Nonparametric Bayesian T-Process Algorithm for Heterogeneous Gene Regulatory Network

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1 IPSJ SIG Tecncal Report Vol.-MPS-9 No.5 Vol.-BIO-3 No.5 //6 T,a,b,c,d,e T Drosopla melanogaster RJMCMC Nonparametrc Bayesan T-Process Algortm for Heterogeneous Gene Regulatory Network HIROKI MIYASHITA,a TAKUMA NAKAMURA,b YASUTOSHI IDA,c TOMOHIKO SUZUKI TAKASHI MATSUMOTO,d TAKASHI KABURAGI,e Abstract: A nonparametrc Bayesan model s employed to estmate gene regulatory networks of Drosopla melanogaster A T-process-based algortm s expected to capture nonlnear dynamcs n te lfe penomenon and reconstruct te gene regulatory nteractons wt consderaton of te actual tmng of morpogenc transtons Te wole algortm s mplemented by a reversble jump Markov Can Monte Carlo Keywords: Bonformatcs Macne Learnng Nonparametrc Bayes Bayesan Network. Waseda Unversty, Tokyo, Japan Gakusun Unversty, Tokyo, Japan a myasta@matsumoto.eb.waseda.ac.jp b nakamura@matsumoto.eb.waseda.ac.jp c da@matsumoto.eb.waseda.ac.jp d takas@matsumoto.elec.waseda.ac.jp e takas.kaburag@gakusun.ac.jp Robnson et al. - [] Dondelnger et al. [] c Informaton Processng Socety of Japan

2 IPSJ SIG Tecncal Report.. Dondelnger et al. [] j j j M. = {j, j, } c p s M s = M c s c λ c P c λ λc c! c m= λ m m! c ζ N s N c P ζ λ = / c Λ s λ, Λ.3 Kkuc et al. [3] M T y y {j, j,, j s } x,j x = j,, xt j x,j k, k,t. K = k T, k T,T 3 k p,q k p,q= + ɛ δ j M δ sn x p j M j xq j +exp x p j xq j l RQ ɛ, δ, l I α, β C = α K + β I 5 y fy = C exp y C y 6 y C t t j 6 t T Γ fy = T.4 + Γ C π T + y C y T P c, ζ, s, M y s m= Γ Λ m m! T c+ + Γ λ c N c! N c! C π T + y C Vol.-MPS-9 No.5 Vol.-BIO-3 No.5 //6 c + = y Λ s p s! p! T + 8 c Informaton Processng Socety of Japan

3 IPSJ SIG Tecncal Report.5 RJMCMC [] v 4 c b c = 4 mn, P cc + P c c d c = 4 mn, P cc P c c 9 p c = b c + d c π c = b c + d c + p c.5. ζ = ζ,, ζc ζ ζ new ζ + ζ + = {ζ new } ζ ζ + q ζ + ζ = 3 N 3 c x x ζ ζ new q ζ ζ + = c + 4, α c,c α c,c +ζ, ζ + = mn,r c,c +ζ,ζ + = P c +,ζ+,s+,m+ y P c,ζ,s,m y d c + qζ ζ + bc qζ 5 + ζ. ζ new ζ new L, R. s Λ 3. Λ 4. 3 L, R α c,c + ζ, ζ + 7. u U [,] 8. u α c,c + ζ, ζ + ζnew ζ new ζ ζ ζ U {ζ} 6 ζ α c+,c ζ +, ζ = mn, r c,c +ζ, ζ c ζ ζ ζ U {ζ} 8 ζ [ ζ W, ζ + W ] [ ζ +, ζ + ] 9 W ζ ζ ζ ζ ζ ζ ζ Vol.-MPS-9 No.5 Vol.-BIO-3 No.5 //6 q ζ ζ = c W e q ζ ζ = c W e e, e W/ c Informaton Processng Socety of Japan 3

4 IPSJ SIG Tecncal Report α c ζ, ζ = mn,r c,c +ζ,ζ = P c,ζ,s,m y qζ ζ P c,ζ,s,m y qζ ζ.5.4 M b s, d s b s = mn, P ss + P s s 3 d s = mn, P ss P s s 4 P s s, M M α s,s M, M = mn,r s,s M,M = P c,ζ,s,m y 5 P c,ζ,s,m y. 3 4 b s, d s. u U [,] 3. u b s u > b s u b s + d s α s,s M, M 8. u U [,] 9. u α s,s M, M s M T TP-TVDBN GP-TVDBN Fg Tme pont Syntetc data.blue lnes ndcate te actual postons of cange ponts. X X X X X.. : 3 : 3 56 : 57 8 Fg. Interactons between fve syntetc data troug 8 tme ponts. Black arrows ndcate lnear nteractons, wereas red arrows correspond to nonlnear nteractons. ROC area under te curve BER balanced error rate k p,q = ξ + ɛ δ j M X Vol.-MPS-9 No.5 Vol.-BIO-3 No.5 //6 δ x p j xq j + η j M X X x p j xq j 6 c Informaton Processng Socety of Japan 4

5 IPSJ SIG Tecncal Report Vol.-MPS-9 No.5 Vol.-BIO-3 No.5 //6 Posteror probablty P Tme pont 3 TP-TVDBN GP- TVDBN Fg. 3 Cange ponts n te syntetc data. Posteror probabltes nferred by TP-TVDBN red lne and GP- TVDBN blue lne. Dased lnes ndcate te actual postons of cange ponts. AUC. Table AUC values of eac dynamc Bayesan network. NET NET NET3 allint TP-TVDBN GP-TVDBN BER. Table BER values of eac dynamc Bayesan network. NET NET NET3 allint TP-TVDBN GP-TVDBN Tme pont eve gfl / lmd tw mlc sls mc prm actn up myo6f msp3 Drosopla melanogster Fg. 4 Drosopla melanogaster gene expresson data. Blue osteror probablty Po osteror probablty Po lnes ndcate te morpogeness transtons Tme pont Tme pont ξ η TP-TVDBN GP-TVDBN NET 3 allint AUC BER BER TP-TVDBN GP-TVDBN 5 [] Fg. 5 Cange ponts durng morpogeness n Drosopla melanogaster. Top panel : posteror probablty nferred by TP-TVDBN. Bottom panel: te result by HetDBN. Dased lnes ndcate te morpogeness transtons. 3. Drosopla melanogaster Drosopla melanogaster [6] HetDBN[] c Informaton Processng Socety of Japan 5

6 IPSJ SIG Tecncal Report 3 Table Average and medan value of te posteror probablty among 67 tme ponts. TP-TVDBN.73. HetDBN.85.5 F = 3. Table 4 Precson Recall and F-measure. Ter tresolds 6 Fg. 6 were determned accordng to ter averages. F TP-TVDBN HetDBN mc up msp3 prm mlc sls actn gfl myo6f tw eve =.5 Reconstructed network for te morpologcal pase of an embryo usng TP-TVDBN metod tr =.5. True-Negatve F F [] 3 4 True-Negatve 4. AUC BER Drosopla melanogaster [] T Vol.-MPS-9 No.5 Vol.-BIO-3 No.5 //6 [] J. W. Robnson and A. J. Hartemnk, Learnng Non- Statonary Dynamc Bayesan networks.: Journal of Macne Learnng Researc. [] F. Dondelnger, S. Lebre, and D. Husmeer.: Nonomogeneous dynamc Bayesan networks wt Bayesan regularzaton for nferrng gene regulatory networks wt gradually tme-varyng structure, Macne Learnng. [3] T. Kkuc, T. Suzuk, Y. Nakada, T. Kaburag, T. Matsumoto, T. Kmwada and K. Wada.: Gene Regulatory Network Predcton usng a Dynamc Gaussan Process: MCMC approac, IEICE Tecncal Report Neurocomputng. [4] M. Grzegorczyk and D. Husmeer.: Bayesan regularzaton of non-omogeneous dynamc Bayesan networks by globally couplng nteracton parameters, Proceedngs of te 5t Internatonal Conference on Artfcal Intellgence and Statstcs AISTATS, US [5] Y. Ja and J. Huan.: Constructng non-statonary Dynamc Bayesan Networks wt a flexble lag coosng mecansm, BMC bonformatcs [6] M. N. Arbetman., E. E. M. Furlong, F. Imam, E. Jonson, B. H. Null, B. S. Baker, M. A. Krasnow, M. P. Scott, R. W. Davs and K. P. Wte.: Gene Expresson Durng te Lfe Cycle of Drosopla melanogaster, Scence. [7] J.M. Wang, D. J. Fleet and A. Hertzmann.: Gaussan Process Dynamcal Models, Advances n Neural Informaton Processng Systems NIPS5. [8] C. Andreu, P. Djur c, and A. Doucet.: Jont Bayesan model selecton and estmaton of nosy snusods va reversble jump MCMC, IEEE Trans. On Sgnal Processng999 [9] S. Lébre.: Stocastc process analyss for Genomcs and Dynamc Bayesan Networks nference, PD Tess, Unverstè d Evry-Val-d Essonne, France 7. [] P. Green.: Reversble jump Markov can Monte Carlo computaton and Bayesan model determnaton, Bometrka995. [] C. E. Rasmussen and C. K. I. Wllams.: Gaussan Process for Macne Learnng, Adaptve Computaton and Macne Learnng, MIT Press 5. [] D. J. C. MacKay, Introducton to Gaussan Processes, In C.M. Bsop, Neural Networks and Macne Learnng 998. T c Informaton Processng Socety of Japan 6

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