解决使用 R 的 CMA Bioconductor 包时 SVM 分类交叉验证中的 'model empty' 错误

Question

我正在使用 Bioconductor 包 CMA对微阵列数据集中的 SVM 分类器执行内部蒙特卡洛交叉验证 (MCCV)。 CMA 内部使用 e1071 R 包进行 SVM 工作。

该数据集包含 45 个样本(观测值)的 387 个变量(属性)，这些样本属于两个类之一(标签 0 或 1；比例约为 1:1)。所有数据都是数值数据，没有 NA。我正在尝试使用limma statistics为SVM选择15个变量的1000次迭代MCCV用于差异基因表达分析。在 MCCV 期间，45 个样本集中的一部分用于训练 SVM 分类器，然后用于测试剩余的部分，并且我正在尝试训练集部分的不同值。 CMA 还执行内循环验证(默认情况下在训练集中进行 3 倍交叉验证)，以微调用于针对测试集进行交叉验证的分类器。所有这些都是在 CMA 包内完成的。

有时，对于较小的训练集大小，CMA 会在控制台中显示错误，并停止执行其余的分类代码。

[snip]tuning iteration 575tuning iteration 576tuning iteration 577Error in predict.svm(ret, xhold, decision.values = TRUE) :   Model is empty!

It occurs even when I use a test other than limma's for variable selection, or use two instead of 15 variables for classifier generation. The R code I use should ensure that the training-sets always have members of both classes. I would appreciate any insight on this.

Below is the R code I use, with Mac OS X 10.6.6, R 2.12.1, Biobase 2.10.0, CMA 1.8.1, limma 3.6.9, and WilcoxCV 1.0.2. The data file hy3ExpHsaMir.txt can be downloaded from http://rapidshare.com/files/447062901/hy3ExpHsaMir.txt.

Everything goes OK until g is 9 in the for(g in 0:10) loop (for varying the training/test-set sizes).

# exp is the expression table, a matrix; 'classes' is list of known classes
exp <- as.matrix(read.table(file='hy3ExpHsaMir.txt', sep='\t', row.names=1, header=T, check.names=F))
#best is to use 0 and 1 as class labels (instead of 'p', 'g', etc.) with 1 for 'positive' items (positive for recurrence, or for disease, etc.)
classes <- c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
yesPredVal = 1 # class label for 'positive' items in 'classes'

library(CMA)
library(WilcoxCV)
myNumFun <- function(x, y){round(y(as.numeric(x), na.rm=T), 4)}
set.seed(631)
out = ''
out2 = '\nEffect of varying the training-set size:\nTraining-set size\tSuccessful iterations\tMean acc.\tSD acc.\tMean sens.\tSD sens.\tMean spec.\tSD spec.\tMean PPV\tSD PPV\tMean NPV\tSD NPV\tTotal genes in the classifiers\n'

niter = 1000
diffTest = 'limma'
diffGeneNum = 15
svmCost <- c(0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50)

for(g in 0:10){ # varying the training/test-set sizes
 ntest = 3+g*3 # test-set size
 result <- matrix(nrow=0, ncol=7)
 colnames(result) <- c('trainSetSize', 'iteration', 'acc', 'sens', 'spec', 'ppv', 'npv')
 diffGenes <- numeric()

 # generate training and test sets
 lsets <- GenerateLearningsets(n=ncol(exp), y=classes, method=c('MCCV'), niter=niter, ntrain=ncol(exp)-ntest)

 # actual prediction work
 svm <- classification(t(exp), factor(classes), learningsets=lsets, genesellist= list(method=diffTest), classifier=svmCMA, nbgene= diffGeneNum, tuninglist=list(grids=list(cost=svmCost)), probability=TRUE)
 svm <- join(svm)
 # genes in classifiers
 svmGenes <- GeneSelection(t(exp), classes, learningsets=lsets, method=diffTest)

 actualIters=0
 for(h in 1:niter){
  m <- ntest*(h-1)
  # valid SVM classification requires min. 2 classes
  if(1 < length(unique(classes[-lsets@learnmatrix[h,]]))){
   actualIters = actualIters+1
   tp <- tn <- fp <- fn <- 0
   for(i in 1:ntest){
    pred <- svm@yhat[m+i]
    known <- svm@y[m+i]
    if(pred == known){
     if(pred == yesPredVal){tp <- tp+1}
     else{tn <- tn+1}
    }else{
     if(pred == yesPredVal){fp <- fp+1}
     else{fn <- fn+1}
    }
   }
   result <- rbind(result, c(ncol(exp)-ntest, h, (tp+tn)/(tp+tn+fp+fn), tp/(tp+fn), tn/(tn+fp), tp/(tp+fp), tn/(tn+fn)))
   diffGenes <- c(diffGenes, toplist(svmGenes, k=diffGeneNum, iter=h, show=F)$index)
  } # end if valid SVM
 } # end for h

 # output accuracy, etc.
 out = paste(out, 'SVM MCCV using ',  niter, ' attempted iterations and ', actualIters, ' successful iterations, with ', ncol(exp)-ntest, ' of ', ncol(exp), ' total samples used for training:\nThe means (ranges; SDs) of prediction accuracy, sensitivity, specificity, PPV and NPV in fractions are ', 
myNumFun(result[, 'acc'],mean), ' (', myNumFun(result[, 'acc'], min), '-', myNumFun(result[, 'acc'], max), '; ', myNumFun(result[, 'acc'], sd), '), ', 
 myNumFun(result[, 'sens'], mean), ' (', myNumFun(result[, 'sens'], min), '-', myNumFun(result[, 'sens'], max), '; ', myNumFun(result[, 'sens'], sd), '), ', 
 myNumFun(result[, 'spec'], mean), ' (', myNumFun(result[, 'spec'], min), '-', myNumFun(result[, 'spec'], max), '; ', myNumFun(result[, 'spec'], sd), '), ', 
 myNumFun(result[, 'ppv'], mean), ' (', myNumFun(result[, 'ppv'], min), '-', myNumFun(result[, 'ppv'], max), '; ', myNumFun(result[, 'ppv'], sd), '), and ', 
 myNumFun(result[, 'npv'], mean), ' (', myNumFun(result[, 'npv'], min), '-', myNumFun(result[, 'npv'], max), '; ', myNumFun(result[, 'npv'], sd), '), respectively.\n', sep='')

 # output classifier genes
 diffGenesUnq <- unique(diffGenes)
 out = paste(out, 'A total of ', length(diffGenesUnq), ' genes occur in the ', actualIters, ' classifiers, with occurrence frequencies in fractions:\n', sep='')
 for(i in 1:length(diffGenesUnq)){
  out = paste(out, rownames(exp)[diffGenesUnq[i]], '\t', round(sum(diffGenes == diffGenesUnq[i])/actualIters, 3), '\n', sep='')
 }

 # output split-size effect
 out2 = paste(out2, ncol(exp)-ntest, '\t', actualIters, '\t', myNumFun(result[, 'acc'], mean), '\t', myNumFun(result[, 'acc'], sd), '\t', myNumFun(result[, 'sens'], mean), '\t', myNumFun(result[, 'sens'], sd), '\t', myNumFun(result[, 'spec'], mean), '\t', myNumFun(result[, 'spec'], sd), '\t', myNumFun(result[, 'ppv'], mean), '\t', myNumFun(result[, 'ppv'], sd), 
'\t', myNumFun(result[, 'npv'], mean), '\t', myNumFun(result[, 'npv'], sd), '\t', length(diffGenesUnq), '\n', sep='')
} # end for g

cat(out, out2, sep='')

traceback() 的输出:

20: stop("Model is empty!")19: predict.svm(ret, xhold, decision.values = TRUE)18: predict(ret, xhold, decision.values = TRUE)17: na.action(predict(ret, xhold, decision.values = TRUE))16: svm.default(cost = 0.1, kernel = "linear", type = "C-classification", ...15: svm(cost = 0.1, kernel = "linear", type = "C-classification", ...14: do.call("svm", args = ll)13: function (X, y, f, learnind, probability, models = FALSE, ...) ...12: function (X, y, f, learnind, probability, models = FALSE, ...) ...11: do.call(classifier, args = c(list(X = X, y = y, learnind = learnmatrix[i, ...10: classification(X = c(83.5832768669369, 83.146333099001, 94.253534443549, ...9: classification(X = c(83.5832768669369, 83.146333099001, 94.253534443549, ...8: do.call("classification", args = c(list(X = Xi, y = yi, learningsets = lsi, ...7: tune(grids = list(cost = c(0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50...6: tune(grids = list(cost = c(0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50...5: do.call("tune", args = c(tuninglist, ll))4: classification(X, y = as.numeric(y) - 1, learningsets = learningsets, ...3: classification(X, y = as.numeric(y) - 1, learningsets = learningsets, ...2: classification(t(exp), factor(classes), learningsets = lsets, ...1: classification(t(exp), factor(classes), learningsets = lsets, ...

Answer 1

CMA 包的维护者立即回复了我发送的有关此问题的消息。

CMA 通过在训练集内的 k 倍 CV 步骤(默认 k=3)中测试不同的参数值来调整从训练集生成的分类器。对于较小的训练集大小，如果仅对一个类的观察进行子集化，则此内部循环可能会失败。减少发生这种情况的机会的两种方法是执行 2 倍内部 CV，并指定分层采样，这两种方法都需要通过 CMA 的 tune() 单独调用调整步骤并使用classification() 中的输出。

在我发布的代码中，从classification()内部调用调优，这不允许分层采样或2倍CV。然而，对于分层采样和 2 倍 CV 单独调用 tune() 对我的情况没有帮助。这并不奇怪，因为对于小型训练集，CMA 会遇到只有一个类别的成员集的情况。

我希望当一个学习集遇到这样的问题时，CMA 不会突然结束一切，而是继续处理剩余的学习集。如果在遇到此问题时，CMA 能够为内部 k 倍 CV 步骤尝试不同的 k 值，那就太好了。

[2 月 14 日编辑] CMA 的 CV 学习集生成不会检查训练集中是否存在两个类别的足够成员。因此，以下替换原始帖子中的部分代码应该可以使事情正常工作:

numInnerFold = 3 # k for the k-fold inner validation called through tune()
# generate learning-sets with 2*niter members in case some have to be removed
lsets <- GenerateLearningsets(n=ncol(exp), y=classes, method=c('MCCV'), niter=2*niter, ntrain=ncol(exp)-ntest)
temp <- lsets@learnmatrix
for(i in 1:(2*niter)){
 unq <- unique(classes[lsets@learnmatrix[i, ]])
 if((2 > length(unique(classes[lsets@learnmatrix[i, ]])))
    | (numInnerFold > sum(classes[lsets@learnmatrix[i, ]] == yesPredVal))
    | (numInnerFold > sum(classes[lsets@learnmatrix[i, ]] != yesPredVal))){
  # cat('removed set', i,'\n')
  temp <- lsets@learnmatrix[-i, ]
 }
}
lsets@learnmatrix <- temp[1:niter, ]
lsets@iter <- niter

# genes in classifiers
svmGenes <- GeneSelection(t(exp), classes, learningsets=lsets, method=diffTest)
svmTune <- tune(t(exp), factor(classes), learningsets=lsets, genesel=svmGenes, classifier=svmCMA, nbgene=diffGeneNum, grids=list(cost=svmCost), strat=T, fold=numInnerFold)
# actual prediction work
svm <- classification(t(exp), factor(classes), learningsets=lsets, genesel=svmGenes, classifier=svmCMA, nbgene=diffGeneNum, tuneres=svmTune)