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The Power of Nonconvex Optimization in Solving Random Quadratic Systems of Equations - Lecture 1
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- 1 Intro
- 2 Nonconvex optimization may be super scary
- 3 Example: solving quadratic programs is hard
- 4 Example of convex surrogate: low-rank matrix completion
- 5 Example of lifting: Max-Cut
- 6 Solving quadratic systems of equations
- 7 Motivation: a missing phase problem in imaging science
- 8 Motivation: latent variable models
- 9 Motivation: learning neural nets with quadratic activation
- 10 An equivalent view: low-rank factorization
- 11 Prior art (before our work)
- 12 A first impulse: maximum likelihood estimate
- 13 Interpretation of spectral initialization
- 14 Empirical performance of initialization (m = 12n)
- 15 Improving initialization
- 16 Iterative refinement stage: search directions
- 17 Performance guarantees of TWF (noiseless data)
- 18 Computational complexity
- 19 Numerical surprise
- 20 Stability under noisy data
