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We consider the general problem of learning from labeled and unlabeled data, which is often called semi-supervised learning or transductive inference. A principled approach to semi-supervised learning is to design a classifying function which is sufficiently smooth with respect to the intrinsic structure collectively revealed by known labeled and unlabeled… (More)

- Olivier Bousquet, André Elisseeff
- Journal of Machine Learning Research
- 2002

We define notions of stability for learning algorithms and show how to use these notions to derive generalization error bounds based on the empirical error and the leave-one-out error. The methods we use can be applied in the regression framework as well as in the classification one when the classifier is obtained by thresholding a real-valued function. We… (More)

We propose an independence criterion based on the eigen-spectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous… (More)

- Olivier Chapelle, Vladimir Vapnik, Olivier Bousquet, Sayan Mukherjee
- Machine Learning
- 2002

The problem of automatically tuning multiple parameters for pattern recognition Support Vector Machines (SVMs) is considered. This is done by minimizing some estimates of the generalization error of SVMs using a gradient descent algorithm over the set of parameters. Usual methods for choosing parameters, based on exhaustive search become intractable as soon… (More)

We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense that the Rademacher averages are computed from the data, on a subset of functions with small empirical error. We present… (More)

- Léon Bottou, Olivier Bousquet
- NIPS
- 2007

This contribution develops a theoretical framework that takes into account the effect of approximate optimization on learning algorithms. The analysis shows distinct tradeoffs for the case of small-scale and large-scale learning problems. Small-scale learning problems are subject to the usual approximation–estimation tradeoff. Large-scale learning problems… (More)

The Google search engine has enjoyed huge success with its web page ranking algorithm, which exploits global, rather than local, hyperlink structure of the web using random walks. Here we propose a simple universal ranking algorithm for data lying in the Euclidean space, such as text or image data. The core idea of our method is to rank the data with… (More)

The last few years have witnessed important new developments in the theory and practice of pattern classification. We intend to survey some of the main new ideas that have led to these recent results. Résumé. La pratique et la théorie de la reconnaissance des formes ont connu des développements importants durant cesdernì eres années. Ce survol visè a… (More)

- Olivier Bousquet, Stéphane Boucheron, Gábor Lugosi
- Advanced Lectures on Machine Learning
- 2003

The goal of statistical learning theory is to study, in a statistical framework, the properties of learning algorithms. In particular, most results take the form of so-called error bounds. This tutorial introduces the techniques that are used to obtain such results.

(Reçu le jour mois année, accepté après révision le jour mois année) Abstract. We introduce new concentration inequalities for functions on product spaces They allow to obtain a Bennett type deviation bound for suprema of empirical processes indexed by upper bounded functions. The result is an improvement on Rio's version [6] of Talagrand's inequality [7]… (More)