Closed-form expression

Creator
Creator
Seonglae Cho
Created
Created
2023 Mar 9 2:12
Editor
Edited
Edited
2025 Feb 4 14:10
Refs
Refs
minimize the cost explicitly without relying on an iterative algorithm
  1. take
    Derivation
    of
    Cost Function
    with respect to the model coefficient θ\theta
  1. find
    Local extremum point

Normal Equation

XTXθXTy=0X^TX^\theta - X^T\vec{y} = 0
number 1’s result is d×1d \times 1 dimension if X is n×dn \times d vector (d is number of coefficient count)
 
 
Fancy but Inverse matrix is very expensive
θ=(XTX)1XTy\theta = (X^TX)^{-1}X^T\vec{y}
 
 
 
 
 

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