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

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,CHAPTER 3. HIDDEN MARKOV MODELS 60(a)0.26a1.000.210.570.650.530.510.350.270.00Start0.00a0.43b0.23a bEnd(b)0.270.00 0.210.39 0.250.570.000.471.000.520.610.43Start ab a b0.28EndFigure 3.9: Case study II: BW-derived HMM structures that fail on generalization.Baum-Welch studies As in the previous case study, we looked at various model structures found byBaum-Welch estimation. All examples in this section are from training on the 20 random samples.Figure 3.9(a) shows a structure that is overly general: it generates , %§E#&#%0have an HMM that partly overgeneralizes, but at the same time exhibits a rather peculiar case of overfitting: itw¤07#& # . In (b), weexcludes strings of the >#&6#&# form where"is even. No such cases happened to be present in the trainingset.The accurate model structures of 10 states found by the Baum-Welch method again tended to berather convoluted. Figure 3.10 shows as case in point.Merging studies We also repeated the experiment examining the levels of generalization by the mergingalgorithm, as the value of the global prior weight was increased over three orders of magnitude.Figure 3.11 shows the progression of models for. 6 0£ 018 0£ 18, and 1£ 0. The pattern is similar tothat in in the first case study (Figure 3.11). The resulting models range from a simple merged representation ofthe samples to a plausible overgeneralization from the training data ( , B#&#%07# ). The target model is obtainedfor.values between these two extremes.
CHAPTER 3. HIDDEN MARKOV MODELS 61Start1.000.020.450.450.460.300.520.160.010.00b0.330.36aa0.000.000.410.550.380.17 0.610.590.96 0.031.000.241.000.460.500.010.00a a b bbab a bEndFigure 3.10: Case study II: Redundant BW-derived HMM structure for B#'#%#'# .
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The dissertation of Andreas Stolcke
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Bayesian Learning of Probabilistic
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iAcknowledgmentsLife and work in Be
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iiiContentsList of FiguresList of T
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CONTENTSv4.5.4 Summary and Discussi
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CHAPTER 1. INTRODUCTION 2Instance-b
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CHAPTER 1. INTRODUCTION 4A.0.830.33
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CHAPTER 1. INTRODUCTION 6the ¨ 0 l
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..1 £££1; 450,1 £££1; 450CHAP
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Page 88 and 89: domain. 3 In short, we will leave o
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Page 116 and 117: 104Chapter 5Probabilistic Attribute
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CHAPTER 5. PROBABILISTIC ATTRIBUTE
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122Chapter 6Efficient parsing with
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1z1CHAPTER 6. EFFICIENT PARSING WIT
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and each state in set ( -ÏH ):6)
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NPDetVTVI P CHAPTER 6. EFFICIENT PA
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CHAPTER 6. EFFICIENT PARSING WITH S
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) In particular, the string probabi
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H : d=:6) ¸ÆÆÆ:6) ¸ .V=i£Ù )
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©) 6#=©,©,©,,ÆNNö,²NL++and>+
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) The probabilistic unit-production
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¸0 ¸ 29¸¸ 99W9 [;t£ ? 1 ?1u 6
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The forward and inner probabilities
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9 itself²²NN++9 ¸0ÌLL++??1£,=C
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,,by nonterminals. Multiplying this
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6CHAPTER 6. EFFICIENT PARSING WITH
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description. Again, we ignore this
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for all pairs of states d =¸+= Š
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,9 ¸0 : 0¸ £j9¸ A )z9£CHAPTER
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are then summed over all nontermina
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+CHAPTER 6. EFFICIENT PARSING WITH
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1CHAPTER 6. EFFICIENT PARSING WITH
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= ¸Let t,t) ¸ .V=i£,t,t,6666yyyy
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168Chapter 7-grams from Stochastic
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CHAPTER 7. -GRAMS FROM STOCHASTIC
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)ÅÆÅÅÅÆÅÅÅÆÅÅÅÆÅÅÅ
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-grams CCHAPTER 7. -GRAMS FROM ST
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,?Ó,tÌ?L A0,I 1N I N A A 2 A 3 N
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,,CHAPTER 7. -GRAMS FROM STOCHASTI
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Consider the following problem: sta
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CHAPTER 8. FUTURE DIRECTIONS 1828.2
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184BibliographyAHO, ALFRED V., RAVI
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BIBLIOGRAPHY 186DAGAN, IDO, FERNAND
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BIBLIOGRAPHY 188——, & ——. 1
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BIBLIOGRAPHY 190QUINLAN, J. ROSS, &
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BIBLIOGRAPHY 192WALLACE, C. S., & P
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