Foundations and Random Hashing 
1. 2/1 
Thu 
Course overview. Randomized complexity classes and different types of randomized algorithms. 
Slides. Compressed slides. Reading: Chapters 13 of Mitzenmacher Upfal. 
2. 2/6 
Tue 
Probability review. Linearity of expectation and variance. Application to polynomial identity testing randomized quicksort analysis. 
Slides. Compressed slides. Reading: Chapters 13 of Mitzenmacher Upfal. Greg Valiant's course notes covering polynomial identity testing (Lec 1) and randomized Quicksort (Lec 2). 
3. 2/8 
Thu 
Concentration bounds: Markov's and Chebyshev's inequalities. Union bound. Applications to statistical estimation and coupon collecting. Start on ballsintobins. 
Slides. Compressed slides. Reading: Chapters 13 of Mitzenmacher Upfal. Greg Valiant's course notes covering concentration bounds (Lec 5). 
4. 2/13 
Tue 
Continue on concentration bounds and ballsintobins. Start on exponential tail bounds (Chernoff and Bernstein inequalities). 
Slides. Compressed slides. Reading: Chapter 5 of Mitzenmacher Upfal covering ballsintobins analysis. 
5. 2/15 
Thu 
Exponential tail bounds with applications to ballsintobins and linear probing analysis. 
Slides. Compressed slides.
Reading: Jelani Nelson's course notes, giving a proof of the Chernoff bound (Lec 3) and the linear probing analysis (Lec 4).

6. 2/20 
Tue 
Randomized hash functions and fingerprints. Applications to efficient communication protocols and RabinKarp pattern matching 
Slides. Compressed slides. Reading: Chapter 7 of Motwani Raghavan, with coverage of fingerprinting and its applications. 
2/22 
Thu 
No Class, Monday Schedule. 

Random Sketching and Randomized Numerical Linear Algebra 
7. 2/27 
Tue 
ℓ_{0} sampling with applications to graph sketching. 
Slides. Compressed slides. Reading: Many helpful slides/notes by Prof. McGregor on graph sketching algorithms. A good survey on ℓ_{0} sampling methods.

8. 2/29 
Thu 
Finish ℓ_{0} sampling. Application to graph streaming. Other linear sketching algorithms  Count Sketch for frequency estimation. 
Slides. Compressed slides. Reading: Notes on streaming algorithms by Amit Chakrabarti, including coverage of Count Sketch in Chapter 4 and many related techniques. 
9. 3/5 
Tue 
Finish up ℓ_{2} heavyhitters via Count Sketch. Start on randomized numerical linear algebra  approximate matrix multiplication via sampling. 
Slides. Compressed slides. Reading: Notes on streaming algorithms by Amit Chakrabarti, including coverage of Count Sketch in Chapter 4. Notes on approximate matrix multiplication (Mahoney). General notes on RandNLA, (Drineas and Mahoney) with good background material and coverage of central techniques. 
10. 3/7 
Thu 
Finish up approximate matrix multiplication and importance sampling. Application to randomized lowrank approximation. 
Slides. Compressed slides. Reading: General notes on RandNLA, (Drineas and Mahoney). Some notes on sampling based lowrank approximation (Mahoney).

11. 3/12 
Tue 
Finish up randomized lowrank approximation. Stochastic trace estimation. 
Slides. Compressed slides. Reading: Notes (Tropp) covering stochastic trace estimation. A blog post (Nowozin) listing lots of nice applications of randomized trace estimation in machine learning. Another nice blog post (Epperly) on stochastic trace estimation. 
12. 3/14 
Thu 
Finish stochastic trace estimation. 
Slides. Compressed slides. Reading: Our paper on Hutch++ which gives background on randomized trace estimation and an improved algorithm for PSD matrices. 
3/19 
Tue 
No Class, Spring Recess. 

3/21 
Thu 
No Class, Spring Recess. 

13. 3/26 
Tue 
Midterm Review 
Slides.

3/28 
Thu 
Midterm 
Study guide and review questions. 
14. 4/2 
Tue 
The JohnsonLindenstrauss lemma, epsilonnets, and subspace embedding. 
Slides. Compressed slides.
Reading: Chris Muscos's notes on subspace embedding, on which my proof in class is based.

15. 4/4 
Thu 
Finish up subspace embedding. Proof of the JL Lemma via HansonWright. Sketching for linear regression. 
Slides. Compressed slides. Reading: Jelani Nelson's course notes, which include the proof of distributional JL via HansonWright, along with discussion of subspace embeddings and various applications. 
16. 4/9 
Tue 
Importance sampling and leverage scores. Matrix concentration bounds.

Slides. Compressed slides.

17. 4/11 
Thu 
Finish up leverage scores. Connection to effective resistences and 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. 
4/16 
Tue 
No Class, Prof Traveling. 

Markov Chains 
18. 4/18 
Thu 
Prof Traveling. Class held over Zoom. Introduction to Markov chains and their analysis. Application to randomized algorithms for 2SAT and 3SAT. 
Slides. Compressed slides.. Lecture Recording.
Reading: Chapter 7 of Mitzenmacher Upfal on Markov Chains, including the application to 2SAT and 3SAT. 
19. 4/23 
Tue 
Gambler's ruin. Markov chain analysis and stationary distributions. The Fundamental Theorem of Markov Chains. 
Slides. Compressed slides. Reading: Chapter 7 of Mitzenmacher Upfal. 
20. 4/25 
Thu 
Analysis of Markov chain mixing time via coupling. 
Slides. Compressed slides.
Reading: Notes by Greg Valiant and Mary Wooters covering mixing times/coupling. Also Chapters 10/11 of Mitzenmacher Upfal.

21. 4/30 
Tue 
Finish up coupling. Start on Markov chain Monte Carlo methods (MCMC). 
Slides. Compressed slides. Reading: Notes by Greg Valiant and Mary Wooters covering the MetropolisHastings algorithm. Chapter 10/11 of Mitzenmacher Upfal covering MCMC and approximate counting. 
22. 5/2 
Thu 
Finish up Markov Chains. Metropolis Hastings, sampling to counting reductions. 
Slides. Compressed slides. Reading: Notes by Greg Valiant and Mary Wooters covering the MetropolisHastings algorithm. Chapter 10/11 of Mitzenmacher Upfal covering MCMC and approximate counting.

Other Topics 
23. 5/7 
Tue 
Approximation algorithms via convex relaxation + randomized rounding. Applications to vertex cover, set cover, and maxcut 
Slides. Compressed slides. Reading: Lecture notes by Chekuri covering the relaxations for vertex cover and set cover presented in class. Book on approximation algorithms by Williamson and Shmoys, with lots of coverages of relaxation and rounding. 
24. 5/9 
Thu 
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 algorithmic Lovasz local lemma. 
5/14 
Tue 
Final Exam. 10:30am  12:30pm. Location TBD 
Study guide and review questions. 