1.  proxy

2.  larger, smaller, larger

3.  squared error objective function

4.

library(lme4) 
library(partykit)
data(InstEval) 
ie <- InstEval 
ie <- ie[,-(1:2)] 
for(j in 1:ncol(ie)) print(class(ie[,j]))
ctout <- ctree(y ~ .,data=ie) 
pred <- predict(ctout,data.frame(studage='4',lectage='1',service='1',dept='3'))  
print(pred)  # 3.361668

5.

library(lme4) 
data(InstEval) 
ie <- InstEval 

ie1 <- ie[,c(1,2,7)] 
library(rectools)
ud <- formUserData(ie1) 
invisible(embs <- sapply(ud,function(oneusr) mean(oneusr$ratings))) 
ie_emb <- ie[,-2] 
ie_emb$s <- embs[ie_emb$s] 

print(ie_emb[1,])  # 3.75