Defense Date

4-8-2022

Graduation Date

Summer 8-13-2022

Availability

One-year Embargo

Submission Type

thesis

Degree Name

MS

Department

Computational Mathematics

School

McAnulty College and Graduate School of Liberal Arts

Committee Chair

Lauren Sugden

Committee Member

Stacey Levine

Keywords

Image Processing, Statistical Genetics, Machine Learning

Abstract

Due to a rise in computational power, machine learning (ML) methods have become the state-of-the-art in a variety of fields. Known to be black-box approaches, however, these methods are oftentimes not well understood. In this work, we utilize our understanding of model-based approaches to derive insights into Convolutional Neural Networks (CNNs). In the field of Natural Image Restoration, we focus on the image denoising problem. Recent work have demonstrated the potential of mathematically motivated CNN architectures that learn both `geometric' and nonlinear higher order features and corresponding regularizers. We extend this work by showing that not only can geometric features and corresponding regularizers be learned through ML but also be used to boost the performance of other CNN approaches. In the field of population genetics, we focus on the problem of detecting selective sweeps within genomes where various CNN based approaches have been proposed. We give an overview of these approaches and show how their method of prediction is based on a measure quite similar to the Garud's H test statistic.

Language

English

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