High-Dimensional Data Analysis

3 Credits · Level: Undergraduate

This course will explore different deep learning architectures and their associated mathematics. The architectures we will consider are fully connected neural nets, convolutional neural nets, recurrent neural nets and transformers. Associated with these architectures, we will explore basic ideas in optimization including gradient methods applied to convex and nonconvex optimization, the role of convolution in signal processing, basic models of time series, and probabilistic models in high dimensional spaces. There will likely be some variation from this plan depending on student interest and time constraints. Application of the architectures to datasets will be done through the python package Pytorch. By the end of the course, students should be able to write python code to implement the architectures. However, we will strike a balance between application and theory. By the end of the course, students should be familiar with associated ideas and results in mathematics, particularly relating to computation and modeling in high dimensions. Students who are mainly interested in implementation of the architectures are likely better off taking some of the other neural net classes offered at Georgetown.