2. Regularization: (a) Suppose we have a process described by the joint distribution p(x, (), where & E R" is a feature vector and t e R is the target. Suppose also that we have constructed a neural network that implements the map y : " -+ R, and the network has been trained by minimizing the following error function: Edx ( div(x) - 4' p(tx)(x). Suppose that the feature vectors are perturbed by a distributed vari able { ~ p(() such that the new perturbed error function / becomes: where d P(E) = 1 1 ( LEGSP(E) = DEJN where v is the variance of the noise. Demonstrate that perturbed error function can be expressed as a regularized error function of the form with corrections of O(6 ). Give the explicit form of 2, disregarding corrections of O(6 ). (10 marks) Hint: Expand in Taylor the integrand of the perturbed error func- tion for small values of the perturbation