The dissertation of Andreas Stolcke is approved: University of ...

CHAPTER 3. HIDDEN MARKOV MODELS 46local posterior probability maxima in the space of HMM structures constructed by successive mergingoperations.By far the most common problem found in practice is that the stopping criterion is triggered tooearly, since a single merging step alone decreases the posterior model probability, although additional relatedsteps might eventually increase it. This happens although in the vast majority of cases the first step is inthe right direction. The straightforward solution to this problem is to add a ‘lookahead’ to the best-firststrategy. The stopping criterion is modified to trigger only after a fixed number of steps 1 have producedno improvement; merging still proceeds along the best-first path. Due to this, the lookahead depth does notÌentail an exponential increase in computation as a full tree search would. The only additional cost is the workperformed by looking ahead in vain at the end of a merging sequence. That cost is amortized over severalsamples if incremental merging with a batch size 1 is being used.Best-first merging with lookahead has been our method of choice for almost all applications, usingÌlookaheads between 2 and 5. However, we have also experimented with beam search strategies. In these, aset of working models is kept at each time, either limited in number (say, top! the scoring ones), or by thedifference in score to the current best model. On each inner loop of the search algorithm, all current modelsare modified according to the possible merges, and among the pool thus generated the best ones accordingto the beam criterion are retained. (By including the unmerged models in the pool we get the effect of alookahead.)Some duplication of work results from the fact that different sequences of merges can lead to thesame final HMM structure. To remove such gratuitous duplicates from the beam we attach a list of disallowedmerges to each model, which is propagated from a model to its successors generated by merging. Multiplesuccessors of the same model have the list extended so that later successors cannot produce identical resultsfrom simply permuting the merge sequence.The resulting beam search version of our algorithm does indeed produce superior results on datathat requires aligning long substrings of states, and where the quality of the alignment can only be evaluatedafter several coordinated merging steps. On the other hand, beam search is considerably more expensive thanbest-first search and may not be worth a marginal improvement.All results in Section 3.6 were obtained using best-first search with lookahead. Nevertheless,improved search strategies and heuristics for merging remain an important problem for future research.3.5 Related WorkMany of the ideas used in our approach to Bayesian HMM induction are not new by themselves,and can be found in similar forms in the vast literatures on grammar induction and statistical inference.