| Tue, Aug 25 |
Introduction. Data as samples from a distribution. Python/NumPy basics |
Notes |
Practice 1 out (Python) |
Syllabus |
| Thu, Aug 27 |
Sampling from distributions: uniform, Gaussian; histograms vs. densities; empirical distribution |
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Quiz 0 (ungraded) |
C&O §7.1 |
| Tue, Sep 1 |
Multivariate Gaussians and mixtures, operationally: sampling, mean, covariance |
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Practice 2 out (NumPy + sampling) |
C&O §7.1 |
| Thu, Sep 3 |
Graphs from data: ε- and k-NN graphs; k-NN classification |
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Quiz 1 |
C&O §9.1, §7.4 |
| Tue, Sep 8 |
Adjacency and degree matrices; walks via powers of A; connectivity, shortest paths |
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Practice 3 out (graphs) |
C&O §9.1–9.2, §9.5 |
| Thu, Sep 10 |
The graph Laplacian as bookkeeping; clustering sampled data, experimentally |
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Quiz 2 |
C&O §9.3 |
| Tue, Sep 15 |
Random walks on graphs; the transition matrix; matrix–vector product as one step |
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Practice 4 out (simulation) |
Zitkovic; C&O Ch. 3 |
| Thu, Sep 17 |
Simulation lab: random-walk experiments |
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Quiz 3 |
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| Tue, Sep 22 |
The stationary distribution, empirically; fixed points πP = π as a linear equation |
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Practice 5 out (Markov) |
Zitkovic |
| Thu, Sep 24 |
Hitting times and absorption; linear systems Ax = b |
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Quiz 4 |
Zitkovic; C&O Ch. 3 |
| Tue, Sep 29 |
Convergence as power iteration; eigenvalues and eigenvectors; stationary distribution as eigenvector |
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Midterm 1 practice out |
C&O §5.1 |
| Thu, Oct 1 |
PageRank; review |
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Quiz 5 (optional) |
C&O §9.6.1 |
| Tue, Oct 6 |
Midterm 1: random walks, linear systems, eigenvector fixed points |
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| Thu, Oct 8 |
Coordinates for data and distributions: vector spaces, bases, orthogonality |
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Practice 6 out (linear algebra) |
C&O Ch. 1–2 |
| Tue, Oct 13 |
Projections and best approximation of data by a subspace; Gram–Schmidt, QR |
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C&O §2.4–2.5, §4.7 |
| Thu, Oct 15 |
Spectral theorem: covariance matrices of data; reversible chains and reversing a random walk |
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Quiz 6 |
C&O §5.3 |
| Tue, Oct 20 |
Rayleigh quotients: max-variance directions in data; Perron–Frobenius, spectral gap, convergence rate |
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Midterm 2 practice out |
C&O §5.4–5.6 |
| Thu, Oct 22 |
SVD of the data matrix; low-rank approximation |
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Quiz 7 |
C&O §5.7 |
| Tue, Oct 27 |
Midterm 2: eigen-theory, spectral theorem, convergence of chains, SVD |
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| Thu, Oct 29 |
Lab: k-means clustering hands-on |
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C&O §7.5 |
| Tue, Nov 3 |
Spectral clustering via the graph Laplacian |
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Practice 7 out (SVD/eigen) |
C&O §9.4, §9.7.2 |
| Thu, Nov 5 |
PCA via SVD; the covariance matrix |
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Quiz 8 |
C&O §8.1 |
| Tue, Nov 10 |
PCA compression; best approximating subspace |
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Practice 8 out (PCA) |
C&O §8.2–8.3 |
| Thu, Nov 12 |
The multivariate Gaussian, formally: affine image of N(0, I); sampling via Σ1/2 |
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Quiz 9 |
C&O §7.1 |
| Tue, Nov 17 |
Mixtures of Gaussians: density, latent variables; GMM as soft k-means |
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Practice 9 out (Gaussian sampling) |
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| Thu, Nov 19 |
Generative models I: forward diffusion as a noising Markov chain; convergence to N(0, I) |
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Quiz 10 |
Lecture notes |
| Nov 24 & 26 |
Fall break / Thanksgiving — no classes |
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| Tue, Dec 1 |
Generative models II: reversing the chain; closed-form scores for Gaussian mixtures; GANs (overview) |
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Final practice out |
Lecture notes |
| Thu, Dec 3 |
Review for final |
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| Sat, Dec 12 |
Final Exam, 1:00–3:00 PM (room TBD): cumulative; emphasis on spectral methods, PCA, Gaussians, generative models |
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