Conditional random fields are a form of 🗳️ Markov Random Fields that models the conditional distribution . Our graph contains variables and , and the distribution is
with partition function
This is similar to a standard Markov random field, but it now depends on .
We commonly assume the factors have form
where describes the compatibility between and . Sometimes, the factor may take in the entire and use it to compare . We do this because is given as input, and there's no need to model since we're only looking for .