Learning and Inference for Hierarchically Split Probabilistic Context-Free Grammars Slav Petrov and Dan Klein University of California, Berkeley Evolution of the DT tag during hierarchical splitting and merging. Shown are the top three words for each subcategory and their respective probability. DT the (0.50) a (0.24) The (0.08) that (0.15) this (0.14) some (0.11) this (0.39) that (0.28) That (0.11) this (0.52) that (0.36) another (0.04) That (0.38) This (0.34) each (0.07) some (0.20) all (0.19) those (0.12) some (0.37) all (0.29) those (0.14) these (0.27) both (0.21) Some (0.15) the (0.54) a (0.25) The (0.09) the (0.80) The (0.15) a (0.01) the (0.96) a (0.01) The (0.01) The (0.93) A(0.02) No(0.01) a (0.61) the (0.19) an (0.10) a (0.75) an (0.12) the (0.03) Learning Inference Results Observed categories are too coarse: Adaptive Grammar Refinement: Split each category in k subcategories and fit grammar with the EM algorithm. Reference: Slav Petrov, Adam Pauls and Dan Klein, "Learning Structured Models for Phone Recognition", in EMNLP-CoNLL '07 Smoothing: Reduce overfitting by shrinking the productions of each subcategory towards their common base category. Reference: Slav Petrov, Leon Barrett, Romain Thibaux and Dan Klein, "Learning accurate, compact and interpretable tree annotation", in ACL-COLING '06 Reference: Slav Petrov and Dan Klein, "Improved Inference for Unlexicalized Parsing", in NAACL-HLT '07 The most frequent three words in the subcategories of several part-of-speech tags. VBZ VBZ-0 gives sells takes VBZ-1 comes goes works VBZ-2 includes owns is VBZ-3 puts provides takes VBZ-4 says adds Says VBZ-5 believes means thinks VBZ-6 expects makes calls VBZ-7 plans expects wants VBZ-8 is ’s gets VBZ-9 ’s is remains VBZ-10 has ’s is VBZ-11 does Is Does NNP NNP-0 Jr. Goldman INC. NNP-1 Bush Noriega Peters NNP-2 J. E. L. NNP-3 York Francisco Street NNP-4 Inc Exchange Co NNP-5 Inc. Corp. Co. NNP-6 Stock Exchange York NNP-7 Corp. Inc. Group NNP-8 Congress Japan IBM NNP-9 Friday September August NNP-10 Shearson D. Ford NNP-11 U.S. Treasury Senate NNP-12 John Robert James NNP-13 Mr. Ms. President NNP-14 Oct. Nov. Sept. NNP-15 New San Wall JJS JJS-0 largest latest biggest JJS-1 least best worst JJS-2 most Most least DT DT-0 the The a DT-1 A An Another DT-2 The No This DT-3 The Some These DT-4 all those some DT-5 some these both DT-6 That This each DT-7 this that each DT-8 the The a DT-9 no any some DT-10 an a the DT-11 a this the CD CD-0 1 50 100 CD-1 8.50 15 1.2 CD-2 8 10 20 CD-3 1 30 31 CD-4 1989 1990 1988 CD-5 1988 1987 1990 CD-6 two three five CD-7 one One Three CD-8 12 34 14 CD-9 78 58 34 CD-10 one two three CD-11 million billion trillion PRP PRP-0 It He I PRP-1 it he they PRP-2 it them him RBR RBR-0 further lower higher RBR-1 more less More RBR-2 earlier Earlier later IN IN-0 In With After IN-1 In For At IN-2 in for on IN-3 of for on IN-4 from on with IN-5 at for by IN-6 by in with IN-7 for with on IN-8 If While As IN-9 because if while IN-10 whether if That IN-11 that like whether IN-12 about over between IN-13 as de Up IN-14 than ago until IN-15 out up down RB RB-0 recently previously still RB-1 here back now RB-2 very highly relatively RB-3 so too as RB-4 also now still RB-5 however Now However RB-6 much far enough RB-7 even well then RB-8 as about nearly RB-9 only just almost RB-10 ago earlier later RB-11 rather instead because RB-12 back close ahead RB-13 up down off RB-14 not Not maybe RB-15 n’t not also General technique for learning refined, structured models when only the trace of a complex underlying process is observed. Learns compact and accurate grammars from a treebank without additional human input. Gives best known parsing accuracy on a variety of languages, while being extremely efficient. Interactive demo and download at http://nlp.cs.berkeley.edu Extensions Reference: Percy Liang, Slav Petrov, Michael Jordan and Dan Klein, "The Infinite PCFG using Hierarchical Dirichlet Processes", in EMNLP-CoNLL '07 Hierarchical Dirichlet Processes as a nonparametric Bayesian alternative to split and merge: Merging: Roll back the least useful splits in order to allocate complexity only where needed. Parsing: Grammar Extraction: S NP PRP She VP VBD heard NP DT the NN noise . . Grammar S → NP VP . 1.0 NP → PRP 0.5 NP → DT NN 0.5 ... Lexicon PRP → She 1.0 DT → the 1.0 ... 11% 9% 6% NP PP DT NN PRP All NPs 9% 9% 21% NP PP DT NN PRP NPs under S 7% 4% 23% NP PP DT NN PRP NPs under VP Hierarchical Splitting: Repeatedly split each annotation symbol in two and retrain the grammar, initializing with the previous grammar. S-x NP-x PRP-x She VP-x VBD-x heard NP-x DT-x the NN-x noise .-x . NP NP 1 NP 2 NP 3 NP 4 NP 5 NP 6 NP 7 NP 8 L 1 2 1 2 1 2 1 2 VP NP DT NN 1 2 1 1 2 1 2 VP NP DT NN L With split at NP node With split at NP node reversed Parsing accuracy for different models 74 76 78 80 82 84 86 88 90 100 300 500 700 900 1100 Total number of grammar symbols Parsing accuracy (F1) 50% Merging and Smoothing 50% Merging Hierarchical Training Flat Training Parse Efficiency: Rapidly pre-parse the sentence in a hierarchical coarse-to-fine fashion pruning away unlikely chart items. Parse Selection: Use a variational approximation to select the tree with the maximum number of expected correct rules (since computing the best parse tree is intractable and selecting the best derivation is a poor approximation). β φ B z φ T z φ E z z ∞ z 1 z 2 x 2 z 3 x 3 T Parameters Trees Start a d End a d a d d ae d b c b c b c Automatic refinement of acoustic models learns phone-internal structure as well as phone-external context: Learned grammars are compact and interpretable: S NP DT The NNP Golden NNP Gate NN bridge VP VBZ is ADJP JJ red . . Compute grammars of intermediate complexity by projecting the most refined grammar. The Golden Gate bridge is red. G 3 G 2 G 1 G 0 G 1 G 2 G 3 G 4 G 5 G 6 Learning X-Bar=G 0 G= Projection π i π 0 (G) π 1 (G) π 2 (G) π 3 (G) π 4 (G) π 5 (G) G ... ... ... ... VP QP ... NP1 VP1 ... NP ... VP4 NP4 ... VP2 NP2 ... VP6 VP7 NP4 NP3 VP3 NP3 G0 G1 G2 G3 S NP PRP He VP VBD was ADJP right . . Parse Tree Parse Derivations S-2 NP-17 PRP-2 He VP-23 VBD-12 was ADJP-11 right . . S-1 NP-10 PRP-2 He VP-11 VBD-16 was ADJP-14 right . . ≤ 40 words all Parser F 1 F 1 ENGLISH Charniak & Johnson ’05 90.1 89.6 This Work 90.6 90.1 GERMAN Dubey ’05 76.3 - This Work 80.8 80.1 CHINESE Chiang & Bikel ’02 80.0 76.6 This Work 86.3 83.4 Bracket posterior probabilities during coarse-to-fine decoding Influential members of the House Ways and Means Committee introduced legislation that would restrict how the new s&l bailout agency can raise capital ; creating another potential obstacle to the government ‘s sale of sick thrifts .