Here is a tentative schedule for the course, the contents are subject to modifications.

Additional references are listed at the end of the notes.

Date Contents Slides Notes Deadlines
9-6-2017 Overview of the course
Vector spaces
Linear algebra, nearest-neighbor
classification, projections, denoising
Vector spaces Vector spaces
9-13-2017 Matrices
Linear maps, singular-value decomposition,
principal-component analysis, eigendecomposition
Matrices Matrices
9-20-2017 Matrices
Hw 1 due
9-27-2017 Randomness
Gaussian vectors, random
projections, randomized svd
Randomness Randomness Project proposal due
10-4-2017 The Fourier domain
Frequency representation, convolutions, filtering,
sampling theorem, super-resolution
Fourier Fourier Hw 2 due
10-11-2017 The Fourier domain
Spectral SR
10-18-2017 Multiresolution
Short-time Fourier transform,
wavelets, thresholding
Multiresolution Multiresolution
10-25-2017 Linear models
Linear regression, overfitting
regularization, logistic regression
Linear models Linear models Hw 3 due
11-8-2017 Linear models
Hw 4 due
11-15-2017 Convex optimization
Convexity, differentiable functions,
optimization algorithms
Convex optimization Convex optimization
11-29-2017 Nondifferentiable functions
Sparse regression, robust PCA,
subgradients, algorithms
Nondifferentiable functions Nondifferentiable functions Hw 5 due
12-6-2017 Constrained optimization
Duality, dual certificates,
compressed sensing, matrix completion
Constrained optimization Constrained optimization
12-13-2017 Matrix factorization
Matrix completion, nonnegative
matrix factorization, Sparse PCA
Matrix factorization Matrix factorization Final project due on December 15