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- 2Department of Biological Sciences
- 2Department of Mechanical Engineering
- 1Department of Civil and Environmental Engineering
- 1Department of Computing Science
- 1Department of Public Health Sciences
- 7Frei, Christoph (Mathematical and Statistical Sciences)
- 7Hillen, Thomas (Mathematical and Statistical Sciences)
- 7Kong, Linglong (Mathematical and Statistical Sciences)
- 7Lewis, Mark (Mathematical and Statistical Sciences)
- 6Han, Bin (Mathematical and Statistical Sciences)
- 6Kashlak, Adam (Mathematical and Statistical Sciences)
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Fall 2021
A classic result in the field of Riemannian Geometry is the Splitting Theorem of Cheeger and Gromoll. Since this result there have been numerous alternate versions under a variety of different conditions. Continuing in this vein, we prove structure results on manifolds with boundary components...
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Bayesian hierarchical modeling and its applications to clustering and data privacy preservation
DownloadFall 2024
The evolution of data acquisition technologies and the exponential growth in computing capabilities have inaugurated an epoch wherein researchers are empowered to procure data of unprecedented dimensionality and complexity. Simultaneously, Bayesian hierarchical models distinguish themselves as...
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Fall 2021
The demand for large dataset and demand of privacy protection are in constantly conflicts as the balance between the two is hard to keep. Differential privacy is a mathematical rigor definition that provides the balance bewteen these two opposite sides. It's developed with the purpose of making...
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Fall 2021
Kernel methods are often used for nonlinear regression and classification in machine learning because they are computationally cheap and accurate. Fourier basis and wavelet basis are the bases that can efficiently approximate the kernel functions. In previous research, Bayesian approximate kernel...
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Beyond Static Classification: Long-term Fairness for Minority Groups via Performative Prediction and Distributionally Robust Optimization
DownloadFall 2022
In recent years machine learning (ML) models have begun to be deployed at enormous scales, but too often without adequate concern for whether or not an ML model will make fair decisions. Fairness in ML is a burgeoning research area, but work to define formal fairness criteria has some serious...
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Fall 2011
In this thesis we report on several projects that stemmed out from an attempt to obtain an example for the last class in Doran-Morgan classification of ``variations of Hodge structure which can underlie families of Calabi-Yau threefolds over the thrice-punctured sphere with $b^3 = 4$, or...