JNTU Feed Forward Neural Networks Problem Set

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

minθR, θ0RL(θ,θ0)

where

L(θ,θ0)=t=1n(y(t)θx(t)θ0)2 + λθ2

Here λ0 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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