Randomized Least Squares Regression - Combining Model- and Algorithm-Induced Uncertainties

Explore randomized least squares regression in this 24-minute lecture by Ilse Ipsen from North Carolina State University. Delve into the combination of model- and algorithm-induced uncertainties, covering topics such as regression models, objective functions, and existing work in the field. Examine model-induced uncertainty, perturbed solutions, and multiplicative perturbation bounds. Analyze the hat matrix and its comparison, as well as conditioning on S for mean, variance, and summary. Investigate combined uncertainty in terms of mean and variance, and conclude with an example of the best case for uniform sampling. Gain insights into this advanced topic in randomized numerical linear algebra and its applications.

Intro
Least Squares/Regression Models
Objective
Existing Work
Model-Induced Uncertainty
Perturbed Solution
Example: Hat Matrix, and Comparison Hat Matrix
Multiplicative Perturbation Bounds
Conditioning on S. Mean
Conditioning on S: Variance
Conditioning on S: Summary
Combined Uncertainty: Mean
Combined Uncertainty: Variance
Example: Best Case for Uniform Sampling