainly expressed in terms of the differences between some values of the convex function.