A Wild Bootstrap for Degenerate Kernel Tests

By Kacper P. Chwialkowski, Dino Sejdinovic, Arthur Gretton. 2014

64 citations recorded by the source corpus.

A wild bootstrap method for nonparametric hypothesis tests based on kernel distribution embeddings is proposed. This bootstrap method is used to construct provably consistent tests that apply to random processes, for which the naive permutation-based bootstrap fails. It applies to a large group of kernel tests based on V-statistics, which are degenerate under the null hypothesis, and non-degenerate elsewhere. To illustrate this approach, we construct a two-sample test, an instantaneous independence test and a multiple lag independence test for time series. In experiments, the wild bootstrap gives strong performance on synthetic examples, on audio data, and in performance benchmarking for the Gibbs sampler. The code is available at https://github.com/kacperChwialkowski/wildBootstrap.

Subfields: Artificial Intelligence, Finance, 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. Bernhard Schölkopf
2. Arthur Gretton
3. Kenji Fukumizu
4. Bharath K. Sriperumbudur
5. Jan Peters
6. Krikamol Muandet
7. David Lopez-Paz
8. Michael I. Jordan

In Finance

1. Bernhard Schölkopf
2. Kenji Fukumizu
3. Krikamol Muandet
4. Bharath K. Sriperumbudur
5. Arthur Gretton
6. Jan Peters
7. Kacper P. Chwialkowski
8. Heiko Strathmann

In Statistics and Probability

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

In Statistical Learning Theory

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

Citations in the corpus

• Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “For instance, Gretton et al. (2005a) uses a Hilbert-Schmidt norm of the cross-covariance operator as a measure of statistical dependence between two random variables; see also Chwialkowski and Gretton (2014) and Chwialkowski et al. (2014) for an extension to random processes.”
• Kernel‐based tests for joint independence (2016, methodology): “In Chwialkowski et al. (2014) a similar consistency analysis has been performed for a wild bootstrap approach on time series.”
• A Kernelized Stein Discrepancy for Goodness-of-fit Tests (2016, background): “As a consequence, a line of work has been devoted to approximating the critical values of (15), including bootstrap methods (Arcones & Gine, 1992; Huskova & Janssen, 1993; Chwialkowski et al., 2014) and eigenvalue approximation (Gretton et al.”
• A Kernel Test of Goodness of Fit (2016, methodology): “The validity of this resampling method is guaranteed by the following proposition (which follows from Theorem 2.1 of Leucht and a modification of the Lemma 5 of Chwialkowski et al. (2014)), proved in the supplement.”