Arthur Gretton

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)

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2014

Muandet, K., Fukumizu, K., Sriperumbudur, B., Gretton, A., Schölkopf, B. Kernel Mean Estimation and Stein Effect 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)

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2012

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.

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2012

Song, L., Smola, A., Gretton, A., Bedo, J., Borgwardt, K. Feature Selection via Dependence Maximization Journal of Machine Learning Research, 13, pages: 1393-1434, May 2012 (article)

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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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Gretton, A., Borgwardt, K., Rasch, M., Schölkopf, B., Smola, A. A Kernel Two-Sample Test Journal of Machine Learning Research, 13, pages: 723-773, March 2012 (article)

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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)

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Grünewälder, S., Lever, G., Baldassarre, L., Pontil, M., Gretton, A. Modelling transition dynamics in MDPs with RKHS embeddings 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)

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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]

Sriperumbudur, B., Fukumizu, K., Gretton, A., Schölkopf, B., Lanckriet, G. On the Empirical Estimation of Integral Probability Metrics Electronic Journal of Statistics, 6, pages: 1550-1599, 2012 (article)

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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)

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Grünewälder, S., Lever, G., Baldassarre, L., Patterson, S., Gretton, A., Pontil, M. Conditional mean embeddings as regressors 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)

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Kernel Mean Embeddings of POMDPs

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

21st Machine Learning Summer School , 2012 (poster)

[BibTex]

Nishiyama, Y., Boularias, A., Gretton, A., Fukumizu, K. Kernel Mean Embeddings of POMDPs 21st Machine Learning Summer School , 2012 (poster)

[BibTex]

Kernel Bellman Equations in POMDPs

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

Technical Committee on Infomation-Based Induction Sciences and Machine Learning (IBISML'12), 2012 (talk)

[BibTex]

Nishiyama, Y., Boularias, A., Gretton, A., Fukumizu, K. Kernel Bellman Equations in POMDPs Technical Committee on Infomation-Based Induction Sciences and Machine Learning (IBISML'12), 2012 (talk)

[BibTex]

Hypothesis testing using pairwise distances and associated kernels

Sejdinovic, D., Gretton, A., Sriperumbudur, B., Fukumizu, K.

In Proceedings of the 29th International Conference on Machine Learning, pages: 1111-1118, (Editors: J Langford and J Pineau), Omnipress, New York, NY, USA, ICML, 2012 (inproceedings)

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Sejdinovic, D., Gretton, A., Sriperumbudur, B., Fukumizu, K. Hypothesis testing using pairwise distances and associated kernels In Proceedings of the 29th International Conference on Machine Learning, pages: 1111-1118, (Editors: J Langford and J Pineau), Omnipress, New York, NY, USA, ICML, 2012 (inproceedings)

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Hilbert Space Embeddings of POMDPs

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

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

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Nishiyama, Y., Boularias, A., Gretton, A., Fukumizu, K. Hilbert Space Embeddings of POMDPs In Conference on Uncertainty in Artificial Intelligence (UAI), 2012 (inproceedings)

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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)

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Gretton, A., Sriperumbudur, B., Sejdinovic, D., Strathmann, H., Balakrishnan, S., Pontil, M., Fukumizu, K. Optimal kernel choice for large-scale two-sample tests 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)

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2011

Semi-supervised kernel canonical correlation analysis with application to human fMRI

Blaschko, M., Shelton, J., Bartels, A., Lampert, C., Gretton, A.

Pattern Recognition Letters, 32(11):1572-1583 , August 2011 (article)

Abstract

Kernel canonical correlation analysis (KCCA) is a general technique for subspace learning that incorporates principal components analysis (PCA) and Fisher linear discriminant analysis (LDA) as special cases. By finding directions that maximize correlation, KCCA learns representations that are more closely tied to the underlying process that generates the data and can ignore high-variance noise directions. However, for data where acquisition in one or more modalities is expensive or otherwise limited, KCCA may suffer from small sample effects. We propose to use semi-supervised Laplacian regularization to utilize data that are present in only one modality. This approach is able to find highly correlated directions that also lie along the data manifold, resulting in a more robust estimate of correlated subspaces. Functional magnetic resonance imaging (fMRI) acquired data are naturally amenable to subspace techniques as data are well aligned. fMRI data of the human brain are a particularly interesting candidate. In this study we implemented various supervised and semi-supervised versions of KCCA on human fMRI data, with regression to single and multi-variate labels (corresponding to video content subjects viewed during the image acquisition). In each variate condition, the semi-supervised variants of KCCA performed better than the supervised variants, including a supervised variant with Laplacian regularization. We additionally analyze the weights learned by the regression in order to infer brain regions that are important to different types of visual processing.

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2011

Blaschko, M., Shelton, J., Bartels, A., Lampert, C., Gretton, A. Semi-supervised kernel canonical correlation analysis with application to human fMRI Pattern Recognition Letters, 32(11):1572-1583 , August 2011 (article)

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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)

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Fukumizu, K., Song, L., Gretton, A. Kernel Bayes’ Rule 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)

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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)

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Song, L., Gretton, A., Bickson, D., Low, Y., Guestrin, C. Kernel Belief Propagation 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)

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Parallel Gibbs Sampling: From Colored Fields to Thin Junction Trees

Gonzalez, J., Low, Y., Gretton, A., Guestrin, C.

In Proceedings of the 14th International Conference on Artificial Intelligence and Statistics, Vol. 15, pages: 324-332, (Editors: G Gordon and D Dunson and M Dudík), JMLR, AISTATS, 2011 (inproceedings)

PDF [BibTex]

Gonzalez, J., Low, Y., Gretton, A., Guestrin, C. Parallel Gibbs Sampling: From Colored Fields to Thin Junction Trees In Proceedings of the 14th International Conference on Artificial Intelligence and Statistics, Vol. 15, pages: 324-332, (Editors: G Gordon and D Dunson and M Dudík), JMLR, AISTATS, 2011 (inproceedings)

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2010

Similarities in resting state and feature-driven activity: Non-parametric evaluation of human fMRI

Shelton, J., Blaschko, M., Gretton, A., Müller, J., Fischer, E., Bartels, A.

NIPS Workshop on Learning and Planning from Batch Time Series Data, December 2010 (poster)

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