LINEAR RANDOMIZED ALGORITHMS FOR DATA SCIENCE

ECE/MATH/STAT 888

Advanced topics in the mathematical foundations of data science

STAT 606

A survey of some of the tools and frameworks that are currently popular among data scientists and statisticians working in both academia and industry. Begins with an accelerated introduction to the Python programming language and brief introductions to object-oriented and functional programming. Covers some of the scientific computing platforms available in Python, including tools for numerical and scientific computing; training basic machine learning models; and data visualization. Discusses collecting data from the web both by scraping and using APIs. Concludes with a brief survey of distributed computing platforms, focusing on the MapReduce framework.

COMPSCI 541

Theoretical methods for data science. Topics include: review of probability background, concentration inequalities, geometry of high dimensional random variables, parametric and non-parametric estimation, selected topics from optimization (optimality conditions; deterministic and stochastic gradient descent), PAC learning, sample complexity and algorithms for linear classification and regression, and property/distribution testing. Uses Python programming language.

STAT 613

Provides a thorough grounding in modern statistical methods. Introduces statistical techniques and methods of data analysis, including data description, linear regression models, diagnostic tools, prediction and model selection, and experimental design.

MATH 718

Random solvers have been playing increasingly crucial roles in the modern computational tasks. The recent breakthroughs in applied and computational linear algebra that incorporate techniques of randomization have proven to be of great importance in modern applied math, computational sciences and data science, such as inverse problems, machine learning and scientific computing. The guiding principle is that one may greatly reduce computational and storage expenses at the cost of a small probability of failure. Systematic study of these modern methods of randomized linear algebra solvers will be provided, presenting mathematical backgrounds, algorithms, and concrete applications. Core theoretical topics include randomized Kaczmarz and its generalization to stochastic gradient descent, randomized singular value decomposition, random sketching, matrix completion, and compressive sensing, and corresponding applications.