Abstract
Let (X,Y) be a random couple, X being an observable instance and Y∈ {–1,1} being a binary label to be predicted based on an observation of the instance. Let (X i , Y i ), i = 1, . . . , n be training data consisting of n independent copies of (X,Y). Consider a real valued classifier \({\hat{f}_{n}}\) that minimizes the following penalized empirical risk
over a Hilbert space \({\mathcal H}\) of functions with norm || ·||, ℓ being a convex loss function and λ >0 being a regularization parameter. In particular, \({\mathcal H}\) might be a Sobolev space or a reproducing kernel Hilbert space. We provide some conditions under which the generalization error of the corresponding binary classifier sign \(({\hat{f}_{n}})\) converges to the Bayes risk exponentially fast.
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Koltchinskii, V., Beznosova, O. (2005). Exponential Convergence Rates in Classification. In: Auer, P., Meir, R. (eds) Learning Theory. COLT 2005. Lecture Notes in Computer Science(), vol 3559. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11503415_20
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DOI: https://doi.org/10.1007/11503415_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26556-6
Online ISBN: 978-3-540-31892-7
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