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- Ingo Steinwart
- Journal of Machine Learning Research
- 2001

In this article we study the generalization abilities of several classifiers of support vector machine (SVM) type using a certain class of kernels that we call universal. It is shown that the soft margin algorithms with universal kernels are consistent for a large class of classification problems including some kind of noisy tasks provided that the… (More)

- Ingo Steinwart
- Journal of Machine Learning Research
- 2003

Support vector machines (SVMs) construct decision functions that are linear combinations of kernel evaluations on the training set. The samples with non-vanishing coefficients are called support vectors. In this work we establish lower (asymptotical) bounds on the number of support vectors. On our way we prove several results which are of great importance… (More)

- Ingo Steinwart
- IEEE Transactions on Information Theory
- 2005

It is shown that various classifiers that are based on minimization of a regularized risk are universally consistent, i.e., they can asymptotically learn in every classification task. The role of the loss functions used in these algorithms is considered in detail. As an application of our general framework, several types of support vector machines (SVMs) as… (More)

- Ingo Steinwart
- 2004

We establish learning rates up to the order of n−1 for support vector machines with hinge loss (L1-SVMs) and nontrivial distributions. For the stochastic analysis of these algorithms we use recently developed concepts such as Tsybakov’s noise assumption and local Rademacher averages. Furthermore we introduce a new geometric noise condition for distributions… (More)

- Ingo Steinwart, Don R. Hush, Clint Scovel
- IEEE Transactions on Information Theory
- 2006

Although Gaussian radial basis function (RBF) kernels are one of the most often used kernels in modern machine learning methods such as support vector machines (SVMs), little is known about the structure of their reproducing kernel Hilbert spaces (RKHSs). In this work, two distinct explicit descriptions of the RKHSs corresponding to Gaussian RBF kernels are… (More)

- Ingo Steinwart, Don R. Hush, Clint Scovel
- Journal of Machine Learning Research
- 2005

One way to describe anomalies is by saying that anomalies are not concentrated. This leads to the problem of finding level sets for the data generating density. We interpret this learning problem as a binary classification problem and compare the corresponding classification risk with the standard performance measure for the density level problem. In… (More)

- Ingo Steinwart
- J. Complexity
- 2002

We show that support vector machines of the 1-norm soft margin type are universally consistent provided that the regularization parameter is chosen in a distinct manner and the kernel belongs to a specific class}the so-called universal kernels}which has recently been considered by the author. In particular it is shown that the 1-norm soft margin classifier… (More)

- Ingo Steinwart, Don R. Hush, Clint Scovel
- COLT
- 2009

We establish a new oracle inequality for kernelbased, regularized least squares regression methods, which uses the eigenvalues of the associated integral operator as a complexity measure. We then use this oracle inequality to derive learning rates for these methods. Here, it turns out that these rates are independent of the exponent of the regularization… (More)

- Ingo Steinwart, Clint Scovel
- COLT
- 2005

- Don R. Hush, Patrick Kelly, Clint Scovel, Ingo Steinwart
- Journal of Machine Learning Research
- 2006

We describe polynomial–time algorithms that produce approximate solutions with guaranteed accuracy for a class of QP problems that are used in the design of support vector machine classifiers. These algorithms employ a two–stage process where the first stage produces an approximate solution to a dual QP problem and the second stage maps this approximate… (More)