31391555 15 1/7/8:.1:1 @1. 1 supervisedlearig 1 (classifica@o) regressio SV RadomForest usupervisedlearig k.meas 3 supportvectormachie(sv)
k(x,z) = x T z SV 5 k(x,z) = (x T z + c) $ k(x,z) = exp x z ' & % σ ) ( 7 liear regressio iputspace) featurespace) basisfuc@o) (kerelfuc@o - - - 8 1 x i,x j ( ) k(x j, x i ) = exp β x j x i y = 5si(x) + e e ~ N(,1) exp(-beta * x^).....8 1. Shape of kerel (beta = 1) x,y y = f (x) = α j k(x j, x) x j=1 x x j k(x j, x) α j -3 - -1 1 3 8
y x kerel regressio (lmbd =. ) R α R α iputspace) x - φ x α = (K + λ I) 1 y featurespace) - x α - λ R(α ) = (y Kα )Τ " ( y Kα ) + λα Τ Kα φ λ=. y = j=1α jφ (x j )T φ (x) + e = j=1α j k(x j, x) + e - - - - - - w = j=1α φ (x j ) K 1 y = k=1 wkφk (x) + e = w Tφ (x) + e y = m=1 wm xm + e = w Tx + e 8 kerel regressio (lmbd = ) kerel regressio (lmbd =. ) λ= 8 1 8 1 11 SV Liear kerel -.5. x[,]. -.5 - α 8 1 α = (K Τ K) 1 K T y = K 1y -1. R α -1. R α x[,] = (y Kα )Τ + ( y Kα ) - - R(α ) = yi α j k(x j, xi ) j=1.5.5 kerel regressio without regularizatio 1. k(x1, x1 ) k(x, x1 ) K= k(x1, x ) k(x, x ) Gaussia kerel 1. -1. -.5. x[,1] overfirg 1.5 1. SV -1. -.5..5 1. x[,1] 1
Browetal.PNAS97: SV,779 5 S a S b S S 1 t 1 t t a t b S c t d S d 1 L = π S P S S1 (t 1 )P S1Sa (t a )P S1Sb (t b )P SS (t )P S Sc (t c )P SSd (t d ) S S1 S S π X X 1/ P XY (t)t XY S,S 1,S {A,T,C,G} 3 S a,s b,s c {A,T,C,G} 1 L = π S j P S j S 1 j (t 1 )P S1 j S aj (t a )P S1 j S bj (t b )P S j S j (t )P S j S cj (t c )P S j S dj (t d ) j S j S 1 j S j 13 15 Nei Nei sgee@cdistace NeiNei sgee@cide@ty : I XY = p ix p ix p iy p iy p ix x i XY Nei Nei sgee@cdistace : 1 D XY = l(i XY ) XY 1
p 1 y = (p 1y, p y, p 3y ) θ p 3 1 Distace 1 3 Nei x = (p 1x, p x, p 3x ) 1 D XY = l(i XY ) p 1.....8 1. Idetity I XY = p ix p ix p iy p iy I XY = < x,y > x y = x y cosθ x y ( θ π /) = cosθ θ cosie 17... 1.. 19 Ldh PopX PopY B.3.31 C..5 D..15 p ix =.3 +. +. =.55 p iy =.31 +.5 +.15 =.1 p ix p iy =.3.31+..5 +.15 =. I XY =..55.1 =.97 D XY = l(.97) =.3 hgp://www.gsi.go.jp/wnew/latest/iyake hgp://www.gsi.go.jp/wnew/latest/iyake 1999/1/1 /11/8 18
Polygoumcuspidatumvar.termialisHoda iscathuscodesatushack. Alussieboldiaaatsum. 1 3 7 3 3
PCO PCO DNA 5 DNA bpbp DNA trl(uaa)itro Taberlet (1991) 31 9 7 atpb-rbcl Terachi (1993) 77 atpf itro Weisig ccmp 93 1 7 rbcl-accd Iamura 133 19 1 3 78 1 Wt Vt Ut1 Ut Ut3 Ut Oa Et Kt1 Kt Jt1 Jt Jt3 Ja1 Ja 1 1 1 7 1 1 1 1 1 1 7 3 1 3 1 7 11 1 3 1 1 1 1 17 3 1 1 1 7 1 1 1 1 3 1 9 Ut iimum spaigetwork Idel Vt Wt Ut1, Ut3 Et Ja1 Jt Jt3 Oa Kt1 Ja Jt1 7 Kt G st.18.. iyake G st =.3.. ikura Izu (3.1%). -. ikura Kohzu Izu Niijima (3.%). -. Hachijoh iyake Ohshima Ohshima -. Hachijoh -. -.8 -.8 -. -. -.... PCO1 (3.1%) Nei 197UPGA -. Kohzu -. Niijima -.8-1 -.8 -. -. -.. PCO1 (3.9%) Nei 197UPGA 8
PCO DNA bpbp DNA trl(uaa)itro rpl-5'rps1 trt(ugu)-trl(uaa)5 exo Taberlet (1991) 7 1 3-8bp 38bp 13 trl(uaa)itro Taberlet (1991) 53 3 A G rpl-5'rps1 Hamilto (1999) 1 1 C T 188 TTTAT C T 1 5 (3%) 8 (57%) 1 (7%) 1 19 (9%) (1%) (%) (1%) (%) (%) 8 7 (9%) 1 (%) (%) 1 (95%) 1 (5%) (%) 9 9 (1%) (%) (%) 8 18 (%) 1 (3%) (%) 17 1 (8%) (13%) 1 (1%) 9 DNA bpbp DNA trl(uaa)itro trg itro trl(uaa)itro Taberlet (1991) 589 1 35-33bp 81 trl(uaa)exo-trf(gaa) Taberlet (1991) 35 1 A trg itro Weisig ccmp3 119 1 rpl-5'rps1 Hamilto (1999) 755 1 CTTTTTTTTATATT T 798 15 1 (%) 1 (1%) 8 7 (9%) 1 (%) 8 8 (1%) (%) 8 8 (1%) (%) 8 8 (1%) (%) 5 5 (1%) (%) 7 7 (1%) (%) 17 13 (9%) 11 (%) 31 (9.1%) AFLP AOVA... -. -. Hachijoh Izu ikura iyake Niijima Kohzu Ohshima -. -.8 -. -. -.....8 PCO1 (58.%) Nei Nei&Li1979 UPGA 3 DNA DNA AFLP DNA 3
Q&A 1.. 3.. 5x G 1 w() G BU(bestmatchiguit) BU BU G w(t+1)=w(t)+θ(t)α(t)(g w(t)) θ(t). 3.5 θ(t) α(t) ( 5. α(t) 35 Q. A1. B1. G 5 B.G A. Q. 1 BU w() C&D.BU gi BU G w(t+1)=w(t)+θ(t)α(t)(g. w(t)) θ(t) α(t) gi A D (t t+1) θ(t),α(t) 3 5 A,B 3
R #defieafuc@ofordrawigso drawap<.fuc@o(map){ <.dim(map)[1] m<.dim(map)[] plot.ew() plot.widow(c(,m),c(,)) for(ii1:) for(ji1:m) rect(j.1,i.1,j,i,col=rgb(map[i,j,1],map[i,j,],map[i,j,3])) readlie(prompt="hitaykey") } #createsamplestobeclassified gee<.matrix(ruif(1*3),1,3) #geeratearadompager <. m<. map<.array(ruif(*m*3),dim=c(,m,3)) drawap(map) #SOcycles theta<.1 alpha<.. lambda<.5 for(ti1:lambda){ alpha.t<.alpha*(lambda.t)/lambda sample.gee<.gee[sample(row(gee),1),] d<.null for(ii1:) for(ji1:m) d<.c(d,sum((map[i,j,].sample.gee)^)) id<.which.mi(d) row<.id%/%m+1 col<.id%%+1 for(ii(row.theta):(row+theta)){ for(ji(col.theta):(col+theta)){ if(i>=1&i<=&j>=1&j<=m){ map[i,j,]<.map[i,j,]+alpha.t*(sample.gee.map[i,j,]) } } } prit(paste(t,row,col)) drawap(map) } 37 B 1 (q 1 ) A 1 (p 1 ) A 1 B 1 (p 1 q 1 ) B (q ) A 1 B (p 1 q ) A (p ) A B 1 (p q 1 ) A B (p q ) A 1 B 1 A 1 B A B 1 A B P 11,P 1,P 1,P (P 11 +P 1 +P 1 +P =1 P 11 =p 1 q 1 P 1 =p 1 q P 1 =p q 1 P =p q B 1 (q 1 ) B (q ) A 1 (p 1 ) A 1 B 1 (p 1 q 1 +D) A 1 B (p 1 q D) A (p ) A B 1 (p q 1 D) A B (p q +D) D P 11 =p 1 q 1 +D P 1 =p 1 q D P 1 =p q 1 D P =p q +D 39 Q. Q. 38 A 1 B 1 (1) 1. (1) 1 r r. () r r (1) A 1 B 1 () A 1??B 1 p 1 q 1 A 1 B 1 P 11 A 1 B 1 A1 B1 P 11 =(1 r)p 11 +rp 1 q 1 P 11 p 1 q 1 =(1 r)(p 11 p 1 q 1 ) P 11 p 1 q 1 D D t D t D t =(1 r) t D (1) HartladClark(1989)PriciplesofPopula@o Gee@cs. d edi@o
recom<.fuc@o(r,legth){ } r<.c(.5,rep(r,legth)) d<.cumsum(r>=ruif(legth(r)))%% d<.d+1 d cross<.fuc@o(gamete1,gamete,r){ } recom<.recom(r,legth(gamete1).1) child<.gamete1 child[recom==]<.gamete[recom==] as.vector(child) #ii@alpopula@o.gametes<.1.loci<.1 r<.1/.loci gamete<.matrix(,.gametes,.loci)#represetsaa gamete[51:1,]<.1#halfofgameteshavebb image(t(gamete)) par(ask=t) #advacedgeera@os.geera@os<.1 for(ti1:.geera@os){ } prit(t) ext.gamete<.matrix(na,.gametes,.loci) for(ii1:.gametes){ parets<.sample(.gametes,) child<.cross(gamete[parets[1],],gamete[parets[],],r) ext.gamete[i,]<.child } gamete<.ext.gamete image(t(gamete)) R.....8 1......8 1......8 1......8 1. 1 1 1 1 - - - liear regressio 8 1 x i,x j ( ) k(x j, x i ) = exp β x j x i y = 5si(x) + e e ~ N(,1) exp(-beta * x^).....8 1. Shape of kerel (beta = 1) x,y y = f (x) = α j k(x j, x) x j=1 x x j k(x j, x) α j -3 - -1 1 3 3 5 5 y x x iputspace) x φ φ x featurespace) y = w m x m + e = w T K x + e y = w k φ k (x) + e = w T φ(x) + e k=1 m=1 w = α φ(x j ) j=1 y = α j φ(x j ) T φ(x) + e = α j k(x j, x) + e j=1 j=1
k(x 1, x 1 ) k(x, x 1 ) K = k(x 1, x ) k(x, x ) R(α ) = y i α j k(x j, x i ) j=1 = (y Kα ) Τ +(y Kα ) R α R α α α = (K Τ K) 1 K T y = K 1 y - - - kerel regressio without regularizatio 8 1 overfirg 5 5 7 R(α ) = (y Kα ) Τ "(y Kα ) + λα Τ Kα λ R α R α α α = (K + λi) 1 y λ=. λ= - - - kerel regressio (lmbd =. ) 8 1 - - - - - - kerel regressio (lmbd =. ) 8 1 kerel regressio (lmbd = ) 8 1 supervisedlearig 1 (classifica@o) regressio SV RadomForest usupervisedlearig k.meas " " " 8
5 k.medoids PC 8 - - - PC 9 - - - 8 hgp://lecture.ecc.u.tokyo.ac.jp/~aiwata/ biostat_basic/idex.html Frequecy 8 1 - - pca.tr$x[kmed$id.med, i] - Frequecy Frequecy 8-15 1 PC k-medoids 8 5 kmeas 1 - - pca.tr$x[kmed$id.med, i] - - pca.tr$x[kmed$id.med, i] 51 kmeas 1 15 15 1 PC PC -5-1 5-1 PC 1 kmeas 5 1 PC1 5 5 1 15 - -1 PC1 PC3 37 Kosambi 15 kmeas 1 PC 1 PC 3 k-medoids 1 PC3 - PC k-medoids Frequecy 5 1 1-5 1 PC1 1 PC 1 k-medoids 15 1 5 PC PC 1 5 1 1 pca.tr$x[, i] Haldae 1 1 pca.tr$x[, i] hclust - Frequecy - pca.tr$x[, i] pca.tr$x[kmed$id.med, i] PCA,hierarchicalclusterig, k.meas - pca.tr$x[, i] - 9 PC all 1 3 5 3 1 Frequecy Frequecy 3 Frequecy - PC 3 all 5 PC all - PC3 PC 1 all - hclust PC1 medoid medoid k - 1 medoid medoid - 1-5 k.medoids DNA 1,311SNPs 1-1 -5 5 1 15 PC3 5 5
Haldae (5 o.ormalpheotype) Whiletheormalityassump?oiso@e reasoable,departuresfromormality areotucommo:thepheotypemay bedichotomous,highlyskewedorexhibit spikes.(forexample,ifthepheotypeis themassofgallstoes( ),some idividualsmayhaveogallstoesadso aspikeatwouldbeobserved.)i prac?ce,applica?oofstadarditerval mappigwillgeerallygivereasoable results,eveforadichotomoustrait, providedthatsta?s?calsigificaceis establishedviaapermuta?otest,ad exceptfortheproblemofspuriouslod scoresiregiosoflowgeotype iforma?o. Browma(9)AguidetoQTL mappigwithr/qtl 53 7 55 QTL (5 o.ormalpheotype) Nevertheless,improvedefficiecy maybeobtaiedbyapplyigalterate methods.thesimplestapproachisto trasformthepheotype.( )We geerallys?cktoeithertakiglogs, squareroots,orotrasforma?o.i thischapter,wedescribedseveral altera?veitervalmappigmethods, icludigoparametriciterval mappig(basedotheraksofthe pheotypes),itervalmappigspecific forbiarytraits,adatwovpartmodel forthecaseofapheotype distribu?oexhibi?gaspike(suchas at). 5 Browma(9)AguidetoQTL mappigwithr/qtl 5
8 χ 8 #19 1 1 R S AA a c g aa b d h e f e,f,g,h " P(e, f,g,h) = $ % # e& ' p e q f " $ % # g ' r g s h = () & e f gh pe q f r g s h p=e/,q=f/,r=g/,s=h/ a,b,c,d e,f,g,h " P(a,b,c,d,e, f,g,h) = $ % # e& ' p e q f " $ e% " # a ' r a s b $ f % ' r c s d = e f & # c & e f ab cd pe q f r g s h e,f,g,h a,b,c,d P(a,b,c,d e, f,g,h) = p(a,b,c,d,e, f,g,h) / p(e, f,g,h) = e f gh 1 abcd 57 59 Fisher Fisher sexacttest 58 a,b,c,d 11 3 7 R S AA 11 15 aa 3 7 1 9 5 5 1 11 5 1 8 p x = 111151 " 1 % $ ' =.37 5 # 1137 & p x 5% 3 8 7 13 1 7 7 9 8 3 p x p = 111151 " 1 5 1137 + 1 138 + 1 1319 + 1 111 + 1 5911 + 1 % $ ' # 111& =.8 1 8 Fisher χ 1 1 9 5 9 1 1 1 1 5 11
7 QTL1 GEI 1 3 iforma@o kowledge