This course aims to teach learners how to achieve fast and optimal low-rank tensor regression through importance sketching. The course covers topics such as tensors, low-rank tensor structure, randomized sketching, and dimension-reduced regression. The teaching method involves theoretical analysis, algorithm summaries, and simulations. The intended audience for this course includes faculty, postdoctoral researchers, and Ph.D. students from the UK/EU interested in the intersection of statistics and computer science in machine learning.
Fast and Optimal Low-Rank Tensor Regression via Importance - Garvesh Raskutti, UW-Madison
Alan Turing Institute via YouTube
Overview
Syllabus
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
Taught by
Alan Turing Institute
