  Online alignment in machine translation refers to the task of aligning a
target word to a source word when the target sequence has only been partially
decoded. Good online alignments facilitate important applications such as
lexically constrained translation where user-defined dictionaries are used to
inject lexical constraints into the translation model. We propose a novel
posterior alignment technique that is truly online in its execution and
superior in terms of alignment error rates compared to existing methods. Our
proposed inference technique jointly considers alignment and token
probabilities in a principled manner and can be seamlessly integrated within
existing constrained beam-search decoding algorithms. On five language pairs,
including two distant language pairs, we achieve consistent drop in alignment
error rates. When deployed on seven lexically constrained translation tasks, we
achieve significant improvements in BLEU specifically around the constrained
positions.
