自然言語処理23_175
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- ぎんと あわたけ
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1 2 Sequence Alignment as a Set Partitioning Problem Masaaki Nishino,JunSuzuki, Shunji Umetani, Tsutomu Hirao and Masaaki Nagata Sequence alignment, which involves aligning elements of two given sequences, occurs in many natural language processing (NLP) tasks such as sentence alignment. Previous approaches for solving sequence alignment problems in NLP can be categorized into two groups. The first group assumes monotonicity of alignments; the second group does not assume monotonicity or consider the continuity of alignments. However, for example, in aligning sentences of parallel legal documents, it is desirable to use a sentence alignment method that does not assume monotonicity but can consider continuity. Herein, we present a method to align sequences where block-wise changes in the order of sequence elements exist. Our method formalizes a sequence alignment problem as a set partitioning problem, a type of combinatorial optimization problem, and solves the problem to obtain an alignment. We also propose an efficient algorithm to solve the optimization problem by applying column generation. Key Words: Sequence Alignment, Combinatorial Optimization, Column Generation NTT, NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Graduate School of Information Science and Technology, Osaka University
2 Vol. 23 No. 2 March DNA RNA (Moore 2002; Braune and Fraser 2010; Quan, Kit, and Song 2013) (Nie, Simard, Isabelle, and Durand 1999) (Qu and Liu 2012; 2015; 2012) F E F i f i E j e j F i +1 E j +1 (Qu and Liu 2012; 2015; 2012)
3 1 (Quan et al. 2013) Wikipedia f i e j f i+1 e j 1 F f i f i+1 E 2 (Quan et al. 2013) Bilingual Laws Information System (BLIS) f i e j f i+1 e j f i e j f i+1 e j
4 Vol. 23 No. 2 March BLIS F E (Korte and Vygen 2008) F E S S 1,...,S N S D {S 1,...,S N } D S S = Si DS i i j S i,s j D S i S j = 2 F, E S 1,...,S N S 1,...,S N F, E F, E 178
5 F, E 3 O( F 2 E 2 ) NP (Lübbecke and Desrosiers 2005) 2 (Gale and Church 1993) (Moore 2002; Braune and Fraser 2010) Deng (Deng, Kumar, and Byrne 2007) Deng Quan (Quan et al. 2013) 3 F, E 4 179
6 Vol. 23 No. 2 March 2016 Quan Quan Quan (Qu and Liu 2012) ( 2015) ( 2012) Brown (Brown, Petra, Pietra, and Mercer 1993) Wu (Wu 1997) (Brown et al. 1993) 3 F, E s F, t E S(s, t)
7 S(s, t) Moore (Moore 2002) s F s t E t S(s, t) ( S(s, t) = P (m mt )( s,m t ) m s ms ) (m s +1) m tr(t t j s i ) u(s i ) (1) j=1 i=1 m s, m t s, t s i, t j s i t j tr(t j s i ) s i t j u(s i ) s i P (m s,m t ) i=1 P (m s,m t )= exp ( m sr)(m s r) mt m t! (2) r (Brown et al. 1993) 4 (1) (2) (1) (2)
8 Vol. 23 No. 2 March F, E F E f i F i e k E k F i j f ij F 1 i j F e kl E E k l 1 k l E a ijkl (f ij,e kl ) f(a ijkl )=f ij, e(a ijkl )=e kl f ij e kl seqmatch(f ij,e kl ) f ij e kl X, A ijkl seqmatch(f ij,e kl ) seqmatch(f ij,e kl )= max X A ijkl (s,t) X S(s, t) (3) 4.1 seqmatch(f ij,e kl ) f ij e kl seqmatch(f ij,e kl ) a ijkl M M A M A a, a A f(a) f(a )= e(a) e(a )= a A f(a) =F a A e(a) =E 182
9 A A Â =argmax{score(a)} (4) A A Â score(a) F E A score(a) =λ K a A seqmatch(f(a),e(a)) (5) K A λ 0 <λ 1 λ =1 λ λ 1 (5) score(a) a (ILP) ILP maximize ijkl +logλ)y ijkl (6) ijkl(w subject to y ijkl =1 x :1 x F (7) i,j:i x j kl ij k,l:k x l y ijkl =1 x :1 x E (8) y ijkl {0, 1} i, j, k, l (9) w ijkl log seqmatch(f ij,e kl ) y ijkl a ijkl y ijkl =1 a ijkl (7) F x a ijkl 1 (8) E 2 F E 1 (f ij,e kl ) 183
10 Vol. 23 No. 2 March (6) (9) F E ( F +1)( E +1)/4 (Lübbecke and Desrosiers 2005) (6) (9) a ijkl {0, 1} 0 a ijkl 1 (Master problem: MP) M MP (Restricted master problem: RMP) RMP M M RMP RMP f n u n, e m v m RMP RMP RMP MP a ijkl M\M a ijkl 5 f 1 -e 4, f 2 -e 3, f 3 -e 2, f 4 -e 1 (3) seqmatch(f ij,e kl ) 184
11 j l w ijkl = w ijkl +logλ û n ˆv m (10) n=i m=k û n RMP u n ˆv m v m w ijkl RMP RMP MP MP RMP MP F E ( F +1)( E +1)/4 w ijkl 3 (10) û n,ˆv m Smith- Waterman (Smith and Waterman 1981) Smith-Waterman N, M O(NM) 6 q[j, l] f j,e l w ijkl (1 i j, 1 k l) q[j, l] log λ q[j 1,l 1] + S(f j,e l ) û j ˆv l q[j, l] =max (11) q[j 1,l]+S(f j ) û j q[j, l 1] + S(e l ) ˆv l q[0, 0] = log λ S(f j,e l ), S(f j ), S(e l ) (Moore 2002) f j e l f j E 6 185
12 Vol. 23 No. 2 March 2016 e l F log λ f j+1, e l+1 f j, e l 1 j F, 1 l E q[j, l] q[j, l] (11) q[j, l] x ijkl (11) 4 3 q[j 1,l 1], q[j 1,l], q[j, l 1] log λ q[j,l ] i = j +1 k = l +1 i k q[j, l] O( F E ) O( F + E ) Smith-Waterman 4 RMP M = {x 1 F,1 E } (line 1) x 1 F,1 E RMP RMP 7 (line 3) Smith-Waterman (line 4) (line 5) MP RMP (line 8) RMP MP 4 7 RMP RMP 186
13 ,000 2,500 K 60 K =1, 3, 6, 12, 20 K = K =3, 6, 12 2/ K =3, 6, 12 1/3 Moore (Moore) (BM) (1) Moore(Moore 2002) (recall) (precision) F (F-measure) K 5 GIZA++(Och and Ney 2003) ILOG CPLEX λ λ =0.1 λ =
14 Vol. 23 No. 2 March , 2 3 SP + ILP SP + CG BM Moore Moore (Moore 2002) K =1 K λ =0.1 2 F K =1 Moore F λ 1 F K =1 K =3 K =6 F F F SP+ILP (λ =0.1) SP+CG (λ =0.1) SP+ILP (λ =0.01) SP+CG (λ =0.01) BM Moore K =12 K =20 F F SP+ILP (λ =0.1) SP+CG (λ =0.1) SP+ILP (λ =0.01) SP+CG (λ =0.01) BM Moore F K =3 K =6 K =12 F F F SP+ILP (λ =0.1) SP+CG (λ =0.1) SP+ILP (λ =0.01) SP+CG (λ =0.01) BM Moore
15 3 F K =3 K =6 K =12 F F F SP+ILP (λ =0.1) SP+CG (λ =0.1) SP+ILP (λ =0.01) SP+CG (λ =0.01) BM Moore K =1, 3 λ =0.01 λ =0.1 F K =6, 12, 20 λ =0.1 λ λ K λ =0.01 K λ =0.1 Moore F F 0.08 λ = F 4 CPLEX
16 Vol. 23 No. 2 March (a) (λ =0.1) k =1 K =3 K =6 K =12 K =20 SP+ILP SP+CG (b) (λ =0.01) k =1 K =3 K =6 K =12 K =20 SP+ILP SP+CG (c) (λ =0.1) K =3 K =6 K =12 SP+ILP SP+CG (e) (λ =0.1) K =3 K =6 K =12 SP+ILP SP+CG (d) (λ =0.01) K =3 K =6 K =12 SP+ILP SP+CG (f) (λ =0.01) K =3 K =6 K =12 SP+ILP SP+CG NP 5 3,
17 5 (a) (λ =0.1) k =1 K =3 K =6 K =12 K =20 SP+ILP SP+CG (b) (λ =0.01) k =1 K =3 K =6 K =12 K =20 SP+ILP SP+CG (c) (λ =0.1) K =3 K =6 K =12 SP+ILP SP+CG (e) (λ =0.1) K =3 K =6 K =12 SP+ILP SP+CG (d) (λ =0.01) K =3 K =6 K =12 SP+ILP SP+CG (f) (λ =0.01) K =3 K =6 K =12 SP+ILP SP+CG ,000 1,
18 Vol. 23 No. 2 March Braune, F. and Fraser, A. (2010). Improved Unsupervised Sentence Alignment for Symmetrical and Asymmetrical Parallel Corpora. In Proceedings of COLING 2010, pp Brown, P. F., Petra, S. A. D., Pietra, V. J. D., and Mercer, R. L. (1993). The Mathematics of Statistical Machine Translation: Parameter Estimation. Computational Linguistics, 19 (2), pp Deng, Y., Kumar, S., and Byrne, W. (2007). Segmentation and Alignment of Parallel Text for Statistical Machine Translation. Natural Language Engineering, 13 (3), pp Gale, W. A. and Church, K. W. (1993). A Program for Aligning Sentences in Bilingual Corpora. Computational Linguistics, 19 (1), pp Korte, B. H. and Vygen, J. (2008). Combinatorial Optimization: Theory and Algorithms. Springer Verlag. Lübbecke, M. E. and Desrosiers, J. (2005). Selected Topics in Column Generation. Operations Research, 53 (6), pp Moore, R. C. (2002). Fast and Accurate Sentence Alignment of Bilingual Corpora. In Proceedings of AMTA 02, pp Nie, J.-Y., Simard, M., Isabelle, P., and Durand, R. (1999). Cross-language Information Retrieval Based on Parallel Texts and Automatic Mining of Parallel Texts from the Web. In Proceedings of the 22nd Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pp ACM. Och, F. J. and Ney, H. (2003). A Systematic Comparison of Various Statistical Alignment Models. Computational Linguistics, 29 (1), pp
19 Qu, Z. and Liu, Y. (2012). Sentence Dependency Tagging in Online Question Answering Forums. In Proceedings of the 50th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp , Jeju Island, Korea. Association for Computational Linguistics. Quan, X., Kit, C., and Song, Y. (2013). Non-Monotonic Sentence Alignment via Semisupervised Learning. In Proceedings of the 51st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp , Sofia, Bulgaria. Association for Computational Linguistics. Smith, T. F. and Waterman, M. S. (1981). Identification of Common Molecular Subsequences. Journal of Molecular Biology, 147, pp (2012).., 19 (3), pp (2015).., 22 (1), pp Wu, D. (1997). Stochastic Inversion Transduction Grammars and Bilingual Parsing of Parallel Corpora. Computational Linguistics, 23 (3), pp ACL MIT CSAIL NTT ACL INFORMS MOS AAAI 193
20 Vol. 23 No. 2 March NTT 2000 NTT ACL 1987 ACL
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