Blunsom & Cohn (2006) use Viterbi decoding to find an alignment of two sentences given a trained CRF model, a * argmax a P Λ (a|C i , C j ).
the posterior probabilities of the labels at each position can be calculated as well using the forwardbackward algorithm: where α l and β l are the forward and backward vectors that are computed with the forward-backward algorithm (Lafferty et al., 2001).