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DTSTART;TZID=America/Los_Angeles:20261019T093000
DTEND;TZID=America/Los_Angeles:20261019T113000
DTSTAMP:20261013T161027Z
CREATED:20261013T161027Z
LAST-MODIFIED:20261013T161027Z
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SUMMARY:Kawano\, S. (STAT) - Model Validation and Dependent Shrinkage Priors for Small Area Estimation
DESCRIPTION:This dissertation addresses two questions in survey methodology: How can we produce granular\, reliable estimates? And how can we validate them without ground truth? We develop three methods: (1) Gaussian data thinning enables out-of-sample model validation using only direct survey estimates and their sampling variances. We characterize its bias–variance tradeoff to guide model comparison. — (2) Spatially selected and dependent random effects use similarities between neighboring areas to inform both effect selection and effect values. — (3) Cascading tree spike-and-slab priors select random effects from coarse to fine resolutions\, removing unnecessary branches of effects. — We evaluate these methods through simulations and applications to rent burden in the South Atlantic United States\, employment in California\, contraceptive use in Kenya\, and industry payroll in New England. \nEvent Host: Sho Kawano\, Ph.D. Candidate\, Statistical Science  \nAdvisors: Paul Parker & Zehang Richard Li \nZoom: https://ucsc.zoom.us/j/97616141146?pwd=eEKbv8zyM5p3dPZ2s86oaO79vNs6SF.1 \nPasscode: 454321
URL:https://live-events-ucsc.pantheonsite.io/event/kawano-s-stat-model-validation-and-dependent-shrinkage-priors-for-small-area-estimation/
LOCATION:Engineering 2\, Engineering 2 1156 High Street\, Santa Cruz\, CA\, 95064
CATEGORIES:Ph.D. Presentations
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CREATED:20261013T161821Z
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SUMMARY:Bondar\, G. (AM) - Geometric and Graph Structured Optimal Transport for Learning and Control
DESCRIPTION:We motivate\, formulate\, and solve several structured optimal transportation (OT) problems for learning and control. The field of OT had its inception in 1781\, when Gaspard Monge sought the optimal map to transport mass from a given initial distribution to a desired terminal distribution. Both OT and its entropy-regularized variant\, the Schrödinger bridge problem (SBP)\, have catalyzed significant developments across mathematics. More recently\, theoretical and algorithmic developments in OT and SBP have found myriad applications in stochastic optimal control and generative AI. \nThe connecting theme across the problems studied in this dissertation is the presence of structure which can be exploited in their solution — for our work\, this structure arises from geometry underlying a solution space or from a graph capturing a correlation structure between distributional data. Our original contributions begin with automated verification and discovery of OT regularity\, followed by stochastic learning and control for resource allocation and scheduling in multi-core real-time systems\, where the problem has a natural graph structure. We also formulate and solve the problem of finding an optimal graph structure in a distribution-valued dataset where none is present. \nWhile graph-structured OT is a natural fit for data-driven stochastic learning problems\, the knowledge of system dynamics can impose geometric structure to the problem. In this dissertation\, we establish the equivalence between the stochastic optimal control and path space formulations of SBP over a compact connected Lie group. Additionally\, we develop\, analyze\, and validate a novel numerical solution scheme for the SBP with control-affine dynamics. Finally\, we investigate the application of Gromov-Wasserstein (GW) OT — a variant of the problem allowing for transport between incomparable spaces — for spatial proteomics. We show throughout our work how careful considerations of the underlying geometry and graph-structures can enable bespoke solutions for practical learning and control problems through optimal transport. \nEvent Host: Georgiy Bondar\, Ph.D. Candidate\, Applied Mathematics  \nAdvisor: Abhishek Halder \nZoom: https://ucsc.zoom.us/j/96361886043?pwd=U73TbafhzI7kgS7MYAFko3YEPVIxTb.1 \nPasscode: 564490
URL:https://live-events-ucsc.pantheonsite.io/event/bondar-g-am-geometric-and-graph-structured-optimal-transport-for-learning-and-control/
LOCATION:Engineering 2\, Engineering 2 1156 High Street\, Santa Cruz\, CA\, 95064
CATEGORIES:Ph.D. Presentations
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