Logistic Regression with Regularization

0.2 Logistic Regression with Regularization (20 points] 1) [10 point] Let the data be (Xi, yi) 1, where xi e Rd and yi {0,1}. Logistic regression is a binary classification model, with the probability of yi being 1 as: 1 P(Yi;Xi,) = 0 (0+x) 4 1+e where 0 is the model parameter. Assume we impose an L2 regularization term on the parameter, defined as: AT > Xi R(0) = 2 with a positive constant 1. Write out the final objective function for this logistic regression with regularization model. 2) [10 point] If we use gradient descent to solve the model parameter. Derive the updating rule for 0. Your answer should contain the derivation, not just the final answer. 0.2 Logistic Regression with Regularization (20 points] 1) [10 point] Let the data be (Xi, yi) 1, where xi e Rd and yi {0,1}. Logistic regression is a binary classification model, with the probability of yi being 1 as: 1 P(Yi;Xi,) = 0 (0+x) 4 1+e where 0 is the model parameter. Assume we impose an L2 regularization term on the parameter, defined as: AT > Xi R(0) = 2 with a positive constant 1. Write out the final objective function for this logistic regression with regularization model. 2) [10 point] If we use gradient descent to solve the model parameter. Derive the updating rule for 0. Your answer should contain the derivation, not just the final