Course Schedule (Evolving)

Lecture recordings from Echo360 can be accessed here.

Lecture      Day Topic Materials/Reading
Foundations and Random Hashing
1. 1/26 Wed Course overview. Probability review. Example applications: polynomial identity testing, Frievald's algorithm Slides. Compressed slides. Reading: Chapters 1-3 of Mitzenmacher Upfal, with good coverage of probability basics, concentration bounds, and algorithmic applications. Greg Valiant's course notes covering the full analysis of polynomial identity testing (Lec 1).
2. 2/2 Wed Concentration bounds: Markov's, Chebyshev's. Union bound. Applications to Quicksort analysis, coupon collecting, statistical estimation, balls into bins. Slides. Compressed slides. Reading: Chapters 1-3 of Mitzenmacher Upfal, which cover most of the tools and applications from class. Greg Valiant's course notes covering randomized Quicksort (Lec 2) and concentration bounds (Lec 5).
3. 2/9 Wed Finish concentration inequalities: exponential tail bounds and application to linear probing analysis. Start on randomized hash functions and fingerprints. Slides. Compressed slides. Lecture recording. Reading: Jelani Nelson's course notes, giving a proof of the Chernoff bound (Lec 3) and the linear probing analysis (Lec 4). Chapter 7 of Motwani Raghavan, with coverage of fingerprinting and its applications.
4. 2/16 Wed Finish fingerprints. Rabin-Karp pattern matching algorithm. Randomized communication protocols. ℓ0 sampling with applications to graph sketching and streaming. Slides. Compressed slides. Reading: Chapter 7 of Motwani Raghavan, with coverage of fingerprinting and its applications. Many helpful slides/notes by Prof. McGregor on graph sketching algorithms. A good survey on ℓ0 sampling methods.
Random Sketching and Randomized Numerical Linear Algebra
5. 2/23 Wed Prof away. Class to be held over Zoom. Intro to randomized numerical linear algebra. Approximate matrix multiplication and Hutchinson's trace estimator. Slides. Compressed slides. Lecture recording. Reading: Original paper on sampling based approximate matrix multiplication, with the analysis covered in class. General notes on RandNLA, (from Drineas and Mahoney) with good background material and coverage of approximate matrix multiplication.
6. 3/2 Wed Randomized low-rank approximation. Adaptive sampling and k-means++. Slides. Compressed slides. Reading: Original k-means++ paper. Some notes on sampling based low-rank approximation (Mahoney at UC Berkeley).
3/9 Wed Midterm Study guide and review questions.
3/16 Wed No Class, Spring Recess.
7. 3/23 Wed The Johnson-Lindenstrauss lemma. Proof via Hanson-Wright. Epsilon-nets and subspace embedding. Sketching for linear regression. Slides. Compressed slides. Reading: Jelani Nelson's course notes, which include the proof of distributional JL via Hanson-Wright, along with discussion of subspace embeddings and various applications. Chris Muscos's notes on subspace embedding, on which my proof in class was based.
8. 3/30 Wed Importance sampling and leverage scores. Matrix concentration bounds. Spectral graph sparsifiers. Slides. Compressed slides. Reading: Dan Spielman's great book on spectral graph theory, including Chapter 32 on spectral sparsification via sampling, and analysis via matrix Chernoff bounds, which is equivilant to the leverage score analysis shown in class.
Markov Chains
9. 4/6 Wed Finish up graph sparsification. Introduction to Markov chains and their analysis. Applications to randomized algorithms for satisfiability problems (2-SAT and 3-SAT). Slides. Compressed slides. Reading: Chapter 7 of Mitzenmacher Upfal on Markov Chains, including the application to 2-SAT and gambler's ruin.
10. 4/13 Wed Markov chains continued. Gambler's ruin. Stationary distributions and start on mixing time analysis via coupling. Slides. Compressed slides. Reading: Notes by Greg Valiant and Mary Wooters covering stationary distributions and mixing times/coupling. Also Chapters 10/11 of Mitzenmacher Upfal covering mixing time and coupling.
4/20 Wed No Class, Monday Schedule.
11. 4/27 Wed Finish Markov chains: coupling and Markov chain Monte Carlo methods (MCMC). Slides. Compressed slides. Reading: Notes by Greg Valiant and Mary Wooters covering the Metropolis-Hastings algorithm and mixing times/coupling. Also Chapters 10/11 of Mitzenmacher Upfal covering MCMC, mixing time, coupling, and counting via sampling.
Other Topics
12. 5/4 Wed Probabilistic method and the Lovasz Local Lemma. Slides. Compressed slides. Reading: Chapter 6 of Mitzenmacher Upfal. Greg Valiant's lecture notes on probabilistic method and algortihmic Lovasz local lemma.
5/6 Fri Final Exam. 10:30am - 12:30pm Study guide and review questions.