CONDITIONAL RANDOM FIELDS

logistic regression CRFs can be seen as a generalization of logistic regression. So we will begin by reviewing logistic regression. This is the simplest example of a " log-linear model " where the log-odds of the probability of a binary label y ∈ {0, 1} are a linear function of the data x ∈ R d : logit(P (y = 1|x)) = log P (y = 1|x) P (y = 0|x) = log P (y = 1|x) 1 − P (y = 1|x) = β T x = β 0 + d k=1 β k x k. Rearranging terms, we find that the probability that y = 1 is given by the sigmoid function P (y = 1|x) = 1 1 + exp(−β T x) = S(β T x).