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Solving quadratic systems of equations
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Classroom Contents
Random Initialization and Implicit Regularization in Nonconvex Statistical Estimation - Lecture 2
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- 1 Intro
- 2 Statistical models come to rescue
- 3 Example: low-rank matrix recovery
- 4 Solving quadratic systems of equations
- 5 A natural least squares formulation
- 6 Rationale of two-stage approach
- 7 What does prior theory say?
- 8 Exponential growth of signal strength in Stage 1
- 9 Our theory: noiseless case
- 10 Population-level state evolution
- 11 Back to finite-sample analysis
- 12 Gradient descent theory revisited
- 13 A second look at gradient descent theory
- 14 Key proof idea: leave-one-out analysis
- 15 Key proof ingredient: random-sign sequences
- 16 Automatic saddle avoidance
