7. The Laplace distribution, parameterized by and , is defined as follows: Laplace(x;,)=21exp(x) Consider a variant of Bayesian linear regression where we assume the prior over the weights w consists of an independent zero-centered Laplace distribution for each dimension (wj), with shared parameter : wjtwLaplace(0,)N(t;wT(x),) For reference, the Gaussian PDF is: N(x;,)=21exp(22(x)2) (1) Suppose you have a labelled training set {(x(i),t(i))}i=1N. Please give the cost function you would minimize to find the MAP estimate of w. (It should be expressed in terms of mathematical operations.) (2) Based on your answer to part (1), how might the MAP solution for a Laplace prior differ from the MAP solution if you use a Gaussian prior