21 Pitman-Yor Pitman- Yor [7] n -gram W w n-gram G Pitman-Yor P Y (d, θ, G 0 ) (1) G P Y (d, θ, G 0 ) (1) Pitman-Yor d, θ, G 0 d 0 d 1 θ Pitman-Yor G

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1 ol2013-nl-214 No6 1,a) 2,b) n-gram 1 M [1] (TG: Tree ubstitution Grammar) [2], [3] TG TG 1 2 a) ohno@ilabdoshishaacjp b) khatano@maildoshishaacjp [4], [5] [6] 2 Pitman-Yor 3 Pitman-Yor 1

2 21 Pitman-Yor Pitman- Yor [7] n -gram W w n-gram G Pitman-Yor P Y (d, θ, G 0 ) (1) G P Y (d, θ, G 0 ) (1) Pitman-Yor d, θ, G 0 d 0 d 1 θ Pitman-Yor G 0 = [G 0 (w)] w W G o Pitman-Yor d Pitman-Yor Pitman-Yor d = 0 Pitman-Yor (2) DP (θ, G 0 ) G DP (θ, G 0 ) = θg 0 (2) (2) G r (3) Dir(θG 0 (w 1 ),, θg 0 (w r )) (G(w 1 ),, G(w r )) Dir(θG 0 (w 1 ),, θg 0 (w r ))(3) n-gram G [8] n-gram G (G 0 ) G 0 θ + d ( ) G 0 (w k ) t w k c k Pitman-Yor G c (4) Pitman-Yor P Y (d, θ, G 0 ) = c k d θ + c + θ + dt θ + c G 0 (w k ) (4) Pitman-Yor d, θ G 0 22 Pitman-Yor Pitman-Yor [9] Pitman-Yor n-gram Pitman-Yor Pitman-Yor n 1 u n-gram n-gram n-gram G u u n-gram G π(u) Pitman-Yor G u P Y (d u, θ u, G π(u) ) (5) θ u d u u u π(u) u G πu (5) n-gram n 1 G ϕ Pitman-Yor n uffix-array n 1 Pitman-Yor n 1 Kneser and Ney [10] n-gram 3 ol2013-nl-214 No6 (TG)[11] (CFG: Context Free Grammar) TG, CFG CFG 1 2

3 TG TG TG G = (T, N,, R) T, N N R TG P John books 1 John TG P cookies 1 (P ( like) ) ( (P ( ) )) ( John) ( cookies) TG (PTG:Probabilistic Tree ubstitution Grammar) TG e c P (ec) P (ec) PTG G c Pitman-Yor [9] (6) G c PY(d c, θ c, G π(c) ) (6) d c θ c c Pitman-Yor G π(c) c e G ϕ c 1,, c m e 1 e 2,, e m G π(c1),, G π(cm) John P cookies 2 John cookies P TG c e PTG Gibbs 2 TG [5] TG TG 4 41 ngram n-gram n-gram ol2013-nl-214 No6 n-gram n P 3

4 トムは この 本を ジムを見た 女性に <s> トムは 渡した ( )</s> 渡した ( ) (a) ol2013-nl-214 No6 <s> この <s> ジムを 渡した ( )</s> 本を 見た女性に 渡した ( )</s> (b) トムは この 本を ジムを 見た 女性に 渡した ( ) 3 トムは この 本を ジムを 見た 女性に 渡した ( ) Pitman-Yor n Pitman-Yor [12] 3 <s> </s> P D ( ) CYK [13] [6] 4 4(a) P D ( ) P D ( ) P D ( ) 4(a) P D ( ) P D ( ) P D ( ) P D ( ) 4(b) [1] [6] 4

5 ol2013-nl-214 No6 トムは この 本を トムは この 5 ジムを見た 女性に 本を美しい 女性に <s> トムは 渡した ( )</s> 2 <s> この <s> ジムを <s> 美しい 渡した ( )</s> 2 本を 見た女性に 女性に 渡した ( ) 渡した ( ) 渡した ( )</s> 渡した ( )</s> Pitman-Yor <s> トムは 渡した ( )</s> 2 <s> この 6 渡した ( )</s> 2 本を 女性に 渡した ( )</s> 2 <s> 美しい <s> ジムを 女性に 見た女性に Pitman-Yor 43 [6] Pitman-Yor Pitman-Yor n-gram n-gram n-gram 5 Pitman-Yor 6 Pitman-Yor Pitman-Yor Nested Hierarchical Pitman-Yor [14] Nested Hierarchical Pitman-Yor Nested Hierarchical Pitman-Yor Gibbs 50 Nested Hierarchical Pitman-Yor uni-gram Pitman-Yor Nested Hierarchical Pitman-Yor uni-gram Pitman-Yor bi-gram 5

6 (7)[1] X = Y = = X Y 1 uni-gram CaboCha-066 (%) (7) ( : ) ol2013-nl-214 No6 [1] Kudo, T and Matsumoto, Y: Japanese Dependency Analysis using Cascaded Chunking, CoNLL 2002: Proceedings of the 6th Conference on Natural Language Learning 2002 (COLING 2002 Post-Conference Workshops), pp (2002) [2] Cohn, T, Blunsom, P and Goldwater, : Inducing Tree-ubstitution Grammars, Journal of Machine Learning Research, ol 11, pp (2010) [3] Post, M and Gildea, D: Weight Pushing and Binarization for Fixed-Grammar Parsing, Proceedings of the 11th International Conference on Parsing Technologies (IWPT 09), Association for Computational Linguistics, pp (2009) [4] Blunsom, P and Cohn, T: Unsupervised induction of tree substitution grammars for dependency parsing, Proceedings of the 2010 Conference on Empirical Methods in Natural Language Processing, (EMNLP 10), Association for Computational Linguistics, pp (2010) [5] hindo, H, Miyao, Y, Fujino, A and Nagata, M: Bayesian symbol-refined tree substitution grammars for syntactic parsing, Proceedings of the 50th Annual Meeting of the Association for Computational Linguistics: Long Papers - olume 1, ACL 12, Association for Computational Linguistics, pp (2012) [6] 2013 (2013) [7] Pitman, J and Yor, M: The Two-Parameter Poisson- Dirichlet Distribution Derived from a table ubordinator, The Annals of Probability, ol 25, No 2, pp (1997) [8] Pitman, J: Exchangeable and partially exchangeable random partitions, Probability Theory and Related Fields, ol 102, No 2, pp (1995) [9] Teh, Y W: A hierarchical Bayesian language model based on Pitman-Yor processes, Proceedings of the 21st International Conference on Computational Linguistics and the 44th annual meeting of the Association for Computational Linguistics, ACL-44, Association for Computational Linguistics, pp (2006) [10] Kneser, R and Ney, H: Improved backing-off for M- gram language modeling, Acoustics, peech and ignal Processing, ol 1, pp (1995) [11] Cohn, T and Lapata, M: entence Compression as Tree Transduction, Journal of Artificial Intelligence Research (JAIR), ol 34, pp (2009) [12] Mochihashi, D and umita, E: The Infinite Markov Model, Advances in Neural Information Processing ystems 20 (NIP 2007), pp (2007) [13] Jurafsky, D and Martin, J H: peech and Language Processing (2nd Edition) (Prentice Hall eries in Artificial Intelligence), Prentice Hall, 2nd edition (2008) [14] Mochihashi, D, Yamada, T and Ueda, N: Bayesian unsupervised word segmentation with nested Pitman-Yor language modeling, In Proc of ACL (2009) 6

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