CRFs learn a conditional probability model p λ (l|x) from a set of labeled training data, where x = (x 1 , ..., x n ) is a random sequence of input words, l = (l 1 , ..., l n ) is the sequence of label variables (NER tags) for x, and l has certain Markov properties conditioned on x.
a general-order CRF with order o assumes that label variable l i is dependent on a fixed number o of previous label variables l i−1 , ..., l i−o , with the following conditional distribution: where f k 's are feature functions, λ k 's are weights of the feature functions (parameters to learn), and Z λ (x) is a normalization constant.