The Power of Nonconvex Optimization in Solving Random Quadratic Systems of Equations - Lecture 1

The Power of Nonconvex Optimization in Solving Random Quadratic Systems of Equations - Lecture 1

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Intro

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1 of 20

Intro

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The Power of Nonconvex Optimization in Solving Random Quadratic Systems of Equations - Lecture 1

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

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