Bayesian Kernel Two-Sample Testing

Zhang, Qinyi; Wild, Veit; Filippi, Sarah; Flaxman, Seth; Sejdinović, Dino

doi:10.1080/10618600.2022.2067547

Cited by 1 publication

(1 citation statement)

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“…Another strategy is to compute a discrepancy measure between BNP posteriors of two unknown distributions F 1 and F 2 , denoted by δ(F pos 1 , F pos 2 ) and compare it with the corresponding difference between BNP priors, δ(F pri 1 , F pri 2 ) through the RB ratio (Al-Labadi et al, 2022a;Al-Labadi, 2021;Al-Labadi and Zarepour, 2017;Zhang et al, 2022). The con-centration of δ(F pos 1 , F pos 2 ) around zero being smaller than δ(F pri 1 , F pri 2 ) indicates that the samples support the null hypothesis and vice versa.…”

Section: Previous Workmentioning

confidence: 99%

A Semi-Bayesian Nonparametric Hypothesis Test Using Maximum Mean Discrepancy with Applications in Generative Adversarial Networks

Fazeli-Asl¹,

Zhang²,

Lin³

2023

Preprint

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A classic inferential problem in statistics is the two-sample hypothesis test, where we test whether two samples of observations are either drawn from the same distribution or two distinct distributions. However, standard methods for performing this test require strong distributional assumptions on the two samples of data. We propose a semi-Bayesian nonparametric (semi-BNP) procedure for the two-sample hypothesis testing problem. First, we will derive a novel BNP maximum mean discrepancy (MMD) measure-based hypothesis test. Next, we will show that our proposed test will outperform frequentist MMD-based methods by yielding a smaller false rejection and acceptance rate of the null. Finally, we will show that we can embed our proposed hypothesis testing procedure within a generative adversarial network (GAN) framework as an application of our method. Using our novel BNP hypothesis test, this new GAN approach can help to mitigate the lack of diversity in the generated samples and produce a more accurate inferential algorithm compared to traditional techniques.

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Section: Previous Workmentioning

confidence: 99%