Testing Hypotheses by Regularized Maximum Mean Discrepancy

By Somayeh Danafar, Paola M. V. Rancoita, Tobias Glasmachers, Kevin Whittingstall, J. Urgen Schmidhuber. 2013

9 citations recorded by the source corpus.

Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare distributions by the distance between their embeddings. We show that Regularized Maximum Mean Discrepancy (RMMD), our novel measure for kernel-based hypothesis testing, yields substantial improvements even when sample sizes are small, and excels at hypothesis tests involving multiple comparisons with power control. We derive asymptotic distributions under the null and alternative hypotheses, and assess power control. Outstanding results are obtained on: challenging EEG data, MNIST, the Berkley Covertype, and the Flare-Solar dataset.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistics and Probability, Statistical Learning Theory

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Bharath K. Sriperumbudur
2. Kenji Fukumizu
3. Bernhard Schölkopf
4. Krikamol Muandet
5. Arthur Gretton
6. David Lopez-Paz
7. Dino Sejdinovic
8. Le Song

In Computer Vision and Pattern Recognition

1. Bernhard Schölkopf
2. Kenji Fukumizu
3. Bharath K. Sriperumbudur
4. Krikamol Muandet
5. Arthur Gretton
6. Luc Van Gool
7. David Lopez-Paz
8. Dacheng Tao

In Statistics and Probability

1. Kenji Fukumizu
2. Arthur Gretton
3. Bernhard Schölkopf
4. Bharath K. Sriperumbudur
5. Krikamol Muandet
6. Dino Sejdinovic
7. Le Song
8. Jan Peters

In Statistical Learning Theory

1. Kenji Fukumizu
2. Bharath K. Sriperumbudur
3. Bernhard Schölkopf
4. Arthur Gretton
5. Krikamol Muandet
6. Dino Sejdinovic
7. Le Song
8. David Lopez-Paz

Citations in the corpus

• Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Furthermore, Danafar et al. (2014) used the RKHS norm of the mean embeddings to directly regularize the distance between them, resulting in estimates which are similar to (3.”
• Kernel Mean Estimation and Stein's Effect (2013, positive): “Regularized version of MMD was adopted by [22] in the context of kernel-based hypothesis testing.”