consider fitting a 2 regularized linear regression model to data x 1 y 1 x n y n where x t y t r are scalar values for each t 1 n to fit the parameters of this model one solves min r 0 rl 0 where l 0 t 1n y t x

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Consider fitting a

â„“2
-regularized linear regression model to data

(x(1),y(1)),…,(x(n),y(n))
where

x(t),y(t)∈R
are scalar values for each

t=1,…,n
. To fit the parameters of this model, one solves



minθ∈R, θ0∈RL(θ,θ0)

where



L(θ,θ0)=∑t=1n(y(t)−θx(t)−θ0)2 + λθ2

Here

λ≥0
is a pre-specified fixed constant, so your solutions below should be expressed as functions of

λ
and the data. This model is typically referred to as ridge regression .

Write down an expression for the gradient of the above objective function in terms of

θ
.

Important: If needed, please enter

∑nt=1(…)
as a function sum_t(...), including the parentheses. Enter

x(t)
and

y(t)
as x^{t} and y^{t}, respectively.

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