Road map. Machine learning and its antecedents in microarray statistics. Metadata administration. QC/Preprocessing. VJ Carey

Transcription

1 Rad map and its antecedents in micrarray statistics 1 1 Channing Labratry Brigham and Wmen s Hspital Bstn, MA, USA 1 Preprcessing Differential epressin 2 3 June / CSHL C-DATA05 Preprcessing Differential epressin Preprcessing Differential epressin Metadata administratin QC/Preprcessing affy users: use read.phendata at an early stage, and bind this t the affybatch cdna users: place relevant sample-level infrmatin in the targets file use read.miame at an early stage, and bind this t the eprset befre dwnstream wrk begins variatin in eperimental results: bth structural and randm ppulatin-level phenmena individual-level phenmena measurement technique: bth structural and randm we are interested primarily in bilgical variatin technical surces f variatin are an bscuring nuisance

2 Preprcessing Differential epressin Preprcessing: micrarray nrmalizatin premises Preprcessing Differential epressin Preprcessing: micrarray nrmalizatin bjectives within-slide: intensity-dependent bias, crrectible print tip r sectr defects between-slide: changes in verall level, r scale, that have n bilgical basis many f the prminent methds assume majrity f genes are NOT differentially epressed variatin bserved in genes that are nt differentially epressed can be used t epse/estimate bilgically irrelevant variatin within-slide: variatin due t structural factrs such as print tip r sectr can be islated intensity-dependent bias in lg ratis estimable/remvable under assumptin that majrity f genes are nt differentially epressed between-slide: lcatin and/r scale and/r cmplete distributin can be made cmparable Preprcessing Differential epressin Preprcessing: micrarray nrmalizatin tls Preprcessing Differential epressin Preprcessing: micrarray nrmalizatin tls affy, epress: > bgcrrect.methds [1] "mas" "nne" "rma" "rma2" > nrmalize.affybatch.methds [1] "cnstant" "cntrasts" [3] "invariantset" "less" [5] "qspline" "quantiles" [7] "quantiles.rbust" cdna (marray), manrm: > args(manrm) functin (mbatch, nrm = c("printtipless", "nne", "median", "less", "twd", "scaleprinttipmad"), subset = TRUE, span Mlc = TRUE, Mscale = TRUE, ech = FALSE,...) NULL > epress.summary.stat.methds [1] "avgdiff" "liwng" "mas" [4] "medianplish" "playerut"

3 Data structure hierarchies Preprcessing Differential epressin Tls fr differential epressin Preprcessing Differential epressin build frm scanners/cels: affybatch, eprset, marraynrm, RGList instances build by hand: MIAME, phendata instances (widget=true) mutate the affybatch (s that metadata prpagates thrugh prcessing) r eprset: > phendata(myab) <- pdd > phendata(eset) <- pdd > descriptin(eset) <- mymiame use class(bj) and getclass(classname) t learn abut classes t.test(g1, g2): fine fr a single gene acrss tw phentypes r treatments, need either nrmality r relatively large sample fr validity; use av() fr multifactr inference fastt(, inds1, inds2): wrks ver a matri; can fllw with multtest functins t adjust fr multiplicity; can have misleading results with small samples f.sam r (Bicnductr) siggenes functins: imprved analg f t.test that diminishes artifactual significance in small samples limma: general apprach t linear mdels (pssibly multifactr r trends) based n a specified design matri; includes ptins fr crrectins fr multiple testing; limmagui, affylmgui EBarrays, many ther pssibilities Preprcessing Differential epressin QC and claims f differential epressin Stat mdels with additive structure many times scientists ask what is the quantitative threshld f acceptability fr the assay? we lk at varius quality criteria, and smetimes a decisin is clear remember the cncept f sensitivity analysis: if a few chips are questinable, it is helpful t knw that the inferences are nt severely sensitive t their inclusin red the entire analysis withut the questinable chips and cmpare results eplain any imprtant differences befre deciding against the analysis based n the full set data = fit + residual five symbls, many questins start with fit: a mdel instance that has an interpretatin. typically the mdel family cnfers structure n a relatinship between measurements data (Y, p 1 ) Y may dente a phentype, say SBP may dente a crrelate r predictr f the phentype, say CRP epressin

4 a linear mdel a quadratic mdel Y = a + b + e fit = a + b e is a randm variable with 0 mean and specified variance structure putative realizatins f the mdel used fr estimatin f a, b (e.g., by least squares) â is mean SBP fr CRP epressin level 0 ˆb is mean difference in SBP fr tw bservatins differing by ne unit in CRP epressin sme nnlinearity can be accmmdated thrugh y = a + b + c 2 + e parameters a, b, c can be estimated using a linear functin f y, s this is still an instance f the family f linear mdels chsing amng mdels lk at the data! identical bivariate summaries: all mdels are wrng sme are mre useful than thers des the epressin f an asparagine-synthetase like gene vary linearly r nnlinearly in fibrblasts epsed t human serum? prefer apprimate answer t right scientific questin ver eact answer t wrng scientific questin fr each graph, cr(,y) =.816 fr each graph, t.test(,y) has p-value 0.22 fr each graph, the regressin line is estimated as y = 3 +.5, with identical standard errrs beware the cncise statistical summary

5 Basic intentins f machine learning pattern recgnitin: faces are cmple, humans have gd recall capabilities; can image prcessing algrithms be fund t perfrm identificatin? supervised recgnitin: there are labels assciated with bjects that we wish t recver unsupervised recgnitin: n a priri labeling r gruping; seek regularities in data t frm grupings predictin: patients in ER have a cllectin f symptms; under which cnfiguratins is it likely that a heart attack has ccurred r is imminent? ratinalizatin: a recgnitin r predictin algrithm has been cnstructed; des the way in which it emplys the data tell us smething meaningful abut the wrld? bjectivity: the creatin and the deplyment f the algrithm shuld require minimal human invlvement Simple frmalism fr supervised machine learning Training data accumulate in a structure D. D includes a p-vectr f features X and a categrical respnse Y ML is a machine learning prcedure, perating n D t prduce an algrithm (machine) M. M is required t assciate with each X a predicted respnse (an instance f Y, r dubt, r utlier) Typically a test data structure E is used t assess the predictive accuracy f M; we use the features in E t predict respnses Y using M and cmpare them t the true respnses in E Imprtant principle: ML must avid verfitting t D; must try t anticipate the kind f data that will cme but have nt yet been bserved Classical technique: linear discriminant analysis Eample: tw genes in Glub s full data Fisher s linear discriminant analysis (LDA) wrks with a categrical respnse Y and cntinuus inputs X Finds a linear cmbinatin f cmpnents f X fr which the rati (separatin f class-specific means/ within-class variance) is maimized in the case f tw features and tw respnse classes, this criterin determines a line in the plane spanned by the tw features the line separates the data int tw grups; there may be misclassificatin KLK APOA1

6 Upshts Sme etensins f linear discriminants the line drawn abve is regarded as a machine give it the values f APOAI and KLK3 and it will predict r Is it gd? T say hw gd it is we seek t estimate the generalizatin errr Generalizatin errr (GE) is intrinsically unbservable Prcedures fr estimating GE r fr designing learning prcedures that theretically minimize GE are imprtant in machine learning thery and practice Kernel methds f feature transfrmatin when there is n separatin f classes in feature space, transfrm features t a representatin in which there is! Sme etensins f linear discriminants Supprt vectr machines Maimum margin criteria when there are multiple (hyper)planes that can separate the classes, chse the ne maimizing the margin t nearest data pint Supprt vectr machines are learners that eplit rich feature space transfrmatin ptentials emply maimum margin criteria in selecting separating hyperplanes sme thery n generalizatin errr cntrl is available there are varius tuning parameters that need t be set Illustratin with the Glub data:

7 Supprt vectr machine frm package e1071 Classificatin trees: a breast cancer eample SVM classificatin plt KLK APOA1 rpart and tree structured mdeling ptins a filtering f the data > library(rpart) > args(rpart) functin (frmula, data, weights, subset, na.actin = na.rpart, methd, mdel = FALSE, = FALSE, y = TRUE, parms, cntrl, cst,...) NULL > args(rpart.cntrl) ttally artificial, select thse genes with CV greater than 1.2 > library(genefilter) > ff <- filterfun(cv(1.2)) > k <- genefilter(glubmerge, ff) > glubmerge2 <- glubmerge[k, ] functin (minsplit = 20, minbucket = rund(minsplit/3), cp = 0.01, macmpete = 4, masurrgate = 5, usesurrgate = 2, val = 10, surrgatestyle = 0, madepth = 30,...) NULL

8 neural netwrks neural netwrks are very fleible nnlinear mdels architecture f the netwrk, alng with regularizatin, determines the fleibility fleibility f the feed-frward, 1-hidden layer mdel is determined by size and decay parameters A unified interface t machine learning with eprsets basic pattern: [meth]b( es, labelname, traininds, therparms ) > library(mlinterfaces) > nn1 <- nnetb(glubmerge2[1:100, ], ".", + 1:36, size = 5, decay = 0.01) > cnfumat(nn1) predicted given A unified interface t machine learning with eprsets Variable imprtance measures > library(mlinterfaces) > rf1 <- randmfrestb(glubmerge2[1:100, ], + ".", 1:36, imprtance = TRUE) > cnfumat(rf1) predicted given randm frests are sequences f classificatin trees; each is cnstructed frm a randmly reduced dataset, each split f the tree is frmed with a randmly reduced set f variables majrity vting acrss the sequence f trees is used t make classificatins D14664_at AF000234_at D10923_at D10495_at D16626_at AF009426_at D10202_at AF005043_at D13637_at AF009674_at D13264_at AF005037_at D13628_at AFFX M27830_5_at AFFX TrpnX 5_at AB000115_at AFFX DapX 5_at AB002366_at D11428_at D00654_at Mean decrease in accuracy 0.030

9 bsting back t LDA; crss-validatin anther majrity vte ver a sequence f classifiers here each classifier is fairly weak (a small tree) key innvatin: data are re-weighted as sequence grws, dwnweighting the recrds that are easy t classify > gb1 <- gbmb(glubmerge2[1:500, ], ".", + 1:45, n.trees = 5000) > cnfumat(gb1) predicted given > lda2 <- ldab(glubmerge2[1:500, ], ".", + 1:45) > cnfumat(lda2) predicted given > <- val(glubmerge2[1:500, ], ".", + ldab, "LOG", rep(1:6, each = 12)) > table(, glubmerge2$) summary tls fit statistical mdels Overfitting is a real cncern with fleible mdels Crss-validatin (repeatedly setting aside elements f a partitin f the data) and ther appraches t estimatin f generalizatin ability are imprtant interpretatin f fitted mdels can be illuminating; variable imprtance measures? use f classificatin prcesses t define distance/primity metrics seems prmising? Human interventin seems necessary (setting tuning parameters, defining generalizatin errr threshlds) Gd references: Ripley (Pattern Recgnitin), Hastie, Tibshirani and Friedman (Elements f Statistical Learning), Schölkpf and Smla (Learning with Kernels), Vapnik (Nature f statistical learning thery), Duda, Hart and Strk (Pattern Classificatin)