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

CHAPTER 3. HIDDEN MARKOV MODELS 580.50.50.50.51.00.50.50.5 0.5Start a b a b EndFigure 3.7: Case study II: HMM generating the test language $#%#%#&# .magnitude to produce undergeneralized (overfitted) and overgeneralized models, respectively. The series ofmodels found (using the minimal sample) is shown in Figure 3.6.concise manner. For a wide range around. 6 0£ 16, the target HMM is derived, up to different probabilityFor.Ü60£ 016 no structural generalization takes place; the sample set is simply represented in aparameters. A further to.K6 1£ increase 0 produces a model whose structure no longer distinguishes betweenand . One could argue that this overgeneralization is a ‘natural’ one given the data.3.6.1.4 Case study IIThe second test language is >#%#&#%# , generated by the HMM depicted in Figure 3.7.minimal training sample contains the following nine stringsThe The other training sample once again consisted of 20 randomly drawn strings.Figure 3.8 presents the results in graphical form, using the same measures and arrangement as inthe previous case study. (However, note that the ranges on some of the ÷ -axes differ.)Similar to the previous experiment, the merging procedure was successful in finding the targetmodel, whereas the Baum-Welch estimator produced inconsistent results that were highly dependent on theinitial parameter settings. Furthermore, the Baum-Welch success rates seemed to reverse when switchingfrom the minimal to the random sample (from 6/10 and 0/10 to 1/10 and 6/10, respectively). This is disturbingsince it reveals a sensitivity not only to the number of states in the model, but also to the precise statistics ofthe sample data.The overgeneralizations are typically of the form , $#'#%06, where either"ã6 1 or"Ì2.