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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
Description:
Explore the intersection of statistics and computer science in machine learning through this conference talk by Garvesh Raskutti from UW-Madison. Delve into the world of fast and optimal low-rank tensor regression using importance sketching. Discover how the cross-fertilization between statistics and computer science has led to the development of modern machine learning paradigms. Learn about tensors, multi-way data, and higher-order solutions. Understand the challenges of low-rank tensor regression and the importance of tensor structure. Examine randomized sketching techniques and the ISLET algorithm for dimension-reduced regression. Gain insights into theoretical analysis, minimax lower bounds, and practical implementations. See comparisons with previous methods through simulations and explore real-world applications using an ADHD example. This 37-minute talk, presented at the Alan Turing Institute, offers a comprehensive overview of cutting-edge techniques in tensor regression and their implications for big data analysis. Read more

Fast and Optimal Low-Rank Tensor Regression via Importance - Garvesh Raskutti, UW-Madison

Alan Turing Institute
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