STAT 991-302: Mathematics of High-Dimensional Data

Lecture notes

These lecture notes will be updated frequently; see also lectures from previous offerings.

• Spectral methods

  • Reading: Spectral methods for data science: A statistical perspective

• Matrix concentration inequalities

  • Reading: An introduction to matrix concentration inequalities

• Large-scale eigenvalue problems (power method and Lanczos algorithm)

  • Reading: Matrix computations, Chapter 9

• Tensor decomposition

  • Reading: Tensor decompositions for learning latent variable models

  • Reading: Spectral methods for data science: A statistical perspective (Section 3.9)

• Randomized linear algebra

  • Reading: Lecture notes on randomized linear algebra

• Compressed sensing and sparse recovery

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

• Phase transition and convex geometry

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

• Low-rank matrix recovery

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

• Robust principal component analysis

• Nonconvex matrix factorization: Part 1, Part 2, Part 3

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

• Reinforcement learning: Part 1, Part 2

Supplementary readings (not to be covered in class)

• Sparse representation

  • Reading: Uncertainty principles and ideal atomic decomposition