lect12-pcfg.key

# lect12-pcfg.key - Probabilistic Context Free Grammars...

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Unformatted text preview: Probabilistic Context Free Grammars Lecture #14 Computational Linguistics CMPSCI 591N, Spring 2006 Andrew McCallum (including slides from Jason Eisner) ndrew McCallum, UMass Ambiguity in Parsing • Time flies like an arrow. • Fruit flies like a banana. • I saw the man with the telescope. ndrew McCallum, UMass How to solve this combinatorial explosion of ambiguity? 1. First try parsing without any weird rules, throwing them in only if needed. 2. Better: every rule has a weight. A tree’s weight is total weight of all its rules. Pick the overall “lightest” parse of sentence. 3. Can we pick the weights automatically? We’ll get to this later … ndrew McCallum, UMass CYK Parser Input: A string of words, grammar in CNF Output: yes/no Data structure: n x n table rows labeled 0 to n-1, columns 1 to n cell (i,j) lists constituents spanning i,j For each i from 1 to n Add to (i-1,i) all Nonterminals that could produce the word at (i-1,i) time 1 fies 2 like 3 an 4 arrow 5 NP 3 Vst 3 1 NP 4 VP 4 2 P 2 V 5 3 Det 1 4 N 8 1 S → NP VP 6 S → Vst NP 2 S → S PP 1 VP → V NP 2 VP → VP PP 1 NP → Det N 2 NP → NP PP 3 NP → NP NP 0 PP → P NP ndrew McCallum, UMass CYK Parser For width from 2 to n For start from 0 to n-width Define end to be start+width For mid from start+1 to end-1 For every constituent in ( start, mid ) For every constituent in ( mid,end ) For all ways of combining them (if any) Add the resulting constituent to ( start,end ). time 1 fies 2 like 3 an 4 arrow 5 NP 3 Vst 3 1 NP 4 VP 4 2 P 2 V 5 3 Det 1 4 N 8 1 S → NP VP 6 S → Vst NP 2 S → S PP 1 VP → V NP 2 VP → VP PP 1 NP → Det N 2 NP → NP PP 3 NP → NP NP 0 PP → P NP time 1 fies 2 like 3 an 4 arrow 5 NP 3 Vst 3 NP 10 1 NP 4 VP 4 2 P 2 V 5 3 Det 1 4 N 8 1 S → NP VP 6 S → Vst NP 2 S → S PP 1 VP → V NP 2 VP → VP PP 1 NP → Det N 2 NP → NP PP 3 NP → NP NP 0 PP → P NP time 1 fies 2 like 3 an 4 arrow 5 NP 3 Vst 3 NP 10 S 8 1 NP 4 VP 4 2 P 2 V 5 3 Det 1 4 N 8 1 S → NP VP 6 S → Vst NP 2 S → S PP 1 VP → V NP 2 VP → VP PP 1 NP → Det N 2 NP → NP PP 3 NP → NP NP 0 PP → P NP time 1 fies 2 like 3 an 4 arrow 5 NP 3 Vst 3 NP 10 S 8 S 13 1 NP 4 VP 4 2 P 2 V 5 3 Det 1 4 N 8 1 S → NP VP 6 S → Vst NP 2 S → S PP 1 VP → V NP 2 VP → VP PP 1 NP → Det N 2 NP → NP PP 3 NP → NP NP 0 PP → P NP time 1 fies 2 like 3 an 4 arrow 5 NP 3 Vst 3 NP 10 S 8 S 13 1 NP 4 VP 4 2 P 2 V 5 3 Det 1 4 N 8 1 S → NP VP 6 S → Vst NP 2 S → S PP 1 VP → V NP 2 VP → VP PP 1 NP → Det N 2 NP → NP PP 3 NP → NP NP 0 PP → P NP time 1 fies 2 like 3 an 4 arrow 5 NP 3 Vst 3 NP 10 S 8 S 13 1 NP 4 VP 4 2 P 2 V 5 3 Det 1 NP 10 4 N 8 1 S → NP VP 6 S → Vst NP 2 S → S PP 1 VP → V NP 2 VP → VP PP 1 NP → Det N 2 NP → NP PP 3 NP → NP NP 0 PP → P NP time 1 fies 2 like 3 an 4 arrow 5 NP 3 Vst 3 NP 10 S 8 S 13 1 NP 4 VP 4 2 P 2 V 5 3 Det 1 NP 10 4 N 8 1 S → NP VP 6 S → Vst NP 2 S → S PP 1 VP → V NP 2 VP → VP PP 1 NP → Det N 2 NP → NP PP 3 NP → NP NP 0 PP → P NP time...
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lect12-pcfg.key - Probabilistic Context Free Grammars...

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