TOPICS IN MATHEMATICAL DATA SCIENCE

COMPSCI/ECE/STAT 861

Advanced mathematical theory and methods of machine learning. Statistical learning theory, Vapnik-Chevronenkis Theory, model selection, high-dimensional models, nonparametric methods, probabilistic analysis, optimization, learning paradigms.

STAT 772

Introduce new algorithms that leverage randomization to address the scale, speed, and sensitivity needs of modern data science. Develop the mathematical foundations of such randomized algorithms. Criticize these algorithms through the lens of computational resource utilization. Implement these algorithms to address linear problems in data science.

STAT 611

Probability, random variables and their distributions, joint and conditional distributions, moments and inequalities, generating functions, transformations of random variables, sampling and distribution theory, convergence concepts and limit theorems for sequences of random variables.

MATH/STAT 833

Advanced topics in probability and stochastic processes.

MATH 535

A rigorous introduction to mathematical concepts important for modern data science. Topics include: matrix factorizations, optimization theory and algorithms, probabilistic models, finite Markov chains. Mathematical techniques are motivated by and illustrated on a range of applied problems from machine learning and statistics.