Feature selection by lasso and cross validation of model with low sample number I have a set of RNA-Seq data with 20 samples (so ~14000 features and 20 observations), of which I have 3 groups with 3,3 and 4 samples respectively and other just scattered around which I will group them into the 4th "others" group. If I wish to do a supervised feature selection, is lasso a good option?
And if lasso is good enough (r package glmnet always gives warning when there is less than 8 samples in one group) how should I determine the lambda and what cross-validation method should I use? I usually use k-fold cross validation through cv.glmnet() function in glmnet and use the suggested lambda value, but it seems like k-fold cross validation is out of the picture with this number of samples.
 A: The limited feature selection provided by LASSO (particularly with so few members of each class, a handful of features at most) would be unlikely to be very useful. The particular features selected would certainly be highly dependent on your particular data sample. Generalization to further cases could be poor.
You should instead take advantage of the many biological correlations among gene-expression values, within each of your classes, to find sets of genes whose expression levels best distinguish among the classes. There has been extensive work in bioinformatics to develop tools for that type of analysis, many of which are available through the Bioconductor website.
In particular, the geNetClassifier seems well suited to your work. It identifies genes that best distinguish among pre-defined classes (and thus represents supervised learning), returns a support-vector-machine multi-class classifier with estimates of discrimination power and generalizability, and displays a network of interactions and co-expressions that illustrate how the selected sets of genes distinguish among the classes. Although you only have 20 samples, the examples in the vignette for the package were based on only 60 samples, so there might be some hope of nevertheless getting useful results (if only to guide future work in this direction).
