Dates |
Topics covered |
Slides |
Week 1 (Jan 13, 2025) |
Lecture 1: Vector spaces, matrices, and norms.
Lecture 2: Probability review, concentration of measure. |
Lecture 1
Lecture 2 |
Week 2 (Jan 20, 2025) |
Martin Luther King, Jr. Day
Lecture 3: Least squares regression, kernel methods. |
Lecture 3 |
Week 3 (Jan 27, 2025) |
Lecture 4: Matrix factorizations I - SVD, QR.
Lecture 5: Matrix factorizations II - eigenvalue decomposition, PCA. |
Lecture 4
Lecture 5 |
Week 4 (Feb 3, 2025)
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Lecture 6: Approximate matrix product, sampling.
Lecture 7: Johnson–Lindenstrauss(JL) lemma, subspace embedding. |
Lecture 6
Lecture 7 |
Week 5 (Feb 10, 2025)
|
Lecture 8: Sketching, types of sketching matrices.
Lecture 9: Sketch and solve - least squares regression. |
Lecture 8
Lecture 9 |
Week 6 (Feb 17, 2025)
|
Lecture 10: Sampling for least squares, preconditioned LS.
Lecture 11: Randomized SVD. |
Lecture 10
Lecture 11 |
Week 7 (Feb 24, 2025)
|
Lecture 12: Subspace iteration (power) method.
Lecture 13: Krylov subspace method. |
Lecture 12
Lecture 13 |
Week 8 (Mar 3, 2025)
|
Lecture 14: Stochastic trace estimation.
Lecture 15: Introduction to tensors, tensor-matrix product. |
Lecture 14,
Spectral sums Lecture 15 |
Week 9 (Mar 10, 2025)
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Lecture 16: Canonical Polyadic (CP) decomposition.
Lecture 17: Randomized CP - I. |
Lecture 16
Lecture 17 |
Week 10 (Mar 17, 2025) |
Spring Break
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Week 11 (Mar 24, 2025)
|
Lecture 18: Randomized CP - II.
Lecture 19: Tucker decomposition, HOSVD. |
Lecture 18
Lecture 19 |
Week 12 (Mar 31, 2025)
|
Lecture 20: Randomized Tucker, TensorSketch.
Lecture 21: Tube-fiber product, t-product. |
Lecture 20
Lecture 21 |