Topics in Mathematical Data Science

Tentative content:

+ Machine Learning: general concepts, VC dimension, learnability of binary classification, support vector machines, regression, clustering, reinforcement learning
+ Optimal Recovery: general concepts and basic theorems, approximability classes, information-based complexity, curse of dimensionality
+ Compressive Sensing: sparse recovery, optimality in terms of sample complexity, low-rank recovery, one-bit compressive sensing
+ Optimization: convex programming, linear programming, semidefinite programming, duality, robust optimization
+ Neural Networks: general concepts, expressiveness of shallow networks, the advantages of depth, training by back-propagation

Prerequisite: some basic knowledge of linear algebra, analysis, and probability; familiarity with a programming language is a plus.

Textbook: lecture notes provided by the instructor.

Grading: to be determined.