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HomeMIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018Lecture 19: Saddle Points Continued, Maxmin Principle
Lecture 19: Saddle Points Continued, Maxmin Principle
52:13
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
