Mathematical and Computational Foundations of Data Science (Spring 2023)

Course Description

The emphasis is on fundamental mathematical ideas (basic functional analysis, reproducing kernel Hilbert spaces, concentration inequalities, uniform central limit theorems), basic statistical modeling techniques (e.g. linear regression, parametric and non-parametric methods), basic machine learning techniques for unsupervised (e.g. clustering, manifold learning), supervised (classification, regression), and semi-supervised learning, and corresponding computational aspects (linear algebra, basic linear and nonlinear optimization to attack the problems above). Applications will include statistical signal processing, imaging, inverse problems, graph processing, and problems at the intersection of statistics/machine learning and physical/dynamical systems (e.g. model reduction for stochastic dynamical systems).

Supervised Projects

For each project, the paper, code and the data are provided in below:

• Manifold Learning and Diffusion Maps, Anshika Agrawal, Bryan Munoz, Nubaira Milki, Krutal Patel
• Semi-Supervised Learning, Christian Bakhit, Jonathan Bakhit, Bryan Olivo, Rongrong Liu, Yiyang Han
• Spectral Clustering: Application to Synthetic Examples Roxana Leal, Nader Najjar, Kyle Schneider
• Tensor Decomposition, Taher Haitami, Divya Kranthi, Elsie Ye, Anny Zhao
• A Survey of Topological Data Analysis Samuel Salander
• Hyperspectral Images Mubai Zhang, Zhanxiang Xu, Rui Sun
• The Impact of Socioeconomic and Vaccination Statuses on COVID-19 Cases in Maryland Jay Jung, Ana Kuri, and Zhaoxu Zhang