Interpretable Probabilistic Methods for Genetic Association Mapping and Shape Generation

Winn-Nunez, Emily Taylor

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Year:: 2024
Contributor:: Winn-Nunez, Emily Taylor (creator); Crawford, Lorin (Advisor); Sandstede, Bjorn (Reader); Wong, Ian (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Machine Learning; Applied mathematics; Shape; Computational biology; nonlinear model fitting; topological data analysis; Quantitative genetics; Bayesian Statistics; Computational modeling; Generative Models; Shapes; Ranking and selection (Statistics)
Extent:: xvii, 187 p.

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Description

Abstract:: As data structures become larger and more complex, methods of data analysis must evolve to harness the most accurate insights. Inspired by the challenges presented by genetic data and shape data, this thesis explores the process of developing probabilistic, interpretable methods of data analysis while balancing theoretical rigor with computational feasibility. First, we present a score operator quantifying variable importance for variation in a characteristic of interest at the local, neighborhood, and global levels of data. Second, we both develop the theory and implement the transparent algorithm for generating new shapes either from a known manifold or a reference data set. Finally, we extend this theory to include shapes where vertices not only have structural importance but also direct interpretation to the application.
Notes:: Thesis (Ph. D.)--Brown University, 2024

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Citation

Winn-Nunez, Emily Taylor, "Interpretable Probabilistic Methods for Genetic Association Mapping and Shape Generation" (2024). Applied Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://repository.library.brown.edu/studio/item/bdr:mnacwem2/

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Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.
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