Let λ be a parameter vector and f (y s−1 , y s , x) be a (local) feature vector obtained from the corresponding position s given x. CRFs define the conditional probability, p(y|x), as being proportional to a product of potential functions on the cliques.
p(y|x) on a (linear-chain) CRF can be defined as follows: is a normalization factor over all output values, Y, and is also known as the partition function.