[9, 10] [2] [4] [10] Kyoto University, Yoshida Honmachi, Sakyo, Kyoto, , Japan 2. Yamaha Corporation. Waseda University a)

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Ὡρος Παπαδάκης
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1 ,2,a) 3. [ 3 [4 [5 8 Kyoto Univerity, Yohida Honachi, Sakyo, Kyoto, 66 85, Japan 2 Yaaha Corporation 3 Waeda Univerity a) akira.aezawa@gail.co [9, [2 [ c 24 Inforation Proceing Society of Japan

2 Generative Model of Muic Copoition Perforance Perforance Perforance 2 Perforance 3 Tie Generative Model of Muic Copoition Generative Model of Shared Teporal Interpretation Perf. iilar! Perf. 3 Perf. 2 Tie iilar! Perf. Perf. 2 Perf. 3 ) 2) 3) [ N S Z {z n } N n z n S z n θ θ z z z π τ 2 π τ S pl n,d) z z n- ϕ d, z n z N ϕ d,t- ϕ d,t ϕ d,td x d, x d,t- x d,t x d,td pl n, d) d n l ergodic : pz π, τ ) π z, n2 θ S D τ z n, zn, ) τ Dirichlet τ Dirτ, ) π π Dirπ ) τ, π τ π 2.2 θ n d T d N Left-to-right Φ d {ϕ d,t } T d t ϕ d, ϕ d,td N Z T d > N ϕ dt [... N [... L n, l) n l d n l pl n, d) c 24 Inforation Proceing Society of Japan 2

3 3 υ ξ M Λ u a μ u n- u n a n- a n μ n- μ n To pl n,d) u N μ N a N µ 2 pl n, d) : pϕ d,t{ Td }) L pl n, d)δn, ) ϕ d,,n, δn, S) ϕ d,t d,n, l T d [ L pl n, d) ϕ d,t,n,ϕ d,t,n,l t n2 l L l2 ϕ d,t,n,lϕ d,t,n,l 2) pl n, d) d t ϕ dt n z n z n θ zn : px dt z, ϕ, θ) n px dt θ ) znϕ dtn 3) px θ ) x θ pθ ; θ ) px dt θ ) dix dt ) θ Noral-Gaa θ { µ, λ } θ {, ν, u, k } x dt µ, λ N µ, λ ) µ i, λ i N G,i, ν,i, u,i, k,i ) d n l nd n d n a n a n µ n [µ n, µ n,d * a n µ l n : pl n a n, µ n, λ ) N l n a n µ n, λ ) 4) : pa n κ, ι) N a n κ, ι ) 5) κ ι µ µ µ * µ c 24 Inforation Proceing Society of Japan 3

4 µ a aµ µ.6.4 µ aµ aµ2 zt µ µ µ2 µ µ a aµ µ Mean-reverting AR) µ n µ n : µ n µ n α µ n ) + ϵ n 6) ϵ n Λ n Λ n µ n + α) 2 ) < α < µ n α µ Λ n 4 µ a a µ µ Λ n Λ n M u M u u ξ υ µ µ µ µ 2 µ 2 µ 3 pu ξ, υ) υ u, n ξ un,u n,, 7) u n d 3 u n n µ Switching-tate Kalan filter : pµ n µ n, Λ, u n )N µ n µ ) un n +α + α, Λ 8) u ξ υ Dirichlet Λ Wihart Wn, W ) 5 2 pl n, d) : pl) [ [ n N l n,d a n µ n,d, λ d N µ n µ n, Λ Dirυ; υ ) 3.3 ) un, υ u, ) N Gan, λ a n,, a n,l ) ξ un,u n,, [ Dirξ ; ξ )WΛ ; n, W ) 9) 2 c 24 Inforation Proceing Society of Japan 4

5 q KL : N µ Σ : N d,n,t z n, ϕ d,t,n 7) qϕ, z, θ, π, τ, µ, a, u, υ, ξ, Λ) qϕ d, )qz)qπ) qθ )qτ )) d qµ)qu)qυ) qa n )qξ n )) qλ) ) n µ Σ N z n, ϕ d,t,n x d,t 8) d,n,t N z n, ϕ d,t,n x d,t µ ) 2 9) d,n,t KL qϕ) qz) HMM x t n O t,n n n T n,n p tn x t ) n O t,nt n,np t,n x t ) px t+ T tn ) n px t T t,n )O t+,n T n,n p tn ) px t+ T tn )p tn x t ) qz) n g n v : log g n, d,t ϕ d,t,n log px d,t θ ) ) log v, log τ, 2) fx) q fx) π qπ) Dirπ + z ) τ qτ ) Dirτ, + N n> z n,z n ) qϕ d,t ) qz) h d,n n, l ) n, l) w d,n,l),n,l ) : log h d,t,n z n, log px d,t θ ) 3) l >, n n log w d,n,l ),n,l) E l,n l, n n + 4) otherwie E l,n : E l,n 2 λ l nd a n µ nd ) 2 + D 2 log λ 5) a n µ n l n n θ : q µ, λ ) N G ν + N, ν + N µ ν + N, u + N 2, k + N Σ + ν N ) )) 2 µ 2 ν + N 6) Switching-tate Kalan filter [ Switching-tate Kalan filter µ Kalan oother u HMM : T d X ndl ϕ d,t,n, t )ϕ d,t,n,l t) 2) C nd t L X ndl 2) l M nd C nd L lx ndl 22) l u HMM O n T, : log O n 2 trγ nλ ) + 2 log det Λ 23) log T, log ξ, 24) υ qυ) Dirυ + u ) ξ qξ,: ) Dirξ + N n> u n,z n,: ) µ pµ n X n, ) N µ n g n, V n ) Kalan oother g V : γ α + α 25) β + α 26) Γ n µ n βµ n γ)µ n βµ n γ) T 27) M S n u n Λ 28) A n diag a n 29) : c 24 Inforation Proceing Society of Japan 5

6 P n V n + β 2 S n 3) V n S n + A n Λ n A n β 2 S n P n S n 3) g n Vn βs n P n V n g n βs n γ) ) + S n γ + A n Λ n M n 32) px n+n µ n, ) N µ n h n, W n ) h W : Error DTW HMM Independent Coupled Coupled+Dynaic Q n W n + S n + A n Λ n A n 33) W n β 2 S n I Q n S n ) 34) h n βwn S n Q n W n h n +S n γ+a n Λ n M n ) γ) 35) µ n : qµ n ) N U n V n g n +W n h n ), U n ) 36) U n V n +W n ) Γ n µ n µ n µ n µ n : µ n µ n U n 37) µ n µ n βpn S n Q n + β 2 Sn T Pn S n ) 38) a : D ικ+λ d a n N C nd µ nd M nd D ι+λ d C nd µ 2 nd, D ι + λ C nd µ 2 nd ) ) d Λ : ) N N ) Λ W n + u n, W + u n Γ n n n 39) 4) HMM Kalan oother Chopin Mazurka9 2 5 [ Chroa 6 % 3% 5% 7% 9% Percentile * Krukal-Walli DTW p.5) vector [2 -chroa kHz DTW DTW [3 ) HSMM HMM HMM 2) HSMM Independent 3) Coupled 4) Coupled+Dynaic α. W I d n D λ 3 ι. κ ξ. υ. 6 DTW Independent Coupled 4.2 J.S.Bach 5 c 24 Inforation Proceing Society of Japan 6

7 Phraing d{5,6,7,8}+8 d{,2,3,4}+8 d{3,4,7,8}+8 d{,2,5,6}+8 d{2,4,6,8}+8 d{,3,5,7}+8 : low : ediu 2 : fat 8 u Λ gn Λ ) ) log ab Λ ) 7 2 3 d 7 8 d... 4 d 5... 8, 2 5. [2 - [ Sa

7 7 Phraing d{5,6,7,8}+8 d{,2,3,4}+8 d{3,4,7,8}+8 d{,2,5,6}+8 d{2,4,6,8}+8 d{,3,5,7}+8 : low : ediu 2 : fat 8 u Λ gn Λ ) ) log ab Λ ) d 7 8 d... 4 d , 2 5. [2 - [ Sapp, C. S.: Coparative Analyi of Multiple Muical Perforance, ISMIR, pp ). [2 Stowell, D. and Chew, E.: Maxiu a Poteriori Etiation of Piecewie Arc in Tepo Tie-Serie, Fro Sound to Muic and Eotion, LNCS79), Springer, pp ). [3 Konz, V.: Autoated Method for Audio-Baed Muic Analyi with Application to Muicology, PhD Thei, Saarland Univerity 22). [4 Miki, S., Baba, T. and Katayoe, H.: PEVI: Interface for retrieving and analyzing expreive uical perforance with cape plot, SMC, pp ). [5 Raphael, C.: A Hybrid Graphical Model for Aligning Polyphonic Audio with Muical Score, ISMIR, pp ). [6 Cont, A.: A Coupled Duration-Focued Architecture for Real-Tie Muic-to-Score Alignent, PAMI, Vol. 32, No. 6, pp ). [7 Otuka, T., Nakadai, K., Ogata, T. and Okuno, H. G.: Increental Bayeian Audio-to-Score Alignent with Flexible Haronic Structure Model, ISMIR, pp ). [8 Sako, S., Yaaoto, R. and Kitaura, T.: Ryry: A Real-Tie Score-Following Autoatic Accopanient Playback Syte Capable of Real Perforance with Error, Repeat and Jup, AMT, pp ). [9 Miotto, R., Montecchio, N. and Orio, N.: Statitical Muic Modeling Aied at Identification and Alignent, Ad- MIRe, pp ). [, 24-MUS-3 24). [ Ghahraani, Z. and Hinton, G. E.: Variational learning for witching tate-pace odel, Neural Coputation, Vol. 2, pp ). [2 Fujihia, T.: Realtie Chord Recognition of Muical Sound: A Syte Uing Coon Lip Muic, ICMC, pp ). [3 Hu, N., Dannenberg, R. B. and Tzanetaki, G.: Polyphonic Audio Matching and Alignent for Muic Retrieval, WASPAA, pp ). c 24 Inforation Proceing Society of Japan 7

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