Bayesian Statistics (ISYE 6420) This course covers the fundamentals of Bayesian statistics, including both the underlying models and methods of Bayesian computation, and how they are applied. Modeling topics include conditional probability and Bayes’ formula, Bayesian inference, credible sets, conjugate and noninformative priors, hypothesis testing, Bayesian regression, empirical Bayes models, and hierarchical Bayesian models. Computational topics include Monte Carlo methods, MCMC, Metropolis-Hasting algorithms, Gibbs sampling, variational Bayes, and other methods for posterior approximation. Various applications of Bayesian statistics will be discussed. Prerequisite: Calculusbased Introductory Statistics Course
Computational Data Analysis (ISYE 6740) Machine learning is a field of computer science that gives computers the ability to learn without being explicitly programmed. The course is designed to answer the most fundamental questions about machine learning: What are the most important methods to know about, and why? How can we answer the question ‘is this method better than that one’ using asymptotic theory? How can we answer the question ‘is this method better than that one’ for a specific dataset of interest? What can we say about the errors our method will make on future data? What’s the ‘right’ objective function? What does it mean to be statistically rigorous? This course is designed to give graduate students a thorough grounding in the methods, theory, mathematics and algorithms needed to do research and applications in machine learning. The course covers topics from machine learning, classical statistics, and data mining. Students entering the class with a pre-existing working knowledge of probability, statistics and algorithms will be Analytical Tools an advantage, but the class has been designed so that anyone with a strong numerate background can catch up and fully participate. Some experience with coding are expected.Regression Analysis (ISYE 6414) This course covers the fundamentals of Bayesian statistics, including both the underlying models and methods of Bayesian computation, and how they are applied. Modeling topics include conditional probability and Bayes’ formula, Bayesian inference, credible sets, conjugate and noninformative priors, hypothesis testing, Bayesian regression, empirical Bayes models, and hierarchical Bayesian models. Computational topics include Monte Carlo methods, MCMC, Metropolis-Hasting algorithms, Gibbs sampling, variational Bayes, and other methods for posterior approximation. Various applications of Bayesian statistics will be discussed. Prerequisite: Calculus-based Introductory Statistics Course Time Series Analysis (ISYE 6402) Basic forecasting and methods, ARIMA models, transfer functions.
Data Mining and Statistical Learning (ISYE 7406) An introduction to some commonly used data mining and statistical learning algorithms such as K-nearest neighbor (KNN) algorithm, linear methods for regression and classification, tree-based methods, ensemble methods, support vector machine, neural networks, and Kmeans clustering algorithm. This course focuses on the understanding of methodology, motivation, and assumptions of different algorithms as well as implementation of these algorithms with data examples using the R statistical software.
High-dimensional Data Analytics (ISYE 8803) This course focuses on analysis of high-dimensional structured data including profiles, images, and other types of functional data using statistical machine learning. A variety of topics such as functional data analysis, image processing, multilinear algebra and tensor analysis, and regularization in highdimensional regression and its applications including low rank and sparse learning is covered. Optimization methods commonly used in statistical modeling and machine learning and their computational aspects are also discussed – convex conic optimization, which is a significant generalization of linear optimization. The fourth and final module is on integer optimization, which augments the previously covered optimization models with the flexibility of integer decision variables. The course blends optimization theory and computation with various applications to modern data analytics.