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

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= ¸Let t,t) ¸ .V=i£,t,t,6666yyyy¸ Æ—@_,6)1yt,“ ·“ ·Õ· “Æ—@ è ,>è1tÖ0 Ȩ½£=ï1CHAPTER 6. EFFICIENT PARSING WITH STOCHASTIC CONTEXT-FREE GRAMMARS 166to show that (6.5)) ¸@B0 be the probability for LR item ) ¸@(with a dot somewhere in the RHS). We want.—£ ˜M0) ¸position of the last input symbol processed; a reduce action of the parser effectively resets H to the beginningof the reduced nonterminal.The computation of LR item sets begins with the initial item £j9, whichthereby agreeing with (6.5).¸The first operation for constructing item sets is closure, whereby for each item ) ¸has t 6 1 by definition,.—£=¤˜ , all items.—£ ˜M0%6@A?for any item ) ¸ 0å…å…å 10.—£ ˜ , regardless of position H and start index". Note that H is not always equal to theC+-,9£j@corresponding to the available productions=¸@are added to the set. This operation is recursiveand corresponds obviously to Earley’s prediction step. Also, the way in whicht values are propagated followsexactly the way forward probabilities are handled during prediction. (The left-corner relation ©ë could beused to compute closure probabilities exactly, but Wright suggests using a truncated recursion instead.) Sinceclosure and prediction are thus isomorphic, and since the prefix relative to the items does not change, (6.5)also remains valid during this step.Finally, a successor set ² Ù of kernel items is constructed from an existing closed set ² in whatcorresponds to Earley’s scanning or completion. Specifically, ) ¸forI ²each current item , an itemis placed in , reachable by scanning a or reducing (completing) a nonterminal=..—£=§˜terminal= ² Ù¸ .V=i£ )let= (We stand for either terminal or nonterminal to treat both cases jointly.) The new item probability iscomputed as) ¸ .V=i£) ¸(6.6)˜.—£=ë˜M0˜M0&6,> Ȩ½£=ï 0This can be understood as scaling the total probability of items matching= to unity.By substituting (6.5) into (6.6) we get“ ·ž'¼å‘îÇ ^ Õ ”'/å‘KÖ0¿j¿j¿^ˆ‡1 H¾zÃƒ˜M0c6Æ @ ,>“ · C+-,90å…å…å@A?10Æ @ ,) ¸.M£=§˜M0ž'¼å‘î0ž'¼å‘îÆ—@;,> ¸~½£=ïÆ @ ,) ¸.M£=§˜M0Š@ è ,=ë00Š@ èè ,) ¸ .V=i£Æ—@˜M0(6.7)ž'¼å‘î,=ë0Æ—@;,> ¸~½£=ï0Ȩ½=Œ£ ïî@ è ,) ¸ .V=i£Æ˜M0(6.8)@ è ?ž'¼ ‘å+-,9 10C 0å…å…å
W ‘W'ÁåŠ@7,=) ¸ .V=i£,1CHAPTER 6. EFFICIENT PARSING WITH STOCHASTIC CONTEXT-FREE GRAMMARS 167t ˜M06The HCÙ position is that of the current next input. We have used abbreviationŠ@è ,=ã0 the for the sum of innerprobabilities pertaining to the completed=, i.e.,Two steps in the derivation above need justification. In (6.7) we are computing forward probabilitiesjust as in an Earley completion step (see equation (6.1)). To get (6.8) we observe that the set ² Ù containsall possible kernel items after having processed the prefix 1 0å…å…å@ è ?1 (by definition of the LR parsing method).Hence the sum of è represents all possible partial derivations generating the prefix, i.e., +-,9 C @ Æ10 .Š@ ,=ë0&6Àµ1is terminal@>£…0 if= is nonterminal.¸0å…å…å@ è ?
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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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VU=@U@@=U===UCHAPTER 2. FOUNDATIONS
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,,vv,v,v,,directly. However, note t
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4@@@@-@b@6@˜--@@@0@@@@@CHAPTER 2.
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6tt,u ·¥¸¹u ,10ºtu ,2 10Yt ¸
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CHAPTER 2. FOUNDATIONS 18As more da
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CHAPTER 2. FOUNDATIONS 20Global mod
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CHAPTER 2. FOUNDATIONS 22¡An expli
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ÊS==66@N,ÆÆ=NÆ00ÆÊ=S=N0Æ=#@0
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666CHAPTER 2. FOUNDATIONS 262.5.7 P
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It, u¦¸¹u Ù 0w6¬tt,_, u Ù 0
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, uu!¸¹u Ù 0c6,u ,ÔÔ0 ö1 ö1
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CHAPTER 3. HIDDEN MARKOV MODELS 32T
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CHAPTER 3. HIDDEN MARKOV MODELS 34R
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4ÿ= ê•4TÃE0&Ò¢¡? •ç1 Lht
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6666ò U1ò +9,9. 4 20+-,¡ . 4 10C
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2. For each candidate"I!computeLet"
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6\“ç%&ät\“ç tè ä, u¦¸¹u
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, u1 ¸¼u Ù 0 and , u3 ¸¹u Ù 0
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CHAPTER 3. HIDDEN MARKOV MODELS 46l
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CHAPTER 3. HIDDEN MARKOV MODELS 48c
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CHAPTER 3. HIDDEN MARKOV MODELS 50d
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CHAPTER 3. HIDDEN MARKOV MODELS 520
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correlation between initial and fin
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,CHAPTER 3. HIDDEN MARKOV MODELS 56
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,CHAPTER 3. HIDDEN MARKOV MODELS 60
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CHAPTER 3. HIDDEN MARKOV MODELS 62b
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CHAPTER 3. HIDDEN MARKOV MODELS 64t
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CHAPTER 3. HIDDEN MARKOV MODELS 66t
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CHAPTER 3. HIDDEN MARKOV MODELS 68s
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CHAPTER 3. HIDDEN MARKOV MODELS 74b
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domain. 3 In short, we will leave o
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,,,,,£CHAPTER 4. STOCHASTIC CONTEX
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9 ¸)Ô ¸ 9 ¸Ô 1 2 £££;,ÔÔC
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¸= ¸= ¸.1.2¸¸) 1_) 20&6#=,,,,
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CHAPTER 4. STOCHASTIC CONTEXT-FREE
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==Ì==ÌCHAPTER 4. STOCHASTIC CONTE
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,= ===I¸theybÜ„thiscg„\\ ¸¸
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104Chapter 5Probabilistic Attribute
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,1makingandCHAPTER 5. PROBABILISTIC
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CHAPTER 5. PROBABILISTIC ATTRIBUTE
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Page 128 and 129: CHAPTER 5. PROBABILISTIC ATTRIBUTE
Page 134 and 135: 122Chapter 6Efficient parsing with
Page 136 and 137: 1z1CHAPTER 6. EFFICIENT PARSING WIT
Page 138 and 139: and each state in set ( -ÏH ):6)
Page 140 and 141: NPDetVTVI P CHAPTER 6. EFFICIENT PA
Page 142 and 143: CHAPTER 6. EFFICIENT PARSING WITH S
Page 144 and 145: ) In particular, the string probabi
Page 146 and 147: H : d=:6) ¸ÆÆÆ:6) ¸ .V=i£Ù )
Page 148 and 149: ©) 6#=©,©,©,,ÆNNö,²NL++and>+
Page 150 and 151: ) The probabilistic unit-production
Page 152 and 153: ¸0 ¸ 29¸¸ 99W9 [;t£ ? 1 ?1u 6
Page 154 and 155: The forward and inner probabilities
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Page 158 and 159: ,,by nonterminals. Multiplying this
Page 160 and 161: 6CHAPTER 6. EFFICIENT PARSING WITH
Page 162 and 163: description. Again, we ignore this
Page 164 and 165: for all pairs of states d =¸+= Š
Page 166 and 167: ,9 ¸0 : 0¸ £j9¸ A )z9£CHAPTER
Page 170 and 171: are then summed over all nontermina
Page 172 and 173: +CHAPTER 6. EFFICIENT PARSING WITH
Page 174 and 175: 1CHAPTER 6. EFFICIENT PARSING WITH
Page 180 and 181: 168Chapter 7-grams from Stochastic
Page 182 and 183: CHAPTER 7. -GRAMS FROM STOCHASTIC
Page 184 and 185: )ÅÆÅÅÅÆÅÅÅÆÅÅÅÆÅÅÅ
Page 186 and 187: -grams CCHAPTER 7. -GRAMS FROM ST
Page 188 and 189: ,?Ó,tÌ?L A0,I 1N I N A A 2 A 3 N
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Page 192 and 193: Consider the following problem: sta
Page 194 and 195: CHAPTER 8. FUTURE DIRECTIONS 1828.2
Page 196 and 197: 184BibliographyAHO, ALFRED V., RAVI
Page 198 and 199: BIBLIOGRAPHY 186DAGAN, IDO, FERNAND
Page 200 and 201: BIBLIOGRAPHY 188——, & ——. 1
Page 202 and 203: BIBLIOGRAPHY 190QUINLAN, J. ROSS, &
Page 204: BIBLIOGRAPHY 192WALLACE, C. S., & P
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