Probabilistic and sequence join costs

Another way of improving on the basic acoustic-distance join cost is the probabilistic sequence join function, which takes more frames into account than just those near the join. Vepa and King [469] used a Kalman filter to model the dynamics of frame evolution, and then converted this into a cost, measured in terms of how far potential joins deviated from this model. A full probabilistic formulation, which avoids the idea of cost altogether, was developed by Taylor [438]. 

The idea is to measure the probability of this for the sequence of frames across every pair of candidate units across a join, and use the result as a measure of join qnality in the search. P 0) is too difiicnlt to estimate in full, so we make the n-gram assumption and estimate it on a shorter seqnence of frames (say two before and two after the join). The powerful thing abont this approach is that the model can be trained on all the data in the speech database, not jnst examples near unit boundaries. This often results in many 

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