Y 3/1 1 Um S Rewrite J(w, b, A) in matriz form. 1 , and 8: - [. .

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ISBN:9781337282291
Author:Ron Larson
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Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
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Given a dataset D = {(z,y), i=1,2,...,m} consisting of m predictors x = =(Ti,..., Tin) €
R" and m corresponding responses y, E R. Consider the following linear ridge regression model:
(P)
minimize J(w, b, x):=
m
;Σ((x₁, w) + b - y)² + (|||| +8²)
i=1
2m
where (w, b) ER" x R is a vector of parameters to be determined and A> 0 is a penalty
parameter to be tuned for finding the best regression function.
Transcribed Image Text:Given a dataset D = {(z,y), i=1,2,...,m} consisting of m predictors x = =(Ti,..., Tin) € R" and m corresponding responses y, E R. Consider the following linear ridge regression model: (P) minimize J(w, b, x):= m ;Σ((x₁, w) + b - y)² + (|||| +8²) i=1 2m where (w, b) ER" x R is a vector of parameters to be determined and A> 0 is a penalty parameter to be tuned for finding the best regression function.
Question 1.
Let
Y =
3/1
1
Um
5
X :-
Rewrite J(w, b, A) in matriz form.
Define
J(w, b) :=
[1 211
1
Iml
1
Ilm
.
and 8:=
- [].
m
2mΣ((x, w) + b - y)².
i=1
Transcribed Image Text:Question 1. Let Y = 3/1 1 Um 5 X :- Rewrite J(w, b, A) in matriz form. Define J(w, b) := [1 211 1 Iml 1 Ilm . and 8:= - []. m 2mΣ((x, w) + b - y)². i=1
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