Consider a simplified logistic regression problem. Given m training samples (x,y), i = 1,...,m. The data...

 

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Consider a simplified logistic regression problem. Given m training samples (x,y), i = 1,...,m. The data re R, and y = {0, 1}. To fit a logistic regression model for classification, we solve the following optimization problem, where ER is a parameter we aim to find: max (0), 0 (1) where the log-likelhood function m (e) { log(1+ exp{-x'})+(y-1)0x'}. = i=1 1. (5 points) Show step-by-step mathematical derivation for the gradient of the cost func- tion (0) in (1). Consider a simplified logistic regression problem. Given m training samples (x,y), i = 1,...,m. The data re R, and y = {0, 1}. To fit a logistic regression model for classification, we solve the following optimization problem, where ER is a parameter we aim to find: max (0), 0 (1) where the log-likelhood function m (e) { log(1+ exp{-x'})+(y-1)0x'}. = i=1 1. (5 points) Show step-by-step mathematical derivation for the gradient of the cost func- tion (0) in (1).