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Bernhard Schölkopf (Project leader)
Director
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Ilya Tolstikhin
Research Scientist
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34 results

2016


Kernel Mean Shrinkage Estimators

Muandet, K., Sriperumbudur, B., Fukumizu, K., Gretton, A., Schölkopf, B.

Journal of Machine Learning Research, 17(48):1-41, 2016 (article)

link (url) Project Page [BibTex]

2016

link (url) Project Page [BibTex]

2015


Towards a Learning Theory of Cause-Effect Inference

Lopez-Paz, D., Muandet, K., Schölkopf, B., Tolstikhin, I.

In Proceedings of the 32nd International Conference on Machine Learning, 37, pages: 1452–1461, JMLR Workshop and Conference Proceedings, (Editors: F. Bach and D. Blei), JMLR, ICML, 2015 (inproceedings)

Web Project Page [BibTex]

2015

Web Project Page [BibTex]


The Randomized Causation Coefficient

Lopez-Paz, D., Muandet, K., Recht, B.

Journal of Machine Learning, 16, pages: 2901-2907, 2015 (article)

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]

2014


A Permutation-Based Kernel Conditional Independence Test

Doran, G., Muandet, K., Zhang, K., Schölkopf, B.

In Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence (UAI2014), pages: 132-141, (Editors: Nevin L. Zhang and Jin Tian), AUAI Press Corvallis, Oregon, UAI2014, 2014 (inproceedings)

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2014

PDF Project Page [BibTex]


Kernel Mean Estimation via Spectral Filtering

Muandet, K., Sriperumbudur, B., Schölkopf, B.

In Advances in Neural Information Processing Systems 27, pages: 1-9, (Editors: Z. Ghahramani, M. Welling, C. Cortes, N.D. Lawrence and K.Q. Weinberger), Curran Associates, Inc., 28th Annual Conference on Neural Information Processing Systems (NIPS), 2014 (inproceedings)

Web link (url) Project Page [BibTex]

Web link (url) Project Page [BibTex]


Single-Source Domain Adaptation with Target and Conditional Shift

Zhang, K., Schölkopf, B., Muandet, K., Wang, Z., Zhou, Z., Persello, C.

In Regularization, Optimization, Kernels, and Support Vector Machines, pages: 427-456, 19, Chapman & Hall/CRC Machine Learning & Pattern Recognition, (Editors: Suykens, J. A. K., Signoretto, M. and Argyriou, A.), Chapman and Hall/CRC, Boca Raton, USA, 2014 (inbook)

Project Page [BibTex]

Project Page [BibTex]


Kernel Mean Estimation and Stein Effect

Muandet, K., Fukumizu, K., Sriperumbudur, B., Gretton, A., Schölkopf, B.

In Proceedings of the 31st International Conference on Machine Learning, W&CP 32 (1), pages: 10-18, (Editors: Eric P. Xing and Tony Jebara), JMLR, ICML, 2014 (inproceedings)

PDF Project Page [BibTex]

PDF Project Page [BibTex]


Visualizing Uncertainty in HARDI Tractography Using Superquadric Streamtubes

Wiens, V., Schlaffke, L., Schmidt-Wilcke, T., Schultz, T.

In Eurographics Conference on Visualization, Short Papers, (Editors: Elmqvist, N. and Hlawitschka, M. and Kennedy, J.), EuroVis, 2014 (inproceedings)

Abstract
Standard streamtubes for the visualization of diffusion MRI data are rendered either with a circular or with an elliptic cross section whose aspect ratio indicates the relative magnitudes of the medium and minor eigenvalues. Inspired by superquadric tensor glyphs, we propose to render streamtubes with a superquadric cross section, which develops sharp edges to more clearly convey the orientation of the second and third eigenvectors where they are uniquely defined, while maintaining a circular shape when the smaller two eigenvalues are equal. As a second contribution, we apply our novel superquadric streamtubes to visualize uncertainty in the tracking direction of HARDI tractography, which we represent using a novel propagation uncertainty tensor.

link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


Causal discovery via reproducing kernel Hilbert space embeddings

Chen, Z., Zhang, K., Chan, L., Schölkopf, B.

Neural Computation, 26(7):1484-1517, 2014 (article)

DOI Project Page [BibTex]

2013


Domain adaptation under Target and Conditional Shift

Zhang, K., Schölkopf, B., Muandet, K., Wang, Z.

In Proceedings of the 30th International Conference on Machine Learning, W&CP 28 (3), pages: 819–827, (Editors: S Dasgupta and D McAllester), JMLR, ICML, 2013 (inproceedings)

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2013

PDF Web Project Page [BibTex]


One-class Support Measure Machines for Group Anomaly Detection

Muandet, K., Schölkopf, B.

In Proceedings 29th Conference on Uncertainty in Artificial Intelligence (UAI), pages: 449-458, (Editors: Ann Nicholson and Padhraic Smyth), AUAI Press, Corvallis, Oregon, UAI, 2013 (inproceedings)

PDF Project Page [BibTex]

PDF Project Page [BibTex]


Domain Generalization via Invariant Feature Representation

Muandet, K., Balduzzi, D., Schölkopf, B.

In Proceedings of the 30th International Conference on Machine Learning, W&CP 28(1), pages: 10-18, (Editors: S Dasgupta and D McAllester), JMLR, ICML, 2013, Volume 28, number 1 (inproceedings)

Web Project Page [BibTex]

Web Project Page [BibTex]


HiFiVE: A Hilbert Space Embedding of Fiber Variability Estimates for Uncertainty Modeling and Visualization

Schultz, T., Schlaffke, L., Schölkopf, B., Schmidt-Wilcke, T.

Computer Graphics Forum, 32(3):121-130, (Editors: B Preim, P Rheingans, and H Theisel), Blackwell Publishing, Oxford, UK, Eurographics Conference on Visualization (EuroVis), 2013 (article)

DOI Project Page [BibTex]

DOI Project Page [BibTex]


Statistical analysis of coupled time series with Kernel Cross-Spectral Density operators

Besserve, M., Logothetis, N., Schölkopf, B.

In Advances in Neural Information Processing Systems 26, pages: 2535-2543, (Editors: C.J.C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K.Q. Weinberger), 27th Annual Conference on Neural Information Processing Systems (NIPS), 2013 (inproceedings)

PDF Project Page Project Page [BibTex]

PDF Project Page Project Page [BibTex]


Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders

Sgouritsa, E., Janzing, D., Peters, J., Schölkopf, B.

In Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI), pages: 556-565, (Editors: A Nicholson and P Smyth), AUAI Press Corvallis, Oregon, USA, UAI, 2013 (inproceedings)

PDF Project Page Project Page [BibTex]

PDF Project Page Project Page [BibTex]

2012


A Kernel Two-Sample Test

Gretton, A., Borgwardt, K., Rasch, M., Schölkopf, B., Smola, A.

Journal of Machine Learning Research, 13, pages: 723-773, March 2012 (article)

Abstract
We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD). We present two distribution-free tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.

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2012

PDF Web Project Page [BibTex]


Feature Selection via Dependence Maximization

Song, L., Smola, A., Gretton, A., Bedo, J., Borgwardt, K.

Journal of Machine Learning Research, 13, pages: 1393-1434, May 2012 (article)

Abstract
We introduce a framework of feature selection based on dependence maximization between the selected features and the labels of an estimation problem, using the Hilbert-Schmidt Independence Criterion. The key idea is that good features should be highly dependent on the labels. Our approach leads to a greedy procedure for feature selection. We show that a number of existing feature selectors are special cases of this framework. Experiments on both artificial and real-world data show that our feature selector works well in practice.

PDF Project Page [BibTex]

PDF Project Page [BibTex]


On the Empirical Estimation of Integral Probability Metrics

Sriperumbudur, B., Fukumizu, K., Gretton, A., Schölkopf, B., Lanckriet, G.

Electronic Journal of Statistics, 6, pages: 1550-1599, 2012 (article)

Web DOI Project Page [BibTex]

Web DOI Project Page [BibTex]


Optimal kernel choice for large-scale two-sample tests

Gretton, A., Sriperumbudur, B., Sejdinovic, D., Strathmann, H., Balakrishnan, S., Pontil, M., Fukumizu, K.

In Advances in Neural Information Processing Systems 25, pages: 1214-1222, (Editors: P Bartlett and FCN Pereira and CJC. Burges and L Bottou and KQ Weinberger), Curran Associates Inc., 26th Annual Conference on Neural Information Processing Systems (NIPS), 2012 (inproceedings)

PDF Project Page [BibTex]

PDF Project Page [BibTex]


Conditional mean embeddings as regressors

Grünewälder, S., Lever, G., Baldassarre, L., Patterson, S., Gretton, A., Pontil, M.

In Proceedings of the 29th International Conference on Machine Learning, pages: 1823-1830, (Editors: J Langford and J Pineau), Omnipress, New York, NY, USA, ICML, 2012 (inproceedings)

PDF Project Page [BibTex]

PDF Project Page [BibTex]


Modelling transition dynamics in MDPs with RKHS embeddings

Grünewälder, S., Lever, G., Baldassarre, L., Pontil, M., Gretton, A.

In Proceedings of the 29th International Conference on Machine Learning, pages: 535-542, (Editors: J Langford and J Pineau), Omnipress, New York, NY, USA, ICML, 2012 (inproceedings)

PDF Project Page [BibTex]

PDF Project Page [BibTex]


Learning from distributions via support measure machines

Muandet, K., Fukumizu, K., Dinuzzo, F., Schölkopf, B.

In Advances in Neural Information Processing Systems 25, pages: 10-18, (Editors: P Bartlett, FCN Pereira, CJC. Burges, L Bottou, and KQ Weinberger), Curran Associates Inc., 26th Annual Conference on Neural Information Processing Systems (NIPS), 2012 (inproceedings)

PDF Project Page [BibTex]

PDF Project Page [BibTex]


Hilbert Space Embeddings of POMDPs

Nishiyama, Y., Boularias, A., Gretton, A., Fukumizu, K.

In Conference on Uncertainty in Artificial Intelligence (UAI), 2012 (inproceedings)

PDF Web Project Page [BibTex]

PDF Web Project Page [BibTex]


Hilbert space embedding for Dirichlet Process mixtures

Muandet, K.

In NIPS Workshop on confluence between kernel methods and graphical models, 2012 (inproceedings) To be published

Project Page [BibTex]

Project Page [BibTex]

2011


Kernel Bayes’ Rule

Fukumizu, K., Song, L., Gretton, A.

In Advances in Neural Information Processing Systems 24, pages: 1737-1745, (Editors: J Shawe-Taylor and RS Zemel and P Bartlett and F Pereira and KQ Weinberger), Curran Associates, Inc., Red Hook, NY, USA, Twenty-Fifth Annual Conference on Neural Information Processing Systems (NIPS), 2011 (inproceedings)

PDF Project Page [BibTex]

2011

PDF Project Page [BibTex]


Kernel Belief Propagation

Song, L., Gretton, A., Bickson, D., Low, Y., Guestrin, C.

In Proceedings of the 14th International Conference on Artificial Intelligence and Statistics, Vol. 15, pages: 707-715, (Editors: G Gordon and D Dunson and M Dudík), JMLR, AISTATS, 2011 (inproceedings)

PDF Project Page [BibTex]

PDF Project Page [BibTex]


Kernel-based Conditional Independence Test and Application in Causal Discovery

Zhang, K., Peters, J., Janzing, D., Schölkopf, B.

In pages: 804-813, (Editors: FG Cozman and A Pfeffer), AUAI Press, Corvallis, OR, USA, 27th Conference on Uncertainty in Artificial Intelligence (UAI), July 2011 (inproceedings)

Abstract
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis of conditional independence. The proposed method is computationally efficient and easy to implement. Experimental results show that it outperforms other methods, especially when the conditioning set is large or the sample size is not very large, in which case other methods encounter difficulties.

PDF Web Project Page Project Page [BibTex]

PDF Web Project Page Project Page [BibTex]

2010


Consistent Nonparametric Tests of Independence

Gretton, A., Györfi, L.

Journal of Machine Learning Research, 11, pages: 1391-1423, 2010 (article)

PDF Project Page [BibTex]

2010

PDF Project Page [BibTex]


Hilbert Space Embeddings and Metrics on Probability Measures

Sriperumbudur, B., Gretton, A., Fukumizu, K., Schölkopf, B., Lanckriet, G.

Journal of Machine Learning Research, 11, pages: 1517-1561, April 2010 (article)

PDF Project Page [BibTex]

PDF Project Page [BibTex]


Nonparametric Tree Graphical Models

Song, L., Gretton, A., Guestrin, C.

In Proceedings of the 13th International Conference on Artificial Intelligence and Statistics, Volume 9 , pages: 765-772, (Editors: YW Teh and M Titterington ), JMLR, AISTATS, 2010 (inproceedings)

PDF Project Page [BibTex]

PDF Project Page [BibTex]


Non-parametric estimation of integral probability metrics

Sriperumbudur, B., Fukumizu, K., Gretton, A., Schölkopf, B., Lanckriet, G.

In Proceedings of the IEEE International Symposium on Information Theory (ISIT 2010), pages: 1428-1432, IEEE, Piscataway, NJ, USA, IEEE International Symposium on Information Theory (ISIT), June 2010 (inproceedings)

Abstract
In this paper, we develop and analyze a nonparametric method for estimating the class of integral probability metrics (IPMs), examples of which include the Wasserstein distance, Dudley metric, and maximum mean discrepancy (MMD). We show that these distances can be estimated efficiently by solving a linear program in the case of Wasserstein distance and Dudley metric, while MMD is computable in a closed form. All these estimators are shown to be strongly consistent and their convergence rates are analyzed. Based on these results, we show that IPMs are simple to estimate and the estimators exhibit good convergence behavior compared to fi-divergence estimators.

PDF Web DOI Project Page [BibTex]

PDF Web DOI Project Page [BibTex]

2009


Kernel Choice and Classifiability for RKHS Embeddings of Probability Distributions

Sriperumbudur, B., Fukumizu, K., Gretton, A., Lanckriet, G., Schölkopf, B.

In Advances in Neural Information Processing Systems 22, pages: 1750-1758, (Editors: Y Bengio and D Schuurmans and J Lafferty and C Williams and A Culotta), Curran, Red Hook, NY, USA, 23rd Annual Conference on Neural Information Processing Systems (NIPS), 2009 (inproceedings)

Abstract
Embeddings of probability measures into reproducing kernel Hilbert spaces have been proposed as a straightforward and practical means of representing and comparing probabilities. In particular, the distance between embeddings (the maximum mean discrepancy, or MMD) has several key advantages over many classical metrics on distributions, namely easy computability, fast convergence and low bias of finite sample estimates. An important requirement of the embedding RKHS is that it be characteristic: in this case, the MMD between two distributions is zero if and only if the distributions coincide. Three new results on the MMD are introduced in the present study. First, it is established that MMD corresponds to the optimal risk of a kernel classifier, thus forming a natural link between the distance between distributions and their ease of classification. An important consequence is that a kernel must be characteristic to guarantee classifiability between distributions in the RKHS. Second, the class of characteristic kernels is broadened to incorporate all strictly positive definite kernels: these include non-translation invariant kernels and kernels on non-compact domains. Third, a generalization of the MMD is proposed for families of kernels, as the supremum over MMDs on a class of kernels (for instance the Gaussian kernels with different bandwidths). This extension is necessary to obtain a single distance measure if a large selection or class of characteristic kernels is potentially appropriate. This generalization is reasonable, given that it corresponds to the problem of learning the kernel by minimizing the risk of the corresponding kernel classifier. The generalized MMD is shown to have consistent finite sample estimates, and its performance is demonstrated on a homogeneity testing example.

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2009

PDF Web Project Page [BibTex]

2008


Nonparametric Indepedence Tests: Space Partitioning and Kernel Approaches

Gretton, A., Györfi, L.

19th International Conference on Algorithmic Learning Theory (ALT08), October 2008 (talk)

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2008

PDF Web Project Page [BibTex]