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