Zoom link for lectures
https://cornell.zoom.us/j/92674518945?pwd=QWl3VlZCblhpL1J0RnJkNDhldU9YZz09.
Textbook for assigned readings
[BHK] = Foundations of Data Science by Avrim Blum, John Hopcroft, and Ravi Kannan (Cambridge University Press, 2020).
Lecture Topics
1/24 — Introduction (Video; Slides; Notebook; to view notebook you must download it and open it on your system, which must have Jupyter installed)
Reading: BHK, Chapter 1.
1/26 — Vectors I: Algebraic properties (Video; Notes)
Reading: Lecture notes on vector spaces, §1.
1/28 — Vectors II: Duality (Video; Notes)
Reading: Lecture notes on vector spaces, §1.3.
1/31 — Vectors III: Convexity, Differentials, and Gradients (Video; Notes)
Reading: Lecture notes on vector spaces, §4.
2/2 — Vectors IV: Gradient Descent (Video; Notes; Notebook)
Reading: Lecture notes on vector spaces, §4.
2/4 — Vectors V: High-dimensional spheres, concentration of volume near boundary (Video; Notes)
Reading: Lecture notes on vector spaces, §2.2 and §3; see also BHK, §2.1-2.5.
2/7 — Vectors VI: High-dimensional spheres, concentration of volume near equator (Video; Notes — first 15 minutes of video omitted because audio was not recorded)
Reading: Lecture notes on vector spaces, §3; see also BHK, §2.1-2.5.
2/9 — Vectors VII: Exponentially many near-orthogonal vectors (Video omitted due to audio problems; Notes)
Reading: None.
2/11 — Matrices I: Introduction (Video; Notes)
Reading: Lecture notes on vector spaces, §4.
2/14 — Matrices II: Change of basis (Video; Notes)
Reading: BHK, §3.1-3.3.
2/16 — Matrices III: Singular value decomposition (Video; Notes)
Reading: BHK, §3.4-3.6.
2/18 — Matrices IV: SVD, part II (Video; Notes)
Reading: BHK, §3.4-3.6.
2/21 — Matrices V: Computing the SVD (Video; Notes)
Reading: BHK, §3.7, §3.9.
2/23 — Matrices VI: SVD wrap-up and quiz review (Video; Notes)
2/25 — Quiz I: Vectors and Matrices
3/2 — Matrices VII: Strongly convex functions, Hessians, and optimization (Video; Notes)
Reading: Abhay Singh's lecture notes on Hessians and optimization.
3/4 — Probability I: Probability distributions (Video; Notes)
Reading: Lecture notes on probability theory, §1.
3/7 — Probability II: Gaussian distributions (Video; Notes)
Reading: BHK, §12.4, §2.6, and lecture notes on probability theory, §2.
3/9 — Probability III: More about Gaussian distributions (Video; Notes)
Reading: Lecture notes on probability theory, §2.1.
3/11 — Probability IV: Chernoff Bound (Video; Notes)
Reading: BHK §12.5, and lecture notes on probability, §3.
3/14 — Probability V: Chernoff Bound Applications (Video; Notes)
Reading: BHK §5.4, and lecture notes on probability, §3.
3/16 — Probability VI: More Chernoff Bound Applications (Video; Notes)
Reading: Lecture notes on probability, §3.
3/18 — Sample Complexity of Singular Vector Estimation, part 1 (Video; Notes)
Reading: Lecture notes on probability, §4.
3/21 — Sample Complexity of Singular Vector Estimation, part 2 (Video; Notes)
Reading: Lecture notes on probability, §4.
3/25 — Sample Complexity of Singular Vector Estimation, part 3 (Video; Notes)
Reading: Lecture notes on probability, §4.
3/25 — Sample Complexity of Singular Vector Estimation, part 3 (Video; Notes)
Reading: Lecture notes on probability, §4.
3/28 — Sample Complexity of Singular Vector Estimation, part 4 (Video)
Reading: Lecture notes on probability, §4.1.
3/30 — Community Detection, part 1 (video and notes unavailable due to technical glitches)
Reading: Lecture notes on probability, §4.2-4.3.
4/1 — Community Detection, part 2 (Video)
Reading: Lecture notes on probability, §4.2-4.3.
4/11 — Random Projections I: Johnson-Lindenstrauss (Video; Notes)
Reading: BHK, §2.7.
4/13 — Random Projections II: Restricted Isometry Property (Video; Notes)
Reading: BHK, §10.2.
4/15 — Random Projections III: Sparse Recovery (Video; Notes)
Reading: BHK, §10.2.
4/18 — Streaming and Sketching I: Frequent Elements (Video; Notes)
Reading: BHK, §6.1 and §6.2.3.
4/22 — Streaming and Sketching II: 2-Universal Hash Families (Video; Notes)
Reading: BHK, §6.2.1.
4/25 — Streaming and Sketching III: Estimating Distinct Elements (Video; Notes)
Reading: BHK, §6.2.1.
4/27 — Streaming and Sketching IV: The Count-Min Sketch and Count Sketch (Video; Notes)
Reading: Lecture notes on probability, §5.3.4.
4/29 — Markov Chains I: Stationary Distributions (Video; Notes)
Reading: Lecture notes on Markov chains, §1-2.
5/2 — Markov Chains II: Markov Chain Monte Carlo (Video; Notes) -->
Reading: Lecture notes on Markov chains, §3.
5/4 — Markov Chains III: Mixing Time and Coupling (Video; Notes) -->
Reading: Lecture notes on Markov chains, §4-5.
5/6 — Markov Chains IV: Sampling Colorings (Video; Notes)
Reading: Lecture notes on Markov chains, §5.1.