A Bayesian nonparametric multi-sample test in any dimension

Al-Labadi, Luai; Asl, Forough Fazeli; Saberi, Zahra

doi:10.1007/s10182-021-00419-3

Cited by 2 publications

(7 citation statements)

References 29 publications

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“…Therefore we cannot arbitrarily drive to type I error rate to zero. Moreover, the p-value in frequentist tests does not allow researchers to provide evidence for the null hypothesis while also exaggerating the evidence against the null hypothesis ( Al-Labadi et al, 2022a). When H 0 should be rejected, the p-value in frequentist tests goes to zero as the sample size increases.…”

Section: Previous Workmentioning

confidence: 99%

“…Previous work has been developed to deal with these problems by proposing Bayesian counterparts to popular frequentist two-sample tests (Kelter, 2021;Al-Labadi and Zarepour, 2017;Al-Labadi, 2021;Al-Labadi et al, 2022a). In BNP hypothesis testing, we model the unknown distributions using infinite dimensional probability distributions as prior beliefs.…”

Section: Previous Workmentioning

confidence: 99%

“…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%

“…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. For instance, Al-Labadi et al (2022a) proposed a BNP multi-sample test based on this strategy by placing the Dirichlet process (DP) prior on unknown distributions and using the energy distance as the discrepancy measure δ with applications in high-dimensional data.…”

Section: Previous Workmentioning

confidence: 99%

“…The DP is the most commonly used prior in BNP inference and can be viewed as an infinite-dimensional generalization of the Dirichlet distribution constructed around a fixed probability measure, whose variation is controlled by a positive real number. Although a particular case of the test of Al-Labadi et al (2022a) can be used to compare distributions F 1 and F 2 , it cannot be considered a convenient discriminator in training GANs. In GANs, the objective is updating the parameter w of the deterministic generative neural network G w .…”

Section: Previous Workmentioning

confidence: 99%

See 4 more Smart Citations

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%