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

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.

Intro
Tensors - Multi-way data
Tensors - Higher-order solutions
Tensors - New challenges
Low-rank tensor regression
Low-rank tensor structure
Matricization
Prior approaches
Randomized Sketching
Recall: Model and data
Probing Importance Sketching Direction
Interpretations of Step 1
Interpretation of Step 2
Dimension-Reduced Regression
Assembling the Final Estimate
Algorithm Summary
Sketching perspective of ISLET
Computation and Implementation of ISLET
ISLET allows parallel computing conveniently
Theoretical Analysis under General Design
Proof overview
Theoretical Analysis under Random Design
Minimax Lower Bound
Theory summary (informal)
Simulation - Comparison with Previous Methods
Simulation - Large p Settings
ADHD example
ADHD comparison
Conclusion