Schedule

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
1-31-2019 Logistics
+
The Singular-Value Decomposition
Principal-component analysis,least
squares, low-rank matrix estimation
Applications: Dimensionality reduction,
linear regression, collaborative filtering
SVD SVD
2-7-2019 The Singular-Value Decomposition
(continued)
2-14-2019 The Frequency Domain
Fourier series, discrete Fourier
transform, translation invariance
Applications: Filtering, signal
sampling, compression, denoising
Fourier Fourier
2-21-2019 The Frequency Domain
(continued)
2-28-2019 Signal representations
Windowing, short-time Fourier
transform, multiresolution analysis
Applications: Denoising
Signal
representations
Signal
representations
3-7-2019 Randomization
Gaussian vectors, randomized
projections, random matrices
Applications: Dimensionality
reduction, compressed sensing
Randomization Randomization Project proposal due
(March 1st at midnight)
3-14-2019 Randomization
(continued)
3-28-2019 Midterm
4-4-2019 Convex Optimization
Convex functions, subgradients,
sparsity and low-rank regularization,
gradient descent, proximal methods
Applications: Sparse regression,
collaborative filtering
Convex Optimization Convex Optimization
4-11-2019 Convex Optimization
(continued)
4-18-2019 Duality
Lagrangian duality, dual certificates
Applications: Compressed sensing,
matrix completion
Duality Duality
4-25-2019 Duality
(continued)
5-2-2019 Nonconvex Optimization
Matrix factorization,
deep neural networks
Applications: Dictionary learning,
topic modeling, image denoising
Nonconvex Optimization Nonconvex Optimization Project + slides due
(May 5th at midnight)
5-6-2019 Project presentations
5-9-2019 Project presentations