MCS 549 - Mathematical Foundations of Data Science
University of Illinois - Chicago
Fall 2019

This course covers the mathematical foundations of modern data science from a theoretical computer science perspective. Topics will include random graphs, small world phenomena, random walks, Markov chains, streaming algorithms, clustering, graphical models, singular value decomposition, and random projections.

Basic Information

Syllabus: pdf
Time and Location: M-W-F 1:00PM-1:50PM, 219 Taft Hall (TH)
Instructor Contact Information: Lev Reyzin, SEO 418, (312)-413-3745,
Online Textbook: Avrim Blum, John Hopcroft, and Ravi Kannan, Mathematical Foundations of Data Science
Office Hours: W 10:00-10:50 AM, F 11:00-11:50 AM


Problem Sets

problem set 1, due 10/4/19

Lectures and Readings

Lecture 1 (8/26/19)
covered material: intro to the course, preview of the material, some basic probability
reading: chapters 1, 2.1, 2.2

Lecture 2 (8/28/19)
covered material: some concentration inequalities, geometry in high dimensions
reading: chapters 2.3 - 2.5

Lecture 3 (8/30/19)
covered material: Gaussian annulus theorem, random projection theorem, Johnson-Lindenstrauss lemma
reading: chapters 2.6 - 2.7

Lecture 4 (9/4/19)
covered material: singular value decomposition (SVD), best-fit subspaces, and optimality of greedy algorithm
reading: chapters 3.1 - 3.6

Lecture 5 (9/6/19)
covered material: principal component analysis (PCA), SVD for clustering mixtures of Gaussians
reading: chapters 2.8, 3.9.2 - 3.9.3
optional reading: chapters 3.9.4 - 3.9.5

Lecture 6 (9/9/19)
covered material: power iteratio for fast computation of SVD
reading: chapter 3.7 (including 3.7.1)

Lecture 7 (9/11/19)
covered material: SVD for an additive approximation algorithm for max-cut
reading: chapter 3.9.6

Lecture 8 (9/13/19)
covered material: intro to Markov chains, stationary distribution, Fundamental Theorem of Markov Chains
reading: intro to chapter 4, chapter 4.1

Lecture 9 (9/16/19)
covered material: Markov chain Monte Carlo (MCMC), Metropolis-Hasting, Gibbs Sampling
reading: chapter 4.2 (including 4.2.1 - 4.2.2)

Lecture 10 (9/18/19)
covered material: MCMC for efficient sampling and volume estimation of convex bodies in high dimension
reading: chapter 4.3

Lecture 11 (9/20/19)
covered material: convergence of random walks on undirected graphs, normalized conductance
reading: begin chapter 4.4