Reliable Decision-Making Under Uncertainty Through the Lens of Statistics and Optimization
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| Vydáno v: | ProQuest Dissertations and Theses (2025) |
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ProQuest Dissertations & Theses
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| 045 | 2 | |b d20250101 |b d20251231 | |
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| 100 | 1 | |a Wang, Jie | |
| 245 | 1 | |a Reliable Decision-Making Under Uncertainty Through the Lens of Statistics and Optimization | |
| 260 | |b ProQuest Dissertations & Theses |c 2025 | ||
| 513 | |a Dissertation/Thesis | ||
| 520 | 3 | |a In this thesis, we develop computationally efficient algorithms with statistical guaranteesfor problems of decision-making under uncertainty, particularly in the presence of largescale, noisy, and high-dimensional data. In Chapter 2, we propose a kernelized projectedWasserstein distance for high-dimensional hypothesis testing, which finds the nonlinearmapping that maximizes the discrepancy between projected distributions. In Chapter 3, weprovide an in-depth analysis of the computational and statistical guarantees of the kernelizedprojected Wasserstein distance. In Chapter 4, we study the variable selection problem intwo-sample testing, aiming to select the most informative variables to determine whethertwo datasets follow the same distribution. In Chapter 5, we present a novel frameworkfor distributionally robust stochastic optimization (DRO), which seeks an optimal decisionthat minimizes expected loss under the worst-case distribution within a specified set. Thisworst-case distribution is modeled using a variant of the Wasserstein distance based onentropic regularization. In Chapter 6, we incorporate Phi-divergence regularization into theinfinity-type Wasserstein DRO, which is a formulation particularly useful for adversarialmachine learning tasks. Chapter 7 concludes with an overview of promising future researchdirections. | |
| 653 | |a Sparsity | ||
| 653 | |a Big Data | ||
| 653 | |a Sample size | ||
| 653 | |a Statistics | ||
| 653 | |a Optimization techniques | ||
| 653 | |a Normal distribution | ||
| 653 | |a Decision making | ||
| 653 | |a Plot (Narrative) | ||
| 653 | |a Feature selection | ||
| 773 | 0 | |t ProQuest Dissertations and Theses |g (2025) | |
| 786 | 0 | |d ProQuest |t ProQuest Dissertations & Theses Global | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3275490271/abstract/embedded/75I98GEZK8WCJMPQ?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3275490271/fulltextPDF/embedded/75I98GEZK8WCJMPQ?source=fedsrch |