1.

CFexact <- function(covsRatData,ratColName,qeFtn)
{
   covsRatData[,ratColName] <- as.factor(covsRatData[,ratColName])
   qeout <- qeFtn(covsRatData,ratColName,holdout=NULL)
   res <- qeout
   class(res) <- c('qeCFexact',class(qeout))
   res
}

predict.qeCFexact <- function(obj,newx) 
{
   class(obj) <- class(obj)[2]
   predout <- predict(obj,newx)
   predout$probs
}

2.  

NOTE:  Instead of a straightforward and efficient loop, two groups
searched the Web for a matrix-power package, and used it.  I gave full
credit for this, but please note that it is very inefficient, since it
does not use the value of one power as a basis to compute the next.

invViaPowers <- function(m,s) 
{
   nr <- nrow(m)
   i <- diag(nr)
   im <- i - m
   frb <- norm(im,'F')
   if (frb >= 1) return(NA)
   tot <- i
   prd <- im
   for (j in 1:10) {
      tot <- tot + prd
      prd <- prd %*% im
   }
   tot
}

m <- rbind(c(1,0.5),c(0.5,1)) 
invViaPowers(m,6) 
          [,1]      [,2]
# [1,]  1.328125 -0.656250
# [2,] -0.656250  1.328125
invViaPowers(m,6) %*% m 
#           [,1]      [,2]
# [1,] 1.0000000 0.0078125
# [2,] 0.0078125 1.0000000