MA 692, Matrix Methods for Data Science, Fall 2023

Lectures: TTh 1:30-2:45pm, MATH 215
Instructor: Prof. Jianlin Xia                                   Email:
Office: MATH 442	Office Hours: TTh 11:00am-12:00pm, and by appointment
Course information, syllabus, and lecture notes: Brightspace

• Course description
  Matrix methods play a key computational role in modern data analysis, scientific computing, and engineering simulations. The course will cover some useful matrix methods for several data science topics. We will focus on fast and efficient matrix computations that can benefit machine learning, data analysis, and also other numerical computations. Selected topics include:
  1. Matrix models of neural networks and machine learning.
  2. Data matrices and matrix decompositions.
  3. Randomized data probing, compression, and approximation.
  4. Stochastic/randomized solvers for linear algebra and optimization.
  5. Kernel matrix methods and fast transformations.
  6. Fast multipole methods and structured matrices.
  7. Fast direct solvers and eigenvalue solvers with applications to data analysis.
  
  Knowledge in basic numerical analysis and linear algebra is strongly suggested. There will be no comprehensive final exam. Reference books/papers, lecture notes, test codes, and other resources will be provided.


• References and lecture notes
  
  • Deep Learning, Ian Goodfellow, Yoshua Bengio and Aaron Courville, MIT Press, 2016.
  • Linear Algebra and Learning from Data, Gilbert Strang, Wellesley-Cambridge Press, 2019.
  • Applied Numerical Linear Algebra, James Demmel, SIAM, 1997.
  • Numerical Linear Algebra, Lloyd N. Trefethen and David Bau, SIAM, 1997.
  • Lecture notes are expected to be posted on Brightspace.