Also, when we want to combine two models for prediction, finding the Viterbi alignment argmax z p 1 (z | x)p 2 (z | x) is intractable for HMM models (by a reduction from quadratic assignment), and a hard intersection argmax z 1 p 1 (z 1 | x) ∩ argmax z 2 p 2 (z 2 | x) might be too sparse.
we can threshold the product of two edge posteriors quite easily: z = {z ij = 1 : We noticed a 5.8% relative reduction in AER (for our best model) by using posterior decoding with a validation-set optimized threshold δ instead of using hard intersection of Viterbi alignments.