Consider the loss function for ridge regression (ignoring the intercept term): L(w) = (y) - w × x(¹))² + A||w||² n i=1 where (x(¹), y(1)),..., (x(n), y(n)) = Rd x R are n data points and labels; and w€ Rd. There is a closed-form equation for the optimal w, but suppose that we decide instead to minimize the function using local search. 1. What is VL(w)? 2. Write down the update step for gradient descent.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the loss function for ridge regression (ignoring the intercept term):
n
L(w) = [(y(¹) – w × x(¹))² + X||w||²
-
i=1
where (x(¹), y(1)),..., (x(n), y(n)) = Rd x R are n data points and labels; and w€ Rd.
There is a closed-form equation for the optimal w, but suppose that we decide instead to
minimize the function using local search.
1. What is VL(w)?
2. Write down the update step for gradient descent.
Transcribed Image Text:Consider the loss function for ridge regression (ignoring the intercept term): n L(w) = [(y(¹) – w × x(¹))² + X||w||² - i=1 where (x(¹), y(1)),..., (x(n), y(n)) = Rd x R are n data points and labels; and w€ Rd. There is a closed-form equation for the optimal w, but suppose that we decide instead to minimize the function using local search. 1. What is VL(w)? 2. Write down the update step for gradient descent.
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