MATRIX METHODS IN MACHINE LEARNING

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.

MATH 443

Review of matrix algebra. Simultaneous linear equations, linear dependence and rank, vector space, eigenvalues and eigenvectors, diagonalization, quadratic forms, inner product spaces, norms, canonical forms. Discussion of numerical aspects and applications in the sciences.

MATH 345

Introduction to linear algebra, differential calculus in several variables, and basic optimization theory with applications to data science and related topics. Vectors, analytic geometry, matrices, linear functions, linear independence, orthogonality, inverses, partial derivatives and gradients, Taylor approximation, gradient descent, Lagrange multipliers, clustering, regression, classification. Implementation in Python.

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.

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.