ELE520: Mathematics of Data Science

Lecture notes

These lecture notes will be updated frequently.

• Spectral methods (last updated: 09/16)

• Matrix concentration inequalities (last updated: 09/22)

  • Reading: An introduction to matrix concentration inequalities

• Large-scale eigenvalue problems (power method and Lanczos algorithm) (last updated: 09/24)

  • Reading: Matrix computations, Chapter 9

• Tensor decomposition (last updated: 10/8)

  • Reading: Tensor decompositions for learning latent variable models

• Randomized linear algebra (last updated: 10/20)

  • Reading: Lecture notes on randomized linear algebra

• Compressed sensing and sparse recovery (last updated: 10/22)

  • Reading: Mathematics of sparsity (and a few other things)

• Low-rank matrix recovery (last updated: 11/28)

  • Reading: Mathematics of sparsity (and a few other things)

• Nonconvex matrix factorization

  • Reading: Nonconvex optimization meets low-rank matrix factorization: An overview

Supplementary readings (not to be covered in class)

• Sparse representation (last updated: 10/22)

  • Reading: Uncertainty principles and ideal atomic decomposition

• Model selection (last updated: 11/4)

• Lasso: algorithms and extensions (last updated: 11/4)

• Gaussian graphical models and graphical lasso (last updated: 11/4)

  • Reading: Sparse inverse covariance estimation with the graphical lasso

• Phase transition and convex geometry (last updated: 11/4)

  • Reading: Living on the edge: Phase transitions in convex programs with random data

• Robust principal component analysis (last updated: 11/4)

• Super-resolution (last updated: 11/4)