Lecture 19: Saddle Points Continued, Maxmin Principle

Description

Professor Strang continues his discussion of saddle points, which are critical for deep learning applications. Later in the lecture, he reviews the Maxmin Principle, a decision rule used in probability and statistics to optimize outcomes.

Summary

\(x'Sx/x'x\) has a saddle at eigenvalues between lowest / highest.
(Max over all \(k\)-dim spaces) of (Min of \(x'Sx/x'x\)) = evalue
Sample mean and expected mean
Sample variance and \(k\)^th eigenvalue variance

Related sections in textbook: III.2 and V.1

Instructor: Prof. Gilbert Strang