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Scalable Structured Low Rank Matrix Optimization Problems
Published on Aug 26, 20133491 Views
We consider a class of structured low rank matrix optimization problems. We represent the desired structure by a linear map, termed mutation, that can encode matrices having entries partitioned into k
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Chapter list
Scalable Structured Low Rank Matrix Optimization Problems00:00
Outline00:14
General Setting00:56
Learn From Empirical Data Via Regularization - 100:57
Learn From Empirical Data Via Regularization - 201:05
Learn From Empirical Data Via Regularization - 301:17
Structure-Inducing Penalties02:21
Composite Penalties03:34
A Class of Structured Low-rank Learning Problem04:53
Structured Low-rank Learning Problem05:10
Encoding Group Structures via Mutations06:28
Application to System Identification07:36
Subspace Identification of Linear Dynamical Systems - 109:11
Subspace Identification of Linear Dynamical Systems - 210:33
Solution Strategies11:26
Proximal Algorithms for Nuclear-norm Problems - 111:37
Proximal Algorithms for Nuclear-norm Problems - 212:23
Proximal Algorithms for Nuclear-norm Problems - 312:46
Proximal Algorithms for Nuclear-norm Problems - 412:56
Proximal Algorithms for Nuclear-norm Problems - 513:10
Implementing Mutations via Linear Indexing13:58
Implementing Mutations via Linear Indexing15:02
Constrained Problem Formulation - 115:48
Constrained Problem Formulation - 216:48
Constrained Problem Formulation - 317:01
SVD-free Solution Strategy - 117:50
SVD-free Solution Strategy - 218:01
SVD-free Solution Strategy - 318:12
SVD-free Solution Strategy - 418:28
Augmented Lagrangian Approach19:20
Experiments - 120:09
Experiments - 221:16
Experiments - 322:11
Experiments - 422:53
Experiments - 523:10
Experiments (cont’d) - 123:43
Experiments (cont’d) - 225:23
Conclusions25:44