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Theoretical Analysis under Random Design
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Classroom Contents
Fast and Optimal Low-Rank Tensor Regression via Importance - Garvesh Raskutti, UW-Madison
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- 1 Intro
- 2 Tensors - Multi-way data
- 3 Tensors - Higher-order solutions
- 4 Tensors - New challenges
- 5 Low-rank tensor regression
- 6 Low-rank tensor structure
- 7 Matricization
- 8 Prior approaches
- 9 Randomized Sketching
- 10 Recall: Model and data
- 11 Probing Importance Sketching Direction
- 12 Interpretations of Step 1
- 13 Interpretation of Step 2
- 14 Dimension-Reduced Regression
- 15 Assembling the Final Estimate
- 16 Algorithm Summary
- 17 Sketching perspective of ISLET
- 18 Computation and Implementation of ISLET
- 19 ISLET allows parallel computing conveniently
- 20 Theoretical Analysis under General Design
- 21 Proof overview
- 22 Theoretical Analysis under Random Design
- 23 Minimax Lower Bound
- 24 Theory summary (informal)
- 25 Simulation - Comparison with Previous Methods
- 26 Simulation - Large p Settings
- 27 ADHD example
- 28 ADHD comparison
- 29 Conclusion
