Basis Function

Creator
Creator
Seonglae Cho
Created
Created
2023 Mar 14 2:14
Editor
Edited
Edited
2023 Apr 6 1:23
Refs

Feature Map ϕ(x)\phi(x), Basis Function h(x)h(x)

hθ(x)=Σl=1Lθlϕl(x)=θTϕ(x)h_\theta(x) = \Sigma_{l=1}^L\theta_l\phi_l(x) = \theta^T\phi(x)
we can extend the linear regression into a linear combination of basis functions
RdR    (xRd){R^d \rightarrow R} \;\; (x \in R^d)
  • polynomial basis xlx^l
  • gaussian basis exp(xμl22σ2)exp(-\frac{||x - \mu_l||^2}{2\sigma^2})
 
 
 
 

Using nonlinear basis functions, we allow the function to be nonlinear

 
 
 
 
 

 

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