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2019

Unbiased estimators for the variance of MMD estimators

Sutherland, Danica J., Deka, Namrata

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Understand

The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al.

2012), bearing a simple estimator with pleasing computational and statistical properties.
Being able to efficiently estimate the variance of this estimator is very helpful to various problems in two-sample testing.
Towards this end, Bounliphone et al.

Unbiased estimators for the variance of MMD estimators · Around

Built on

“Approximation Theorems of Mathematical Statistics”
Robert. Serfling · 1980
Earlier work this paper cites.
“A Kernel Two-Sample Test”
Arthur Gretton, Karsten. Borgwardt, Malte Rasch, Bernhard Schölkopf and Alex. Smola · 2012
Earlier work this paper cites.
“A Test of Relative Similarity For Model Selection in Generative Models”
Original
Wacha Bounliphone, Eugene Belilovsky, Matthew. Blaschko, Ioannis Antonoglou and Arthur Gretton · 2016
Earlier work this paper cites.

Similar

“Kernel Mean Embedding of Distributions: A Review and Beyond”
Original
Krikamol Muandet, Kenji Fukumizu, Bharath Sriperumbudur and Bernhard Schölkopf · 2017
Cited alongside, same era.
“Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy”
Original
Danica. Sutherland, Hsiao-Yu Tung, Heiko Strathmann, Soumyajit De, Aaditya Ramdas, Alex Smola and Arthur Gretton · 2017
Cited alongside, same era.

Then

“Learning Deep Kernels for Non-Parametric Two-Sample Tests”
Feng Liu, Wenkai Xu, Jie Lu, Guangquan Zhang, Arthur Gretton and Danica. Sutherland · 2020
Closest in time.
“MMD-B-Fair: Learning Fair Representations with Statistical Testing”, 2022
Namrata Deka and Danica. Sutherland · 2022
Closest in time.

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