random forest for large number of variables and predictions I have very large number of variables compared to samples they are measured on. The following is example data in R.
set.seed(123)

# matrix of X variable 
xmat <- matrix(sample(-1:1, 2000000, replace = TRUE), ncol = 10000)
colnames(xmat) <- paste ("M", 1:10000, sep ="")
rownames(xmat) <- paste("sample", 1:200, sep = "")
xmat[1:10,1:10] # print partial data 
         M1 M2 M3 M4 M5 M6 M7 M8 M9 M10
sample1  -1  1  0  1 -1  1  1  1  0   1
sample2  -1 -1  1  0  0  1 -1  0  1   0
sample3   1  1 -1 -1 -1  0  1  1  1  -1
sample4   1  1 -1  0 -1  1 -1  0 -1  -1
sample5  -1  1  0  1  0  1  0 -1  0   1
sample6   1  1 -1 -1  0 -1 -1  0 -1   0
sample7   1 -1 -1  1  1 -1  0  0  0  -1
sample8   1 -1  0 -1 -1  1  0  1  0   0
sample9   1  1  0  0  1  0  0 -1  0  -1
sample10  0  0  1  1 -1  0  0  1  1  -1

# y variable matrix 
set.seed(1234)
ymat <- matrix (c(rnorm(100, 50,20), rep(NA, 100)), ncol =1)

Here sample 1 to 100 have y value but 101 to 200 do not. I want use the random forest to predict the y values of the missing samples.
Here are my question - 
Can I use random forest to do so ? How ? Which r package (or any other software) would be best suited to my above needs?
Edits: Note:
Although I sampled values of X {1,0,-1} randomly, they are not random. They are correlated in different degree to each other or with y. 
 A: Using the vanilla implementation of Random Forest in R you would just do:
library(randomForest) # load random forest package

train_set = xmat[ymat==1,] # meaning you subset your xmat covariables to just
                           # include those which are labeled

rf_model = randomForest(y=ymat,x=xmat,ntree=500) # train random forest model

?randomForest # to understand the training funcion usage

plot(rf_model) # plot of error against number of trees grown

cor(rf_model$predicted,ymat) # usual Pearson correlation between observed training values and OOB predictions

imputation_set = xmat[ymat!=1,] # unlabeled data

imputation_prediction = predict(rf_model,imputation_set) # fill in values

You should definitely read about Random Forest before using them, they are relatively easy to understand and will help you a lot during this model building process.
Random Forest scales well on large and/or high dimensional data. If you really have a huge amount of covariables or training observations you should consider using the paralellized version which is much faster and memory efficient. Although only available for Linux.
A: I've only used random forests a couple of times with much fewer variables. Intuitively it seems to me that with 10,000 variables and a training set of only 100, you could run into trouble with noise variables. However, random forest seem to be incredibly robust and this paper, for example, suggests that the approach shouldn't be thrown off by unrelated variables as long as you have strong ones.
http://jmlr.org/papers/volume13/biau12a/biau12a.pdf
