THEORETICAL FOUNDATIONS OF MACHINE LEARNING

COMPSCI/ECE 561

Probabilistic tools for machine learning and analysis of real-world datasets. Introductory topics include classification, regression, probability theory, decision theory and quantifying information with entropy, relative entropy and mutual information. Additional topics include naive Bayes, probabilistic graphical models, discriminant analysis, logistic regression, expectation maximization, source coding and variational inference.

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.

COMPSCI/ECE 761

Mathematical foundations of machine learning theory and algorithms. Probabilistic, algebraic, and geometric models and representations of data, mathematical analysis of state-of-the-art learning algorithms and optimization methods, and applications of machine learning. Knowledge of probability [such asMATH/​STAT  431orCOMP SCI/​E C E  561] and linear algebra [such asMATH 341orM E/​COMP SCI/​E C E  532] is required.

STAT 841

Statistical function estimation and classification; reproducing kernel machines, support vector machines; high dimensional model selection and estimation; Bayesian, empirical Bayesian interpretation of nonparametric learning methods; log density ANOVA and graphical models; tree ensemble methods including bagging, boosting, and random forest.

ECE 826

Mathematical foundations of large-scale machine learning and optimization. Focus on recent texts in machine learning, optimization, and randomized algorithms, focused on tradeoffs that are driving algorithmic design in this new discipline. These trade-offs revolve around speed of convergence, statistical accuracy, robustness, scalability, algorithmic complexity, and implementation.