Assume that we independently collect n observations, where each observation has features stored in a vector x; E RP and a label yi for i = 1, ..., n. Logistic regression is used to construct a model with parameters w such that +1 with probability o(w xi) yi = -1 with probability 1 - o(w xi), where o(a) = 1 The loss function is given by negative likelihood n I( W = logo (yiw Xi) n i=1