!!! 2014/7/24!!!8:40.10:10! support!vector!machine!(svm)! supervised!learning! unsupervised!learning! !!! ! 1 regression!

HTML
DOWNLOAD

Μέγεθος: px

Εμφάνιση ξεκινά από τη σελίδα:

Download "!!! 2014/7/24!!!8:40.10:10! support!vector!machine!(svm)! supervised!learning! unsupervised!learning! !!! ! 1 regression!"

Τρύφων Δοξαράς
6 χρόνια πριν
Προβολές:

1 supervisedlearig 1 (classifica@o) regressio SV RadomForest usupervisedlearig k.meas 3 supportvectormachie(sv)

2 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 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^) 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 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= SV Liear kerel -.5. x[,] 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 x[,1] overﬁrg SV x[,1] 1

(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

4 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 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 =

Idetity I XY = p ix p ix p iy p iy I XY = < x,y > x y =

... 1.. 19 Ldh PopX PopY B.3.31 C..5 D..15 p ix =.3 +.

.55.1 =.97 D XY = l(.97) =.3 hgp://www.gsi.go.

5 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 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 Ldh PopX PopY B.3.31 C..5 D..15 p ix = =.55 p iy = =.1 p ix p iy = =. I XY = =.97 D XY = l(.97) =.3 hgp:// hgp:// 1999/1/1 /11/8 18

6 Polygoumcuspidatumvar.termialisHoda iscathuscodesatushack. Alussieboldiaaatsum

7 PCO PCO DNA 5 DNA bpbp DNA trl(uaa)itro Taberlet (1991) atpb-rbcl Terachi (1993) 77 atpf itro Weisig ccmp rbcl-accd Iamura Wt Vt Ut1 Ut Ut3 Ut Oa Et Kt1 Kt Jt1 Jt Jt3 Ja1 Ja 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 PCO1 (3.1%) Nei 197UPGA -. Kohzu -. Niijima PCO1 (3.9%) Nei 197UPGA 8

8 PCO DNA bpbp DNA trl(uaa)itro rpl-5'rps1 trt(ugu)-trl(uaa)5 exo Taberlet (1991) bp 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) bp 81 trl(uaa)exo-trf(gaa) Taberlet (1991) 35 1 A trg itro Weisig ccmp rpl-5'rps1 Hamilto (1999) CTTTTTTTTATATT T (%) 1 (1%) 8 7 (9%) 1 (%) 8 8 (1%) (%) 8 8 (1%) (%) 8 8 (1%) (%) 5 5 (1%) (%) 7 7 (1%) (%) (9%) 11 (%) 31 (9.1%) AFLP AOVA Hachijoh Izu ikura iyake Niijima Kohzu Ohshima PCO1 (58.%) Nei Nei&Li1979 UPGA 3 DNA DNA AFLP DNA 3

9 Q&A x 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

10 R <.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

11 } 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 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^) 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 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

12 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 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 =. ) kerel regressio (lmbd =. ) 8 1 kerel regressio (lmbd = ) 8 1 supervisedlearig 1 (classifica@o) regressio SV RadomForest usupervisedlearig k.meas " " " 8

13 5 k.medoids PC PC hgp://lecture.ecc.u.tokyo.ac.jp/~aiwata/ biostat_basic/idex.html Frequecy pca.tr$x[kmed$id.med, i] - Frequecy Frequecy PC k-medoids 8 5 kmeas pca.tr$x[kmed$id.med, i] - - pca.tr$x[kmed$id.med, i] 51 kmeas PC PC PC 1 kmeas 5 1 PC PC1 PC3 37 Kosambi 15 kmeas 1 PC 1 PC 3 k-medoids 1 PC3 - PC k-medoids Frequecy PC1 1 PC 1 k-medoids PC PC 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 Frequecy Frequecy 3 Frequecy - PC 3 all 5 PC all - PC3 PC 1 all - hclust PC1 medoid medoid k - 1 medoid medoid k.medoids DNA 1,311SNPs PC3 5 5

Haldae (5 o.ormalpheotype) Whiletheormalityassump?oiso@e reasoable,departuresfromormality areotucommo:thepheotypemay bedichotomous,highlyskewedorexhibit spikes.

14 Haldae (5 o.ormalpheotype) 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 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

15 8 χ 8 # 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 Fisher Fisher sexacttest 58 a,b,c,d R S AA aa p x = " 1 % $ ' =.37 5 # 1137 & p x 5% p x p = " % $ ' # 111& = Fisher χ

16 7 QTL1 GEI 1 3 iforma@o kowledge

Σχετικά έγγραφα

ΕΚΛΟΓΙΚΗ ΠΕΡΙΦΕΡΕΙΑ ΕΒΡΟΥ

ΕΚΛΟΓΙΚΗ ΠΕΡΙΦΕΡΕΙΑ ΕΒΡΟΥ ΑΣΗΜΑΚΟΠΟΥΛΟΣ ΣΠΥΡΙΔΩΝ του ΔΗΜΗΤΡΙΟΥ ΚΑΛΑΪΤΖΙΔΟΥ ΑΙΚΑΤΕΡΙΝΗ του ΜΙΧΑΗΛ ΚΟΖΑΡΗΣ ΚΥΡΙΑΚΟΣ του ΧΡΗΣΤΟΥ ΜΑΛΚΟΥΚΗΣ ΒΑΣΙΛΕΙΟΣ του ΔΗΜΗΤΡΙΟΥ ΜΟΡΑΛΗΣ ΖΗΣΗΣ του ΙΩΑΝΝΗ ΕΚΛΟΓΙΚΗ ΠΕΡΙΦΕΡΕΙΑ