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Approximate Factoring for A* Search Aria Haghighi, John DeNero, and Dan Klein Computer Science Division University of California Berkeley.

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Presentation on theme: "Approximate Factoring for A* Search Aria Haghighi, John DeNero, and Dan Klein Computer Science Division University of California Berkeley."— Presentation transcript:

1 Approximate Factoring for A* Search Aria Haghighi, John DeNero, and Dan Klein Computer Science Division University of California Berkeley

2 Inference for NLP Tasks A* Search

3 Inference as Search y a1a1 a2a2 a3a3 Partial Hypothesis a2a2

4 VP S NP Bitext Parsing as Search translation is hard, la traducción es dificil Weighted Synchronous Grammar Parsing O(n 6 ) Modified CKY over bi-spans (X[i,j],X’[i’,j’]) Source Target VP S NP SS’

5 A* Search Completion ScoreScore So Far y

6 A* Search  Heuristic Design  Tight small  Admissible  Efficient to compute This way hypothesis! A* Heuristic Man Optimal Result

7 A* Example: Bitext Search Viterbi Inside Score Cost So Far Bi-Span

8 A* Bitext Search Viterbi Outside Score Completion Score O(n6)O(n6) Ideal Heuristic

9 Of Stately Projections ¼ SS’ S S VP S NP S S’ S VP S NP VP’ S’ NP’VP’ S’ NP’

10 A* Bitext Search Suppose, Then, VP S NP S S’ VP S NP S VP’ S’ NP’

11 Projection Heuristic O(n3)O(n3) O(n3)O(n3) O(n6)O(n6) Klein and Manning [2003]

12 When models don’t factorize

13 Pointwise Admissibility y c( a ) x ¼s(y)¼s(y) Ás(a)Ás(a) ¼s(x)¼s(x) ¼t(y)¼t(y) Át(a)Át(a) ¼t(x)¼t(x)

14 When models don’t factorize Admissibility ¼s(y)¼s(y) ¼t(y)¼t(y) y

15 Finding Factored Costs Pointwise Gap How to find Á s and Á t ?

16 Finding Factored Costs Small gaps

17 Finding Factored Costs Pointwise Admissibility

18 Finding Factored Costs

19 Bitext Experiments Synchronous Tree-to-Tree Transducer  Trained on 40k sentences of English-Spanish Europarl [Galley et. al, 2004]  Rare words replaced with POS tags  Tested on 1,200 sent. max length 5-15 Optimization Problem  Solved only once per grammar  206K Variables  160K Constraints  29 minutes

20 Bitext Experiments

21

22 Zhang and Gildea (2006)

23 Bitext Experiments Zhang and Gildea (2006)

24 Lexicalized Parsing NP- (translation,NN) S- (is,VBZ) VP-(is,VBZ) (is,VBZ) (translation, NN) NP S VP Klein and Manning [2003]

25 Lexicalized Parsing

26 Too many constraints to efficiently solve! Over 64e 13 possible lexicalized rules

27 Lexicalized Parsing

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31 Lexicalized Model Experiments Standard Setup  Train on section 2-21 of the treebank  Test on section 23 (length · 40) Models Tested  Factored model [Klein and Manning, 2003]  Non-Factored Model

32 Lexicalized Parsing Factored Model [Klein and Manning, 2003]

33 Lexicalized Parsing Non-Factored Model

34 Conclusions  General technique for generating A* estimates  Can explicitly control admissibility tightness trade-off  Future Work: Explore different objectives and applications

35 Thanks http://nlp.cs.berkeley.edu


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