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Learning Accurate, Compact, and Interpretable Tree Annotation

Learning Accurate, Compact, and Interpretable Tree Annotation. Recent Advances in Parsing Technology WS 2011/2012 Saarland University in Saarbrücken Milo š Ercegovčević. Outline. Introduction EM algorithm Latent Grammars Motivation Learning Latent PCFG

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Learning Accurate, Compact, and Interpretable Tree Annotation

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  1. Learning Accurate, Compact, and Interpretable Tree Annotation Recent Advances in Parsing Technology WS 2011/2012 Saarland University in Saarbrücken Miloš Ercegovčević

  2. Outline • Introduction • EM algorithm • Latent Grammars • Motivation • Learning Latent PCFG • Split-Merge Adaptation • Efficient inference with Latent Grammars • Pruning in Multilevel Coarse-to-Fine parsing • Parse Selection

  3. Introduction : EM Algorithm • Iterative algorithm for finding MLE or MAP estimates of parameters in statistical models • X – observed data; Z – set of latent variables • Θ – a vector of unknown parametes • Likelihood function: • MLE of the marginal likelihood : • However this quantity is intractable • Often we don’t know both Z and Θ

  4. Introduction : EM Algorithm • Find the MLE of the marginal likelihood by iteratively applying two steps: • Expectation step (E-step): • Calculate Z under current Θ • Maximization step (M-step): • Find Θ that maximizes the quantity

  5. Latent PCFG • Standard coarse Treebank Tree • Baseline for parsing F1 72.6

  6. Latent PCFG • Parent annotated trees [Johnson ’98], [Klein & Manning ’03] • F1 86.3

  7. Latent PCFG • Head lexicalized [Collins ’99, Charniak ’00]trees • F1 88.6

  8. Latent PCFG • Automatically clustered categories with F1 86.7 [Matsuzaki et al. ’05] • Same number of subcategories for all categories

  9. Latent PCFG • At each step split the categories into two sets. • After 6 iterations number of subcategories is 64 • Initialize EM with the results of the smaller grammar

  10. Forward X1 X7 X2 X4 X3 X5 X6 . He was right Backward Learning Latent PCFG • Induce subcategories • Like forward-backward for HMMs • Fixed brackets • S

  11. Learning Latent Grammar • Inside-Outside probabilities

  12. Learning Latent Grammar • Expectation step (E-step): • Maximization step (M-step):

  13. Latent Grammar : Adaptive splitting • Want to split more according to the data • Solution: Split everything then merge by the loss • Without loss in Accuracy

  14. Latent Grammar : Adaptive splitting • The likelihood of data for tree T and sentence w: • Then for two annotations the overall loss can be estimated as:

  15. Number of Phrasal Subcategories

  16. Number of Phrasal Subcategories NP VP PP

  17. Number of Phrasal Subcategories NAC X

  18. Number of Lexical Subcategories POS TO ,

  19. Number of Lexical Subcategories RB VBx IN DT

  20. Number of Lexical Subcategories NNP JJ NNS NN

  21. Latent Grammar : Results

  22. Efficient inference with Latent Grammars • Latent Grammar with 91.2 F1 score on Dev Set (1600 sentences) WSJ • Training time 1621: more than a minute per sentence • For usage in real-word applications this is to slow • Improve on inference: • Hierarchical Pruning • Parse Selection

  23. G1 G2 G3 G4 G5 G6 DT DT1 DT2 DT1 DT2 DT3 DT4 Learning DT1 DT2 DT3 DT4 DT5 DT6 DT7 DT8 Intermediate Grammars X-Bar=G0 G=

  24. 0(G) 1(G) 2(G) 3(G) 4(G) 5(G) G1 G2 G3 G4 G5 G6 G1 G2 G3 G4 G5 G6 Learning Learning Projection i G Projected Grammars X-Bar=G0 G=

  25. … S  NP VP S1  NP1 VP1 0.20 S1  NP1 VP2 0.12 S1  NP2 VP1 0.02 S1  NP2 VP2 0.03 S2  NP1 VP1 0.11 S2  NP1 VP2 0.05 S2  NP2 VP1 0.08 S2  NP2 VP2 0.12 Rules in G Rules in (G) … Treebank Infinite tree distribution Estimating Grammars 0.56

  26. Hierarchical Pruning Consider the span: coarse: split in two: split in four: split in eight:

  27. Parse Selection • Given a sentence w and a split PCFG grammar G select the best parse that minimize our beliefs: • Intractable: we cannot generate all the TT

  28. Parse Selection • Possible solutions • best derivation • generate n-best parses and re-rank them • samplingderivations of the grammar • select the minimum risk candidate based on loss function of posterior marginals:

  29. Results

  30. Thank You!

  31. References • S. Petrov, L. Barrett, R. Thibaux, D Klein. Learning Accurate, Compact, and Interpretable Tree Annotation, COLING-ACL 2006 slides. • S. Petrov and D. Klein, NACL Improved Inference for Unlexicalized Parsing : 2007 slides. • S. Petrov, L. Barrett, R. Thibaux, and D. Klein. 2006. Learning accurate, compact, and interpretable tree annotation. In COLING-ACL ’06, pages 443–440. • S. Petrov and D. Klein. 2007. Improved Inference for Unlexicalized Parsing . In NACL ’06. • T. Matsuzaki, Y. Miyao, and J. Tsujii. 2005. Probabilistic CFG with latent annotations. In ACL ’05, pages 75–82.

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