2. Logistic Regression. Consider the logistic gression mod IP(Y-1 X uo un, u) (m+ wiXit w2X2) for a binary classification with a sigmoid function (z) = 1+1 . Assume we train the logistic regression model based on the N training examples a1,..., aM and labels y,...,y" by maximizing the penalized log-likelihood of the labels: i=1 For large (strong regularization), the log-likelihood terms will behave as linear functions of w (you can see this via taylor approximation) 2 1. Express the penalized log-likelihood using this approximation, and derive the expression for MLE w in terms of and training data {(x, yi)1