Alex J. Smola

Learning Graph Matching (2008)

Tibério S. Caetano, Li Cheng, Quoc V. Le, Alex J. Smola

As a fundamental problem in pattern recognition, graph matching has found a variety of applications in the field of computer vision. In graph matching, patterns are modeled as graphs and pattern...

A tutorial on support vector regression (2008)

Alex J. Smola, Bernhard Schölkopf

In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV...

Robust Near-Isometric Matching via Structured Learning of Graphical Models (2008)

McAuley, Julian J., Caetano, Tiberio S., Smola, Alex J.

Models for near-rigid shape matching are typically based on distance-related features, in order to infer matches that are consistent with the isometric assumption. However, real shapes from image...

1 A Short Tour of Kernel Methods for Graphs (2008)

Thomas Gärtner, Fraunhofer Ais. Kd, Schloß Birlinghoven, Sankt Augustin, Quoc V. Le, Alex J Smola

Machine learning research has – apart from some exceptions – originally concentrated on learning from data that can naturally be represented in a single table without links between the instances....

Learning Graph Matching (2008)

Caetano, Tiberio S., McAuley, Julian J., Cheng, Li, Le, Quoc V., Smola, Alex J.

As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as...

Estimating Labels from Label Proportions (2008)

Quadrianto, Novi, Smola, Alex J., Caetano, Tiberio S., Le, Quoc V.

Consider the following problem: given sets of unlabeled observations, each set with known label proportions, predict the labels of another set of observations, also with known label proportions. This...

Learning Graph Matching (2008)

Tibério S. Caetano, Li Cheng, Quoc V. Le, Alex J. Smola

As a fundamental problem in pattern recognition, graph matching has found a variety of applications in the field of computer vision. In graph matching, patterns are modeled as graphs and pattern...

Abstract (2008)

Alex J. Smola, Bernhard Schölkopf, John Shawe-taylor, Robert C. Williamson

Effective methods of capacity control via uniform convergence bounds for function expansions have been largely limited to Support Vector machines, where good bounds are obtainable by the entropy...

LETTER Communicated by John Platt New Support Vector Algorithms (2008)

Bernhard Schölkopf, Alex J. Smola, Robert C. Williamson, Peter L. Bartlett

We propose a new class of support vector algorithms for regression and classi�cation. In these algorithms, a parameter º lets one effectively control the number of support vectors. While this can...

Laplace Propagation Abstract (2008)

Alex J. Smola, Eleazar Eskin

We present a novel method for approximate inference in Bayesian models and regularized risk functionals. It is based on the propagation of mean and variance derived from the Laplace approximation of...

ARTICLE Communicated by Vladimir Vapnik Estimating the Support of a High-Dimensional Distribution (2008)

Bernhard Schölkopf, John C. Platt, John Shawe-taylor, Alex J. Smola, Robert C. Williamson

Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a “simple ” subset S of input space such that the probability that a test point...

Category: Algorithms and Architectures (Support Vectors, Supervised Learning) Presentation Preference: Poster Correspondence: Address to A. Smola Semiparametric Support Vector and Linear Programming Machines (2008)

Alex J. Smola, Thilo T. Frie, Bernhard Scholkopf

fsmola, friess, bsg @ rst.gmd.de Semiparametric models are useful tools in the case where domain knowledge exists about the function to be estimated or emphasis is put onto understandability of the...

Laplace Propagation Abstract (2008)

Alex J. Smola, Eleazar Eskin

We present a novel method for approximate inference in Bayesian models and regularized risk functionals. It is based on the propagation of mean and variance derived from the Laplace approximation of...

The Entropy Regularization Information Criterion (2007)

Alex J. Smola, John Shawe-taylor, Bernhard Schölkopf, Bernhard Sch Olkopf, Robert C. Williamson

Effective methods of capacity control via uniform convergence bounds for function expansions have been largely limited to Support Vector machines, where good bounds are obtainable by the entropy...

LETTER Communicated by John Platt New Support Vector Algorithms (2007)

Bernhard Schölkopf, Alex J. Smola, Robert C. Williamson, Peter L. Bartlett

We propose a new class of support vector algorithms for regression and classification. In these algorithms, a parameter ν lets one effectively control the number of support vectors. While this can...

Laplace Propagation Abstract (2007)

Alex J. Smola, Eleazar Eskin

We present a novel method for approximate inference in Bayesian models and regularized risk functionals. It is based on the propagation of mean and variance derived from the Laplace approximation of...

Integrating structured biological data by kernel maximum mean discrepancy (2006)

Karsten M. Borgwardt, Arthur Gretton, Malte J. Rasch, Hans-peter Kriegel, Bernhard Schölkopf, Alex J. Smola

Motivation: Many problems in data integration in bioinformatics can be posed as one common question: Are two sets of observations generated by the same distribution? We propose a kernel-based...

Learning high-order MRF priors of color images (2006)

Julian J. Mcauley, Tibério S. Caetano, Alex J. Smola, Matthias O. Franz

In this paper, we use large neighborhood Markov random fields to learn rich prior models of color images. Our approach extends the monochromatic Fields of Experts model (Roth & Black, 2005a) to...

Simpler knowledge-based support vector machines (2006)

Quoc V. Le, Alex J. Smola

If appropriately used, prior knowledge can significantly improve the predictive accuracy of learning algorithms or reduce the amount of training data needed. In this paper we introduce a simple...

Step size adaptation in reproducing kernel Hilbert space (2006)

Nicol N. Schraudolph, Alex J. Smola, Thorsten Joachims

This paper presents an online support vector machine (SVM) that uses the stochastic meta-descent (SMD) algorithm to adapt its step size automatically. We formulate the online learning problem as a...

Step size adaptation in reproducing kernel Hilbert space (2006)

Nicol N. Schraudolph, Alex J. Smola, Thorsten Joachims

This paper presents an online Support Vector Machine (SVM) that uses the Stochastic Meta-Descent (SMD) algorithm to adapt its step size automatically. We formulate the online learning problem as a...

Step size adaptation in reproducing kernel Hilbert space (2006)

Nicol N. Schraudolph, Alex J. Smola

This paper presents an online Support Vector Machine (SVM) that uses the Stochastic Meta-Descent (SMD) algorithm to adapt its step size automatically. We formulate the online learning problem as a...

Integrating structured biological data by Kernel Maximum Mean Discrepancy (2006)

Borgwardt, Karsten M., Gretton, Arthur, Rasch, Malte J., Kriegel, Hans-Peter, Schölkopf, Bernhard, Smola, Alex J.

Motivation: Many problems in data integration in bioinformatics can be posed as one common question: Are two sets of observations generated by the same distribution? We propose a kernel-based...

Protein (2005)

Karsten M. Borgwardt, Cheng Soon Ong, Stefan Schönauer, Alex J. Smola, Hans-peter Kriegel

Vol. 21 Suppl. 1 2005, pages i47–i56 doi:10.1093/bioinformatics/bti1007

Kernel Methods for Missing Variables (2005)

Alex Smola Vishwanathan, Alex J. Smola

We present methods for dealing with missing variables in the context of Gaussian Processes and Support Vector Machines. This solves an important problem which has largely been ignored by kernel...

Kernel methods and the exponential family (2005)

Stéphane Canu, Alex J. Smola

Abstract. The success of Support Vector Machine (SVM) gave rise to the development of a new class of theoretically elegant learning machines which use a central concept of kernels and the associated...

Heteroscedastic gaussian process regression (2005)

Quoc V. Le, Alex J. Smola

This paper presents an algorithm to estimate simultaneously both mean and variance of a non parametric regression problem. The key point is that we are able to estimate variance locally unlike...

Invariances in classification : an efficient svm implementation (2005)

Gaëlle Loosli, Stéphane Canu, Alex J. Smola

Abstract. Often, in pattern recognition, complementary knowledge is available. This could be useful to improve the performance of the recognition system. Part of this knowledge regards invariances,...

Kernel methods and the exponential family (2005)

Stéphane Canu, Alex J. Smola

Abstract. The success of Support Vector Machine (SVM) gave rise to the development of a new class of theoretically elegant learning machines which use a central concept of kernels and the associated...

BIOINFORMATICS (2005)

Karsten M. Borgwardt, Cheng Soon Ong, Stefan Schönauer, Alex J. Smola, Hans-peter Kriegel

Vol. 21 Suppl. 1 2005, pages i1–i10 doi:10.1093/bioinformatics/bti1007 Protein function prediction via graph kernels

Protein function prediction via graph kernels (2005)

Borgwardt, Karsten M., Ong, Cheng Soon, Schönauer, Stefan, Vishwanathan, S. V. N., Smola, Alex J., Kriegel, Hans-Peter

Motivation: Computational approaches to protein function prediction infer protein function by finding proteins with similar sequence, structure, surface clefts, chemical properties, amino acid...

A Tutorial on Support Vector Regression (2003)

Alex J. Smola, Bernhard Schölkopf, Bernhard Sch Olkopf

In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV...

Laplace Propagation (2003)

Alex Smola Vishwanathan, Alex J. Smola

We present a novel method for approximate inference in Bayesian models and regularized risk functionals. It is based on the propagation of mean and variance derived from the Laplace approximation of...

Large margin classification for moving targets (2002)

Jyrki Kivinen, Alex J. Smola, Robert C. Williamson

Abstract. We consider using online large margin classification algorithms in a setting where the target classifier may change over time. The algorithms we consider are Gentile’s Alma, and an...

C ○ 2004 Kluwer Academic Publishers. Manufactured in The Netherlands. A tutorial on support vector regression ∗ (2002)

Alex J. Smola, Bernhard Schölkopf

In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV...

Kernel machines and boolean functions (2002)

Adam Kowalczyk, Alex J. Smola, Robert C. Williamson

We give results about the learnability and required complexity of logical formulae to solve classification problems. These results are obtained by linking propositional logic with kernel machines. In...

Learning with Kernels (2002)

Jyrki Kivinen, Alex J. Smola, Robert C. Williamson

We consider online learning in a Reproducing Kernel Hilbert Space. Our method is computationally efficient and leads to simple algorithms. In particular we derive update equations for classification,...

Kernel Machines and Boolean Functions (2002)

Adam Kowalczyk Chief, Adam Kowalczyk, Alex J. Smola, Bob C. Williamson

We give results about the learnability and required complexity of logical formulae to solve classi cation problems. These results are obtained by linking rst order logic with kernel machines. In...

Learning with Kernels (2002)

Jyrki Kivinen, Alex J. Smola, Robert C. Williamson

We consider online learning in a Reproducing Kernel Hilbert Space. Our method is computationally efficient and leads to simple algorithms. In particular we derive update equations for classification,...

Kernel machines and boolean functions (2002)

Adam Kowalczyk, Alex J. Smola, Robert C. Williamson

We give results about the learnability and required complexity of logical formulae to solve classification problems. These results are obtained by linking propositional logic with kernel machines. In...

C ○ 2004 Kluwer Academic Publishers. Manufactured in The Netherlands. A tutorial on support vector regression ∗ (2002)

Alex J. Smola, Bernhard Schölkopf

In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV...

Multi-Instance Kernels (2002)

Thomas Gärtner, Peter A. Flach, Adam Kowalczyk, Alex J. Smola

Learning from structured data is becoming increasingly important. However, most prior work on kernel methods has focused on learning from attribute-value data. Only recently, research started...

Online Learning with Kernels (2002)

Jyrki Kivinen, Alex J. Smola, Robert C. Williamson

We consider online learning in a Reproducing Kernel Hilbert Space. Our method is computationally efficient and leads to simple algorithms. In particular we derive update equations for classification,...

Sparse greedy Gaussian Process regression (2001)

Alex J. Smola, Peter Bartlett

We present a simple sparse greedy technique to approximate the maximum a posteriori estimate of Gaussian Processes with much improved scaling behaviour in the sample size m. In particular,...

Sparse greedy Gaussian Process regression (2001)

Alex J. Smola, Peter Bartlett

We present a simple sparse greedy technique to approximate the maximum a posteriori estimate of Gaussian Processes with much improved scaling behaviour in the sample size m. In particular,...

A generalized representer theorem (2001)

Bernhard Schölkopf, Ralf Herbrich, Alex J. Smola, Robert C. Williamson

Wahba's classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in...

Estimating the Support of a High-Dimensional Distribution (2001)

Bernhard Schölkopf, John C. Platt, John Shawe-taylor, Alex J. Smola, Robert C. Williamson

This article describes an algorithm that finds regions close to C(#). Our class is defined implicitly via a kernel k as the set of half-spaces in an SV feature space. We do not try to minimize the...

A Generalized Representer Theorem (2001)

Bernhard Schölkopf, Ralf Herbrich, Alex J. Smola

Wahba's classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in...

Regularization with dot-product kernels (2000)

Alex J. Smola, Robert C. Williamson

In this paper we give necessary and sucient conditions under which kernels of dot product type k(x; y) = k(x y) satisfy Mercer 's condition and thus may be used in Support Vector Machines (SVM),...

Advances in Large Margin Classifiers (2000)

Alexander J. Smola, Alex J. Smola, Peter Bartlett, Dale Schuurmans (Eds.), Peter Bartlett, Bernhard Schölkopf, ...

Contents Preface vii 1 Introduction to Large Margin Classifiers 1 Alex J. Smola, Peter Bartlett, Bernhard Scholkopf, and Dale Schuurmans 2 Large Margin Rank Boundaries for Ordinal Regression 29 Ralf...

Kernel Method for Percentile Feature Extraction (2000)

Bernhard Schölkopf, John C. Platt, Alex J. Smola

A method is proposed which computes a direction in a dataset such that a specified fraction of a particular class of all examples is separated from the overall mean by a maximal margin. The projector...

Entropy Numbers of Linear Function Classes (2000)

Robert C. Williamson, Alex J. Smola, Bernhard Schölkopf, Bernhard Sch Olkopf

This paper collects together a miscellany of results originally motivated by the analysis of the generalization performance of the "maximum-margin" algorithm due to Vapnik and others. The...

A Generalized Representer Theorem (2000)

Bernhard Schölkopf, Ralf Herbrich, Alex J. Smola, Robert Williamson

Wahba's classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in...

Sparse Greedy Matrix Approximation for Machine Learning (2000)

Alex J. Smola, Bernhard Schölkopf

In kernel based methods such as Regularization Networks large datasets pose signi- cant problems since the number of basis functions required for an optimal solution equals the number of samples. We...

Produced as part of the ESPRIT Working Group in Neural and Computational Learning II, (2000)

Bernhard Scholkopf, Ralf Herbrich, Alex J. Smola, Robert Williamson

Wahba's classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in...

Regularization with dot-product kernels (2000)

Alex J. Smola, Zoltán L. Óvári, Robert C. Williamson

In this paper we give necessary and sufficient conditions under which kernels of dot product type k(x, y) = k(x · y) satisfy Mercer’s condition and thus may be used in Support Vector Machines...

Regularized principal manifolds (1999)

Alex J. Smola, Robert C. Williamson, Sebastian Mika, Bernhard Schölkopf

Abstract. Many settings of unsupervised learning can be viewed as quantization problems — the minimization of the expected quantization error subject to some restrictions. This allows the use of...

Estimating the Support of a High-Dimensional Distribution (1999)

Bernhard Schölkopf, John C. Platt, John Shawe-taylor, Alex J. Smola, Robert C. Williamson

Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test...

Estimating the Support of a High-Dimensional Distribution (1999)

Bernhard Schölkopf, John C. Platt, John Shawe-Taylor, Alex J. Smola, Robert C. Williamson

Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test...

Kernel-Dependent Support Vector Error Bounds (1999)

Bernhard Schölkopf, John Shawe-taylor, Alex J. Smola, Robert C. Williamson

Model selection in Support Vector machines is usually carried out by minimizing the quotient of the radius of the smallest enclosing sphere of the data and the observed margin on the training set. We...

Sparse Kernel Feature Analysis (1999)

Alex Smola Olvi, Alex J. Smola, Olvi L. Mangasarian, Bernhard Scholkopf

Kernel Principal Component Analysis (KPCA) has proven to be a versatile tool for unsupervised learning, however at a high computational cost due to the dense expansions in terms of kernel functions....

Generalization Performance of Regularization Networks and Support Vector Machines via Entropy Numbers of Compact Operators (1999)

Robert C. Williamson, Alex J. Smola, Bernhard Schölkopf

We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs...

Regularized Principal Manifolds (1999)

Alex J. Smola, Sebastian Mika, Bernhard Schölkopf, Robert C. Williamson

. Many settings of unsupervised learning can be viewed as quantization problems --- the minimization of the expected quantization error subject to some restrictions. This allows the use of tools such...

Sparse Kernel Feature Analysis (1999)

Alex J. Smola, Olvi L. Mangasarian, Bernhard Schölkopf

Kernel Principal Component Analysis (KPCA) has proven to be a versatile tool for unsupervised learning, however at a high computational cost due to the dense expansions in terms of kernel functions....

Advances in Large Margin Classifiers (1999)

Alexander J. Smola, Alex J. Smola, Peter Bartlett, Dale Schuurmans (Eds.), Peter Bartlett, Bernhard Schölkopf, ...

this paper are taken from (Herbrich et al., 1999) Smola, Bartlett, Scholkopf, and Schuurmans: Advances in Large Margin Classifiers 1999/03/31 11:08

Estimating the Support of a High-Dimensional Distribution (1999)

Bernhard Scholkopf John, John C. Platt, John Shawe-taylor, Alex J. Smola, Robert C. Williamson

Suppose you are given some dataset drawn from an underlying probability distribution and you want to estimate a "simple" subset of input space such that the probability that a test point...

Entropy Numbers, Operators and Support Vector Kernels (1999)

Robert C. Williamson, Alex J. Smola, Bernhard Schölkopf

We derive new bounds for the generalization error of feature space machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers.

A tutorial on support vector regression (1998)

Alex J. Smola, Bernhard Schölkopf

In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for regression and function estimation. Furthermore, we include a summary of currently used algorithms...

Generalization performance of regularization networks and support vector machines via entropy numbers of compact operators (1998)

Robert C. Williamson, Alex J. Smola, Bernhard Schölkopf

Abstract—We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers....

Entropy Numbers, Operators and Support Vector Kernels (1998)

Robert C. Williamson, Alex J. Smola, Bernhard Schölkopf, Bernhard Scholkopf Gmd

We derive new bounds for the generalization error of feature space machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The...

A Tutorial on Support Vector Regression (1998)

Alex J. Smola, Bernhard Schölkopf, Bernhard Scholkopf Gmd

In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for regression and function estimation. Furthermore, we include a summary of currently used algorithms...

Generalization Bounds for Convex Combinations of Kernel Functions (1998)

Alex J. Smola, Robert C. Williamson, Bernhard Schölkopf, Bernhard Scholkopf Gmd

We derive new bounds on covering numbers for hypothesis classes generated by convex combinations of basis functions. These are useful in bounding the generalization performance of algorithms such as...

General Cost Functions for Support Vector Regression (1998)

Alex J. Smola, Bernhard Schölkopf, Klaus-Robert Müller

The concept of Support Vector Regression is extended to a more general class of convex cost functions. Moreover it is shown how the resulting convex constrained optimization problems can be...

New Support Vector Algorithms (1998)

Bernhard Schölkopf, Bernhard Scholkopf Gmd, Alex J. Smola, Robert Williamson, Peter Bartlett

We describe a new class of Support Vector algorithms for regression and classification. In these algorithms, a parameter lets one effectively control the number of Support Vectors. While this can be...

Semiparametric Support Vector and Linear Programming Machines (1998)

Alex J. Smola, Thilo T. Frieß, Bernhard Schölkopf, Bernhard Scholkopf Gmd

Semiparametric models are useful tools in the case where domain knowledge exists about the function to be estimated or emphasis is put onto understandability of the model. We extend two learning...

Generalization Performance of Regularization Networks and Support Vector Machines via Entropy Numbers of Compact Operators (1998)

Robert C. Williamson, Alex J. Smola, Bernhard Schölkopf, Bernhard Scholkopf Gmd

We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs...

Generalization Performance of Regularization Networks and Support Vector Machines via Entropy Numbers of Compact Operators (1998)

Robert C. Williamson, Alex J. Smola, Bernhard Schölkopf, Bernhard Scholkopf Gmd

We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs...

On a Kernel-based Method for Pattern Recognition, Regression, Approximation, and Operator Inversion (1997)

Alex J. Smola, Bernhard Schölkopf, Leo Van Hemmen, Jorg Lemm, Klaus-robert Muller, Heidrun Mundlein

We present a Kernel--based framework for Pattern Recognition, Regression Estimation, Function Approximation and multiple Operator Inversion. Previous approaches such as ridge-regression, Support...

On a Kernel-based Method for Pattern Recognition, Regression, Approximation, and Operator Inversion (1997)

Alex J. Smola, Bernhard Schölkopf, Jorg Lemm, Klaus-robert Muller, Noboru Murata, Sara Solla

We present a Kernel--based framework for Pattern Recognition, Regression Estimation,Function Approximation and multiple Operator Inversion. Adopting a regularization--theoretic framework, the above...

A Generalized Representer Theorem

Bernhard Schölkopf, Ralf Herbrich, Alex J. Smola, Robert C. Williamson

Wahba's classical representer theorem states that the solutions of certain optimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in term...

Semiparametric Support Vector and Linear Programming Machines

Alex J. Smola, Thilo T. Frieß, Bernhard Schölkopf

Semiparametric models are useful tools in the case where domain knowledge exists about the function to be estimated or emphasis is put onto understandability of the model. We extend two learning...