IPSJ SIG Technical Report Pitman-Yor 1 1 Pitman-Yor n-gram A proposal of the melody generation method using hierarchical pitman-yor language model Aki

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1 Pitman-Yor Pitman-Yor n-gram A proposal of the melody generation method using hierarchical pitman-yor language model Akira Shirai and Tadahiro Taniguchi Although a lot of melody generation method has been proposed, it is difficult to generate a melody that has the features of existing music. Thus, we propose a method using Variable-order Pitman-Yor Language Model, extension of Hierarchical Pitman-Yor Language Model, which generates new melodies that have the features of the data. We also evaluate this method by some experiments.. DTM Ritsumeikan University 2. 2) 3) : ACS : Juice and Candy 3.33, c 20 Information Processing Society of Japan

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2 Web n-gram ) n-gram n 2 n-gram 2 n-gram n n n Variable-order Pitman-Yor Language Model(VPYLM) VPYLM n-gram 3. VPYLM. 3. s = (s, s 2,..., s N ) N 8 VPYLM. & \ \....! E. & C uni- gram rescaling Fig. G n- gram The overview of our method. c = (c, c 2,...c N ) C C 3.2 VPYLM n-gram n-gram n n-gram Hierarchical Pitman-Yor Language Model(HPYLM) 4) VPYLM 6) HPYLM Teh n-gram 2HPYLM Hierarchical Pitman-Yor 2 c 20 Information Processing Society of Japan

3 G 0 /V G PD(d, θ G 0 ) G 2 PD(d 2, θ 2 G ) G 3 PD(d 3, θ 3 G 2 ) p(s h) = p(s, n h) () n = p(s n, h)p(n h) n n HPYLM h n-gram (2) p(s) = N p(s i h) (2) i (2) s i s i s i k 2 n-gram Fig. 2 The hierarchical distribution of n-gram. Process n-gram Kneser-Ney 5) HPYLM HPYLM n-gram VPYLM VPYLM n-gram n-gram n-gram n Gibbs sampler h s n-gram n p(s i = k s i ) p(s i = k h)p(s i+ h )... p(s i+nmax h (n max) ) (3) n max VPYLM n-gram (3) Gibbs Sampler M N note 2 M N note M { exp((n note M)α) if N note < M p(m, N note) = exp( M N note ) otherwise β α β 3 (3) (4) 2 (4) 3 c 20 Information Processing Society of Japan

4 Nnote- M 3 α =, β = 20 Fig. 3 The restriction of mora (α =, β = 20). ˆp(s i = k s i ) = p(s i = k s i )p(m, N note ) (5) Gibbs Sampler uni-gram rescaling uni-gram rescaling p(s i s i n i, c i ) p(si si n i )p(si ci) p(s i ) p(s i c i ) c i s i (5) (6) p(s i s i, c) p(s i = k h, c i)p(s i+ h, c i+) (7) p(s i h, c i )... p(s i+nmax h (n max), c i+nmax ) p(m, N note ) (6) p(s i h, c i ) = n p(s i n, h)p(n h)p(s i c i ) p(s i ) (8) Gibbs Sampler J-Pop 4 A B n-gram n max 0 VPYLM 00 burn-in 200 N 32 4 α = 0, β = 50 (C,G,Am,G) VPYLM n-gram 5, 6-gram 5 VPYLM 6 YouTube (8) 4 c 20 Information Processing Society of Japan

5 4 n-gram 5 Fig. 4 The distribution of the n-gram order. Fig. 5 The transition of a generation probability. 4.3 VPYLM 5. HPYLM n-gram VPYLM VPYLM HPYLM n-gram VPYLM ) : (200). 5 c 20 Information Processing Society of Japan

$& \ E!........ E."............. & \.... -...............#..... 6 Fig. 6 The Generated melody. 2) : Vol.3, No.5, pp.692-703 (998). 3) : Orpheus: 2008-MUS-76 pp.79-84 2008. 4) Teh, Y.W.$

6 & \ E! E." & \ # Fig. 6 The Generated melody. 2) : Vol.3, No.5, pp (998). 3) : Orpheus: 2008-MUS-76 pp ) Teh, Y.W.: A Hierarchical Bayesian Language Model based on Pitman-Yor Processes, Proc.COLING/ACL 2006, pp (2006). 5) Kneser, R. and Ney, H.: Improved backing-off for m-gram language modeling, Proc. ICASSP, Vol., pp.8-84 (995). 6) : Pitman-Yor n-gram Vol.48, No.2, pp (2007). 6 c 20 Information Processing Society of Japan

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

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 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 21 Pitman-Yor