Krikamol Muandet

Research Group Leader

Empirical Inference

Office: N4.002
Max-Planck-Ring 4
72076 Tübingen
Germany

+49 7071 601 559

krikamol.muandet

http://krikamol.org

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My current research aims to develop machine learning techniques that will bridge the gap between randomized experiments and empirical inference, enabling machines to better learn causality from data. It has numerous applications in observational studies, medical diagnosis, economics, and online advertisement, for example. To this end, I am employing tools and analyses from related disciplines including but not limited to

Statistical learning theory
Kernels and reproducing kernel Hilbert spaces (RKHSs)
Hilbert space embedding of probability distributions
Potential outcome framework and Rubin's causal model

In general, I aim to address the most fundamental problems in machine learning and to leverage such insights in solving real-world problems in related disciplines. You can find more information about me and my work at http://krikamol.org.

Kernel methods Observational studies Causal inference RKHS

These are examples of projects I have been working on.

Counterfactual mean embedding
Counterfactual policy gradient for observational studies
Randomization via generalization

My full research statement can also be found at http://krikamol.org/krikamol-research.pdf.

Learning Algorithms

A learning algorithm is the backbone of machine learning that distinguishes it from traditional computer programming by allowing data-driven model building. In the past years, we have developed learning algorithms using a number and tools and for diverse application domains, as outlined below.

Learning with...
Anant Raj Wittawat Jitkrittum Krikamol Muandet Bernhard Schölkopf Giambattista Parascandolo Mateo Rojas-Carulla Rohit Babbar Niki Kilbertus Mehdi S. M. Sajjadi

Statistical Learning Theory

Machine learning algorithms are designed to generalize from past observations across different problem settings. The goal of learning theory is to analyze statistical and computational properties of learning algorithms and to provide guarantees on their performance. To do so, it poses these tasks in a rigorous mathematical fram...

Ilya Tolstikhin Ruth Urner Carl Johann Simon-Gabriel Matej Balog Adam Scibior Krikamol Muandet Paul Rubenstein Bernhard Schölkopf

36 results (View BibTeX file of all listed publications)

2020

Kernel Conditional Moment Test via Maximum Moment Restriction

Muandet, K., Jitkrittum, W., Kübler, J. M.

Proceedings of the 36th International Conference on Uncertainty in Artificial Intelligence (UAI), August 2020 (conference) Accepted

[BibTex]

2020

Muandet, K., Jitkrittum, W., Kübler, J. M. Kernel Conditional Moment Test via Maximum Moment Restriction Proceedings of the 36th International Conference on Uncertainty in Artificial Intelligence (UAI), August 2020 (conference) Accepted

[BibTex]

A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming

Zhu, J., Muandet, K., Diehl, M., Schölkopf, B.

21rst IFAC World Congress, July 2020 (conference) Accepted

arXiv [BibTex]

Zhu, J., Muandet, K., Diehl, M., Schölkopf, B. A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming 21rst IFAC World Congress, July 2020 (conference) Accepted

arXiv [BibTex]

Kernel Conditional Density Operators

Schuster, I., Mollenhauer, M., Klus, S., Muandet, K.

Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), Proceedings of Machine Learning Research, June 2020 (conference) Accepted

[BibTex]

Schuster, I., Mollenhauer, M., Klus, S., Muandet, K. Kernel Conditional Density Operators Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), Proceedings of Machine Learning Research, June 2020 (conference) Accepted

[BibTex]

Fair Decisions Despite Imperfect Predictions

Kilbertus, N., Gomez Rodriguez, M., Schölkopf, B., Muandet, K., Valera, I.

Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), 2020 (conference) Accepted

[BibTex]

Kilbertus, N., Gomez Rodriguez, M., Schölkopf, B., Muandet, K., Valera, I. Fair Decisions Despite Imperfect Predictions Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), 2020 (conference) Accepted

[BibTex]

Counterfactual Mean Embedding

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukatat, S.

Journal of Machine Learning Research, 2020 (article) Accepted

[BibTex]

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukatat, S. Counterfactual Mean Embedding Journal of Machine Learning Research, 2020 (article) Accepted

[BibTex]

2019

Local Temporal Bilinear Pooling for Fine-grained Action Parsing

Zhang, Y., Tang, S., Muandet, K., Jarvers, C., Neumann, H.

In Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), IEEE International Conference on Computer Vision and Pattern Recognition (CVPR) 2019, June 2019 (inproceedings)

Abstract

Fine-grained temporal action parsing is important in many applications, such as daily activity understanding, human motion analysis, surgical robotics and others requiring subtle and precise operations in a long-term period. In this paper we propose a novel bilinear pooling operation, which is used in intermediate layers of a temporal convolutional encoder-decoder net. In contrast to other work, our proposed bilinear pooling is learnable and hence can capture more complex local statistics than the conventional counterpart. In addition, we introduce exact lower-dimension representations of our bilinear forms, so that the dimensionality is reduced with neither information loss nor extra computation. We perform intensive experiments to quantitatively analyze our model and show the superior performances to other state-of-the-art work on various datasets.

Code video demo pdf link (url) [BibTex]

2019

Zhang, Y., Tang, S., Muandet, K., Jarvers, C., Neumann, H. Local Temporal Bilinear Pooling for Fine-grained Action Parsing In Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), IEEE International Conference on Computer Vision and Pattern Recognition (CVPR) 2019, June 2019 (inproceedings)

Code video demo pdf link (url) [BibTex]

Witnessing Adversarial Training in Reproducing Kernel Hilbert Spaces

Mehrjou, A., Jitkrittum, W., Schölkopf, B., Muandet, K.

2019 (conference) Submitted

arXiv [BibTex]

Mehrjou, A., Jitkrittum, W., Schölkopf, B., Muandet, K. Witnessing Adversarial Training in Reproducing Kernel Hilbert Spaces 2019 (conference) Submitted

arXiv [BibTex]

Quantum mean embedding of probability distributions

Kübler, J. M., Muandet, K., Schölkopf, B.

Physical Review Research, 1(3):033159, American Physical Society, 2019 (article)

link (url) DOI [BibTex]

Kübler, J. M., Muandet, K., Schölkopf, B. Quantum mean embedding of probability distributions Physical Review Research, 1(3):033159, American Physical Society, 2019 (article)

link (url) DOI [BibTex]

Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces

Klus, S., Schuster, I., Muandet, K.

Journal of Nonlinear Science, 2019, First Online: 21 August 2019 (article)

DOI [BibTex]

Klus, S., Schuster, I., Muandet, K. Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces Journal of Nonlinear Science, 2019, First Online: 21 August 2019 (article)

DOI [BibTex]

2018

Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S.

Workshop on Machine Learning for Causal Inference, Counterfactual Prediction, and Autonomous Action (CausalML) at ICML, July 2018 (conference)

[BibTex]

2018

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S. Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference Workshop on Machine Learning for Causal Inference, Counterfactual Prediction, and Autonomous Action (CausalML) at ICML, July 2018 (conference)

[BibTex]

Design and Analysis of the NIPS 2016 Review Process

Shah*, N., Tabibian*, B., Muandet, K., Guyon, I., von Luxburg, U.

Journal of Machine Learning Research, 19(49):1-34, 2018, *equal contribution (article)

arXiv link (url) Project Page Project Page [BibTex]

Shah*, N., Tabibian*, B., Muandet, K., Guyon, I., von Luxburg, U. Design and Analysis of the NIPS 2016 Review Process Journal of Machine Learning Research, 19(49):1-34, 2018, *equal contribution (article)

arXiv link (url) Project Page Project Page [BibTex]

Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract

This paper introduces a novel Hilbert space representation of a counterfactual distribution---called counterfactual mean embedding (CME)---with applications in nonparametric causal inference. Counterfactual prediction has become an ubiquitous tool in machine learning applications, such as online advertisement, recommendation systems, and medical diagnosis, whose performance relies on certain interventions. To infer the outcomes of such interventions, we propose to embed the associated counterfactual distribution into a reproducing kernel Hilbert space (RKHS) endowed with a positive definite kernel. Under appropriate assumptions, the CME allows us to perform causal inference over the entire landscape of the counterfactual distribution. The CME can be estimated consistently from observational data without requiring any parametric assumption about the underlying distributions. We also derive a rate of convergence which depends on the smoothness of the conditional mean and the Radon-Nikodym derivative of the underlying marginal distributions. Our framework can deal with not only real-valued outcome, but potentially also more complex and structured outcomes such as images, sequences, and graphs. Lastly, our experimental results on off-policy evaluation tasks demonstrate the advantages of the proposed estimator.

arXiv [BibTex]

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S. Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

arXiv [BibTex]

2017

Kernel Mean Embedding of Distributions: A Review and Beyond

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

Foundations and Trends in Machine Learning, 10(1-2):1-141, 2017 (article)

DOI Project Page [BibTex]

2017

Muandet, K., Fukumizu, K., Sriperumbudur, B., Schölkopf, B. Kernel Mean Embedding of Distributions: A Review and Beyond Foundations and Trends in Machine Learning, 10(1-2):1-141, 2017 (article)

DOI Project Page [BibTex]

Minimax Estimation of Kernel Mean Embeddings

Tolstikhin, I., Sriperumbudur, B., Muandet, K.

Journal of Machine Learning Research, 18(86):1-47, 2017 (article)

link (url) Project Page [BibTex]

Tolstikhin, I., Sriperumbudur, B., Muandet, K. Minimax Estimation of Kernel Mean Embeddings Journal of Machine Learning Research, 18(86):1-47, 2017 (article)

link (url) Project Page [BibTex]

2016

TerseSVM : A Scalable Approach for Learning Compact Models in Large-scale Classification

Babbar, R., Muandet, K., Schölkopf, B.

Proceedings of the 2016 SIAM International Conference on Data Mining (SDM), pages: 234-242, (Editors: Sanjay Chawla Venkatasubramanian and Wagner Meira), May 2016 (conference)

DOI Project Page [BibTex]

2016

Babbar, R., Muandet, K., Schölkopf, B. TerseSVM : A Scalable Approach for Learning Compact Models in Large-scale Classification Proceedings of the 2016 SIAM International Conference on Data Mining (SDM), pages: 234-242, (Editors: Sanjay Chawla Venkatasubramanian and Wagner Meira), May 2016 (conference)

DOI Project Page [BibTex]

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) [BibTex]

Muandet, K., Sriperumbudur, B., Fukumizu, K., Gretton, A., Schölkopf, B. Kernel Mean Shrinkage Estimators Journal of Machine Learning Research, 17(48):1-41, 2016 (article)

link (url) [BibTex]

2015

From Points to Probability Measures: A Statistical Learning on Distributions with Kernel Mean Embedding

Muandet, K.

University of Tübingen, Germany, University of Tübingen, Germany, September 2015 (phdthesis)

[BibTex]

2015

Muandet, K. From Points to Probability Measures: A Statistical Learning on Distributions with Kernel Mean Embedding University of Tübingen, Germany, University of Tübingen, Germany, September 2015 (phdthesis)

[BibTex]

The Randomized Causation Coefficient

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

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

link (url) [BibTex]

Lopez-Paz, D., Muandet, K., Recht, B. The Randomized Causation Coefficient Journal of Machine Learning, 16, pages: 2901-2907, 2015 (article)

link (url) [BibTex]

Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations

Schölkopf, B., Muandet, K., Fukumizu, K., Harmeling, S., Peters, J.

Statistics and Computing , 25(4):755-766, 2015 (article)

DOI [BibTex]

Schölkopf, B., Muandet, K., Fukumizu, K., Harmeling, S., Peters, J. Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations Statistics and Computing , 25(4):755-766, 2015 (article)

DOI [BibTex]

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 [BibTex]

Lopez-Paz, D., Muandet, K., Schölkopf, B., Tolstikhin, I. Towards a Learning Theory of Cause-Effect Inference 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 [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)

PDF [BibTex]

2014

Doran, G., Muandet, K., Zhang, K., Schölkopf, B. A Permutation-Based Kernel Conditional Independence Test 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)

PDF [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) [BibTex]

Muandet, K., Sriperumbudur, B., Schölkopf, B. Kernel Mean Estimation via Spectral Filtering 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) [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)

[BibTex]

Zhang, K., Schölkopf, B., Muandet, K., Wang, Z., Zhou, Z., Persello, C. Single-Source Domain Adaptation with Target and Conditional Shift 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)

[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 [BibTex]

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)

PDF [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)

PDF Web [BibTex]

2013

Zhang, K., Schölkopf, B., Muandet, K., Wang, Z. Domain adaptation under Target and Conditional Shift 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)

PDF Web [BibTex]

Domain Generalization via Invariant Feature Representation

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

30th International Conference on Machine Learning (ICML2013), 2013 (poster)

PDF [BibTex]

Muandet, K., Balduzzi, D., Schölkopf, B. Domain Generalization via Invariant Feature Representation 30th International Conference on Machine Learning (ICML2013), 2013 (poster)

PDF [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 [BibTex]

Muandet, K., Schölkopf, B. One-class Support Measure Machines for Group Anomaly Detection 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 [BibTex]

One-class Support Measure Machines for Group Anomaly Detection

Muandet, K., Schölkopf, B.

29th Conference on Uncertainty in Artificial Intelligence (UAI), 2013 (poster)

PDF [BibTex]

Muandet, K., Schölkopf, B. One-class Support Measure Machines for Group Anomaly Detection 29th Conference on Uncertainty in Artificial Intelligence (UAI), 2013 (poster)

PDF [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 [BibTex]

Muandet, K., Balduzzi, D., Schölkopf, B. Domain Generalization via Invariant Feature Representation 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 [BibTex]

Domain Generalization via Invariant Feature Representation

Muandet, K.

30th International Conference on Machine Learning (ICML2013), 2013 (talk)

PDF [BibTex]

Muandet, K. Domain Generalization via Invariant Feature Representation 30th International Conference on Machine Learning (ICML2013), 2013 (talk)

PDF [BibTex]

2012

Support Vector Machines, Support Measure Machines, and Quasar Target Selection

Muandet, K.

Center for Cosmology and Particle Physics (CCPP), New York University, December 2012 (talk)

[BibTex]

2012

Muandet, K. Support Vector Machines, Support Measure Machines, and Quasar Target Selection Center for Cosmology and Particle Physics (CCPP), New York University, December 2012 (talk)

[BibTex]

Hilbert Space Embedding for Dirichlet Process Mixtures

Muandet, K.

NIPS Workshop on Confluence between Kernel Methods and Graphical Models, December 2012 (talk)

[BibTex]

Muandet, K. Hilbert Space Embedding for Dirichlet Process Mixtures NIPS Workshop on Confluence between Kernel Methods and Graphical Models, December 2012 (talk)

[BibTex]

Support Measure Machines for Quasar Target Selection

Muandet, K.

Astro Imaging Workshop, 2012 (talk)

Abstract

In this talk I will discuss the problem of quasar target selection. The objects attributes in astronomy such as fluxes are often subjected to substantial and heterogeneous measurement uncertainties, especially for the medium-redshift between 2.2 and 3.5 quasars which is relatively rare and must be targeted down to g ~ 22 mag. Most of the previous works for quasar target selection includes UV-excess, kernel density estimation, a likelihood approach, and artificial neural network cannot directly deal with the heterogeneous input uncertainties. Recently, extreme deconvolution (XD) has been used to tackle this problem in a well-posed manner. In this work, we present a discriminative approach for quasar target selection that can deal with input uncertainties directly. To do so, we represent each object as a Gaussian distribution whose mean is the object's attribute vector and covariance is the given flux measurement uncertainty. Given a training set of Gaussian distributions, the support measure machines (SMMs) algorithm are trained and used to build the quasar targeting catalog. Preliminary results will also be presented. Joint work with Jo Bovy and Bernhard Sch{\"o}lkopf

Web [BibTex]

Muandet, K. Support Measure Machines for Quasar Target Selection Astro Imaging Workshop, 2012 (talk)

Web [BibTex]

Learning from Distributions via Support Measure Machines

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

26th Annual Conference on Neural Information Processing Systems (NIPS), 2012 (poster)

PDF [BibTex]

Muandet, K., Fukumizu, K., Dinuzzo, F., Schölkopf, B. Learning from Distributions via Support Measure Machines 26th Annual Conference on Neural Information Processing Systems (NIPS), 2012 (poster)

PDF [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 [BibTex]

Muandet, K., Fukumizu, K., Dinuzzo, F., Schölkopf, B. Learning from distributions via support measure machines 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 [BibTex]

Hilbert space embedding for Dirichlet Process mixtures

Muandet, K.

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

arXiv [BibTex]

Muandet, K. Hilbert space embedding for Dirichlet Process mixtures In NIPS Workshop on confluence between kernel methods and graphical models, 2012 (inproceedings)

arXiv [BibTex]

Krikamol Muandet

Learning with... Anant Raj Wittawat Jitkrittum Krikamol Muandet Bernhard Schölkopf Giambattista Parascandolo Mateo Rojas-Carulla Rohit Babbar Niki Kilbertus Mehdi S. M. Sajjadi

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Learning with...
Anant Raj Wittawat Jitkrittum Krikamol Muandet Bernhard Schölkopf Giambattista Parascandolo Mateo Rojas-Carulla Rohit Babbar Niki Kilbertus Mehdi S. M. Sajjadi