A low variance consistent test of relative dependency

By Wacha Bounliphone, Arthur Gretton, Arthur Tenenhaus, Matthew B. Blaschko. 2014

8 citations recorded by the source corpus.

We describe a novel non-parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables us to determine whether one source variable is significantly more dependent on a first target variable or a second. Dependence is measured via the Hilbert-Schmidt Independence Criterion (HSIC), resulting in a pair of empirical dependence measures (source-target 1, source-target 2). We test whether the first dependence measure is significantly larger than the second. Modeling the covariance between these HSIC statistics leads to a provably more powerful test than the construction of independent HSIC statistics by sub-sampling. The resulting test is consistent and unbiased, and (being based on U-statistics) has favorable convergence properties. The test can be computed in quadratic time, matching the computational complexity of standard empirical HSIC estimators. The effectiveness of the test is demonstrated on several real-world problems: we identify language groups from a multilingual corpus, and we prove that tumor location is more dependent on gene expression than chromosomal imbalances. Source code is available for download at this https URL

Subfields: Artificial Intelligence, Molecular Biology, Statistics and Probability, Information 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. Bharath K. Sriperumbudur
4. Kenji Fukumizu
5. Krikamol Muandet
6. David Lopez-Paz
7. Dino Sejdinovic
8. Le Song

In Molecular Biology

1. Arthur Gretton
2. Kenji Fukumizu
3. Bernhard Schölkopf
4. Bharath K. Sriperumbudur
5. Matthew B. Blaschko
6. Krikamol Muandet
7. Alex Smola
8. Le Song

In Statistics and Probability

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

In Information Theory

1. Kenji Fukumizu
2. Bernhard Schölkopf
3. Arthur Gretton
4. Matthew B. Blaschko
5. Krikamol Muandet
6. Bharath K. Sriperumbudur
7. Dominik Janzing
8. Kun Zhang

Citations in the corpus

• Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Bounliphone et al. (2015) constructs a consistent test for relative dependency which—unlike the Lancaster test of Sejdinovic et al.”
• A Test of Relative Similarity For Model Selection in Generative Models (2015, methodology): “We derive the joint asymptotic distribution of the MMDs in Section 3: this uses similar ideas to the relative dependence test in Bounliphone et al. (2015), with the additional complexity due to there being three independent samples to deal with, rather than a single joint sample.”