Name
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 (Xi, Yi), 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 $$\frac{1}{n}\sum\limits_{i=1}^n \ell(Y_{i}f(X_{i})) + \lambda\|Let (X,Y) be a random couple, X being an observable instance and Y∈ {–1,1} being a binary label to be predicted based on an observation of the instance. Let (Xi, Yi), i=1, . . . , n be training data consisting of n independent copies of (X,Y). Consider a real valued classifier ${\hat{f}_{n}}$ that minimizes the following penalized empirical risk $$\frac{1}{n}\sum\limits_{i=1}^n \ell(Y_{i}f(X_{i})) + \lambda\|f\|^{2} \rightarrow {\rm min}, f\in {\mathcal H}$$ over a Hilbert space ${\mathcal H}$ of functions with norm || ·||, ℓ being a convex loss function and λ 0 being a regularization parameter. In particular, ${\mathcal H}$ might be a Sobolev space or a reproducing kernel Hilbert space. We provide some conditions under which the generalization error of the corresponding binary classifier sign $({\hat{f}_{n}})$ converges to the Bayes risk exponentially fast. $|^{2} \rightarrow {\rm min}, f\in {\mathcal H}$$ 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. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1007/11503415_20 | COLT |
Keywords | Field | DocType |
mathcal h,hilbert space,observable instance,exponential convergence rate,bayes risk exponentially,reproducing kernel hilbert space,n independent copy,corresponding binary classifier sign,sobolev space,following penalized empirical risk,binary label,generalization error,loss function,data consistency | Observable,Sobolev space,Regularization (mathematics),Artificial intelligence,Binary number,Hilbert space,Discrete mathematics,Mathematical optimization,Regular polygon,Machine learning,Mathematics,Reproducing kernel Hilbert space,Lambda | Conference |
Volume | ISSN | ISBN |
3559 | 0302-9743 | 3-540-26556-2 |
Citations | PageRank | References |
4 | 0.60 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vladimir Koltchinskii | 1 | 89 | 9.61 |
| Olexandra Beznosova | 2 | 4 | 0.60 |