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Living on the edge: Phase transitions in convex programs with random data
Published on Oct 29, 20142661 Views
Recent research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the
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Chapter list
Living on the Edge00:00
The Compressed Sensing Problem00:37
Untitled02:37
Convex Programs with Random Data05:20
Research Challenge...07:08
A Theory Emerges...07:24
Geometry of Compressed Sensing Problem08:39
The Core Question10:43
Statistical . Dimension11:14
Statistical Dimension: The Motion Picture11:19
The Statistical Dimension of a Cone12:28
Basic Statistical Dimension Calculations13:09
Circular Cones14:10
Descent Cones14:27
Descent Cone of `1 Norm at Sparse Vector14:53
Statistical Dimension & Phase Transitions16:23
Aside: The Gaussian Width17:22
Regularized Linear Inverse Problems17:59
Setup for Linear Inverse Problems18:15
Geometry of Linear Inverse Problems19:33
Linear Inverse Problems with Random Data20:31
Sparse Recovery via `1 Minimization22:04
Low-Rank Recovery via S1 Minimization23:17
More Examples24:46
But My Measurements aren’t Gaussian!25:35
But My Measurements aren’t Isotropic!26:45
PhD in Computing + Mathematical Sciences28:15