EL ENG 16A Lecture Notes - Lecture 3: Overfitting, Invertible Matrix, Underdetermined System
31 Jan 2018
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Document Summary
Projection theorem: the orthogonal projection is the shortest distance from a point onto a line/space; the closest point in a plane/space to a ve ctor outside the plane/space is the point that forms a perpendicular line to that vector. Least squares least squares - a method for minimizing error by solving overdetermined systems of equations (more equations than variables/unknowns) Find the solution of an inconsistent and overdetermined system of equations. Use least squares in settings with a lot of noise (inconsistency) In all least squares problems: # of equations/measurements we have > # of unknowns. Ordinary least squares is used to solve inconsistent equations. Least squares cannot be used to solve underdetermined systems of equations. Our goal is to try to find the line that minimizes the squared vertical distance between each point and the line.
