MCS 590 - Mathematical Foundations of Data Science
University of Illinois - Chicago
Fall 2017

MCS 590 is a course covering special topics in computer science. This semester, the topic is "foundations of data science." The course will cover topics such as: random graphs, small world phenomena, random walks, Markov chains, streaming algorithms, clustering, graphical models, and belief propogation. Techniques such as SVD and random projections will also be discussed.

Basic Information

Syllabus: pdf
Time and Location: M-W-F 11:00AM-11:50AM, 212 Stevenson Hall (SH)
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: T 2:30-3:20pm, F 1:00-1:50pm


Problem Sets

problem set 1, due 9/29/17

Lectures and Readings

Lecture 1 (8/28/17)
covered material: intro to the course, preview of the material, law of large numbers
reading: chapters 1, 2.1, 2.2

Lecture 2 (8/30/17)
covered material: some concentration inequalities, geometry in high dimensions
reading: chapters 2.3 - 2.5

Lecture 3 (9/1/17)
covered material: Gaussian annulus theorem, random projection theorem, Johnson-Lindenstrauss lemma
reading: chapters 2.6 - 2.7

Lecture 4 (9/6/17)
covered material: singular value decomposition and PCA, best-fit subspaces, and optimality of greedy algorithm
reading: chapters 3.1 - 3.6

Lecture 5 (9/8/17)
covered material: singular vectors vs eigenvectors, power iteration, SVD for clustering mixtures of Gaussians
reading: chapters 3.7 - 3.9

Lecture 6 (9/11/17)
covered material: random walks and Markov chains, fundamental theorem of Markov chains
reading: intro to chapter 4, 4.1

Lecture 7 (9/13/17)
covered material: Markov chain Monte Carlo (MCMC), Metropolis-Hastings
reading: chapter 4.2

Lecture 8 (9/15/17)
covered material: Gibbs sampling, efficient volume estimation for convex bodies in high dimension
reading: chapter 4.3

Lecture 9 (9/18/17)
covered material: convergence of random walks on undirected graphs, normalized conductance
reading: chapter 4.4
other: problem set 1 assigned