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Multivariate Rank-Based Statistic Using Optimal Transport : = Generative Modeling and Change Point Detection.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Multivariate Rank-Based Statistic Using Optimal Transport :/
Reminder of title:	Generative Modeling and Change Point Detection.
Author:	Masud, Shoaib Bin.
Description:	1 online resource (149 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-08, Section: B.
Contained By:	Dissertations Abstracts International85-08B.
Subject:	Electrical engineering. -
Online resource:	click for full text (PQDT)
ISBN:	9798381701876

Multivariate Rank-Based Statistic Using Optimal Transport : = Generative Modeling and Change Point Detection.
Masud, Shoaib Bin.

Multivariate Rank-Based Statistic Using Optimal Transport :Generative Modeling and Change Point Detection. - 1 online resource (149 pages)

Source: Dissertations Abstracts International, Volume: 85-08, Section: B.

Thesis (Ph.D.)--Tufts University, 2024.

Includes bibliographical references

The theory of optimal transport has been utilized to extend the notion of rank to the multivariate setting and develop statistics for measuring the goodness-of-fit (GoF) between two distributions in a distribution-free two-sample testing framework. Two such statistics are rank energy (RE) and rank maximum mean discrepancy (RMMD), which are distribution-free under the null hypothesis and exhibit high power in statistical testing while being robust to outliers. However, these statistics suffer from computational complexity, high sample complexity, sensitivity to small distributional perturbations, and non-differentiability with respect to the data. Unlike other GoF statistics such as MMD and Wasserstein-1 distance, which can be seamlessly integrated into generative modeling frameworks, RE and RMMD cannot serve as objective functions due to their non-differentiability. Additionally, their sensitivity to small perturbations hampers their robustness in sliding window-based change point detection (CPD) frameworks. To address these practical challenges, we propose novel variants of these statistics called soft rank energy (sRE) and soft rank maximum mean discrepancy (sRMMD) by employing entropy-regularized optimal transport maps in place of the rank map. Leveraging the differentiability property, we demonstrate the effectiveness of these statistics in generative modeling tasks, specifically in image generation and generating valid knockoffs for statistically significant feature selection. Furthermore, we apply both RE and sRE statistics to offline, unsupervised change point detection and extensively evaluate their performance using synthetic and real-world data. The results indicate that sRE outperforms RE and other commonly used GoF statistics for change point detection, as measured by performance metrics commonly employed in CPD literature.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798381701876Subjects--Topical Terms:

596380
Electrical engineering.
Subjects--Index Terms:

Change point detectionIndex Terms--Genre/Form:

554714
Electronic books.

Multivariate Rank-Based Statistic Using Optimal Transport : = Generative Modeling and Change Point Detection.
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520 $a The theory of optimal transport has been utilized to extend the notion of rank to the multivariate setting and develop statistics for measuring the goodness-of-fit (GoF) between two distributions in a distribution-free two-sample testing framework. Two such statistics are rank energy (RE) and rank maximum mean discrepancy (RMMD), which are distribution-free under the null hypothesis and exhibit high power in statistical testing while being robust to outliers. However, these statistics suffer from computational complexity, high sample complexity, sensitivity to small distributional perturbations, and non-differentiability with respect to the data. Unlike other GoF statistics such as MMD and Wasserstein-1 distance, which can be seamlessly integrated into generative modeling frameworks, RE and RMMD cannot serve as objective functions due to their non-differentiability. Additionally, their sensitivity to small perturbations hampers their robustness in sliding window-based change point detection (CPD) frameworks. To address these practical challenges, we propose novel variants of these statistics called soft rank energy (sRE) and soft rank maximum mean discrepancy (sRMMD) by employing entropy-regularized optimal transport maps in place of the rank map. Leveraging the differentiability property, we demonstrate the effectiveness of these statistics in generative modeling tasks, specifically in image generation and generating valid knockoffs for statistically significant feature selection. Furthermore, we apply both RE and sRE statistics to offline, unsupervised change point detection and extensively evaluate their performance using synthetic and real-world data. The results indicate that sRE outperforms RE and other commonly used GoF statistics for change point detection, as measured by performance metrics commonly employed in CPD literature.
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653 $a Data science
653 $a Feature selection
653 $a Generative modeling
653 $a Optimal transport
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