ELE538: Mathematics of High-Dimensional Data

Lecture notes

These lecture notes will be updated frequently.

• Spectral methods (last updated: 10/22)

• Matrix concentration inequalities (last updated: 10/22)

  • Reading: An introduction to matrix concentration inequalities

• Large-scale eigenvalue problems (power method and Lanczos algorithm) (last updated: 10/22)

  • Reading: Matrix computations, Chapter 9

• Tensor decomposition (last updated: 10/22)

  • Reading: Tensor decompositions for learning latent variable models

• Sparse representation (last updated: 10/17)

  • Reading: Uncertainty principles and ideal atomic decomposition

• Compressed sensing and sparse recovery (last updated: 10/24)

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

• Phase transition and convex geometry (last updated: 11/5)

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

• Gaussian graphical models and graphical lasso (last updated: 11/5)

  • Reading: Sparse inverse covariance estimation with the graphical lasso

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

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

• Robust principal component analysis (last updated: 11/28)

  • Reading: Robust principal component analysis?

• Nonconvex matrix factorization

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

Supplementary readings (not to be covered in class)

• Randomized linear algebra

• Model selection and Lasso

• Super-resolution