## Sunday, August 23, 2015

### Predicting Titanic deaths on Kaggle IV: random forest revisited

On July 19th I used randomForest to predict the deaths on Titanic in the Kaggle competition. Subsequently I found that both bagging and boosting gave better predictions than randomForest. This I found somewhat unsatisfactory, hence I am now revisiting randomForest. To my disappointment this does not result in predictions as good as bagging and boosting.
Note that all code is at the bottom of the post

### Data

Data has not changed very much.

### Age

Since ipred package has a nice function for obtaining error using cross-validation, getting better predictions for Age when not in the data is the first adaptation. The model parameters to be optimized are mtry and nodesize. The plot shows that mtry=5 and nodesize=4 should give the best predictions.

Using these settings, the following predicted vs observed ages are obtained. I am not really impressed.

### Survival model 1

#### Model building 1

Having complete data, the next step is using cross-validation to select nodesize and mtry for the survival model. The following predictive capability was observed. Note that the error in these models is a bit larger than observed previously with bagging and boosting. However, observing that, does not suggest a remedy. It was chosen to use nodesize=3 mtry=7.

#### Evaluation Model 1

There are a number of ways to have randomForest give predictions. One can just ask for the categories, or the probability of a category. At this point I am looking at those probabilities, since I think the model might be improved. For this improvement, I do need to understand what is happening. Using the model, the following out of bag probabilities per category are found (pp[,1] is the probability of category 0). This is not ideal. Ideally most of the probabilities are close to 0 and 1. But here there are quite a number where this is not the case. Especially category 1 is not easily found and quite a few of the category 1 are seen as category 0. Hence the question becomes if it is possible to get better defined categories. As a first step, I will try to optimize the point where the cut is made between the two categories.

The plot below shows the number of correct predictions as function of the cut off point. It shows that the whole center region is a possible cut off, except near 0.4. The value 0.5 is not optimal.

#### Examination of cut of point

After making this plot I wondered if this shape would be same for other settings of nodesize and mtry.  Since I have a distinct feeling it is all dependent on the luck of the draw, it is repeated a number of times for each setting. Based on this I have chosen that a cut off of 0.55 is appropriate for a a wider range of settings. The best out of box predictions seem to happen with a higher value for mtry and a low value for nodesize. Thinking back on the density plot, it would seem that high nodesize and low mtry has low probabilities in the center region. However, the price for that is quite some errors in out of bag predictions.

### Survival Model 2

#### Model Building 2

Using the cut off of 0.55, again cross validation to select model parameters mtry and nodesize. Again each setting is tried a few times to get an idea of variability of prediction quality. Based on these settings I have chosen nodesize=6 and mtry=6.

#### Submission

Your submission scored 0.75. Not really as much as I had hoped for.

### Code

Note that the code has been reformatted and cleaned after pasting in the blogging application. This should not have caused any coding errors.
# preparation and data reading section
library(randomForest)
library(lattice)
# has cross validation
library(ipred)

train\$status <- 'train'
test\$status <- 'test'
test\$Survived <- NA
tt <- rbind(test,train)

# generate variables
tt\$Pclass <- factor(tt\$Pclass)
tt\$Survived <- factor(tt\$Survived)
tt\$age <- tt\$Age
tt\$age[is.na(tt\$age)] <- 35
tt\$age <- cut(tt\$age,c(0,2,5,9,12,15,21,55,65,100))
tt\$Title <- sapply(tt\$Name,function(x) strsplit(as.character(x),'[.,]')[[1]][2])
tt\$Title <- gsub(' ','',tt\$Title)
tt\$Title[tt\$Title %in% c('Capt','Col','Don','Sir','Jonkheer','Major')] <- 'Mr'
tt\$Title <- factor(tt\$Title)
tt\$A <- factor(grepl('A',tt\$Cabin))
tt\$B <- factor(grepl('B',tt\$Cabin))
tt\$C <- factor(grepl('C',tt\$Cabin))
tt\$D <- factor(grepl('D',tt\$Cabin))
tt\$E <- factor(grepl('E',tt\$Cabin))
tt\$F <- factor(grepl('F',tt\$Cabin))
tt\$ncabin <- nchar(as.character(tt\$Cabin))
tt\$PC <- factor(grepl('PC',tt\$Ticket))
tt\$STON <- factor(grepl('STON',tt\$Ticket))
tt\$cn <- as.numeric(gsub('[[:space:][:alpha:]]','',tt\$Cabin))
tt\$oe <- factor(ifelse(!is.na(tt\$cn),tt\$cn%%2,-1))
tt\$Fare[is.na(tt\$Fare)]<- median(tt\$Fare,na.rm=TRUE)
#end of preparation and data reading

# age section
# get an age without missings
forage <- tt[!is.na(tt\$Age) & tt\$status=='train',names(tt) %in%
c('Age','Sex','Pclass','SibSP',
'Parch','Fare','Title','Embarked','A','B','C','D','E','F',
'ncabin','PC','STON','oe')]

totest <- expand.grid(mtry=4:7,nodesize=3:6)

la <- lapply(1:nrow(totest),function(ii) {
ee <-    errorest(Age ~.,
mtry=totest\$mtry[ii],
nodesize=totest\$nodesize[ii],
model=randomForest,
data=forage)
cc <- c(mtry=totest\$mtry[ii],nodesize=totest\$nodesize[ii],error=ee\$error)
print(cc)
cc
})

sla <- do.call(rbind,la)
sla <- as.data.frame(sla)
xyplot(error ~ mtry, groups= nodesize, data=sla,auto.key=TRUE,type='l')
# chosen 5,4
rfa1 <- randomForest(Age ~ .,
data=forage,
ntree=1000,
mtry=5,
nodesize=4)
plot(tt\$Age,predict(rfa1,tt))
abline(a=0,b=1,col='red')
tt\$AGE <- tt\$Age
tt\$AGE[is.na(tt\$AGE)] <- predict(rfa1,tt[is.na(tt\$AGE),])
tt\$age <- cut(tt\$AGE,c(0,2,5,9,12,15,21,55,65,100))
# end of age section

#final data section
train <- tt[tt\$status=='train',]
test <- tt[tt\$status=='test',]
#end of final data section

#model selection 1
forSurf <- train[,names(train) %in%
c('Survived','age','AGE','Sex','Pclass','SibSP',
'Parch','Fare','Title','Embarked','A','B','C','D','E','F',
'ncabin','PC','STON','oe')]

# rfx <- randomForest(Survived ~.,data=forSurf)
totest <- expand.grid(mtry=6:9,nodesize=3:7)

la <- lapply(1:nrow(totest),function(ii) {
ee <-    errorest(Survived ~.,
mtry=totest\$mtry[ii],
nodesize=totest\$nodesize[ii],
model=randomForest,
data=forSurf,
ntree=1000,
est.para=control.errorest(k=20)
)
cc <- c(mtry=totest\$mtry[ii],
nodesize=totest\$nodesize[ii],
sampsize=totest\$sampsize[ii],
error=ee\$error)
print(cc)
cc
})
sla <- do.call(rbind,la)
sla <- as.data.frame(sla)
xyplot(error ~ mtry, groups= nodesize, data=sla,auto.key=TRUE,type='l')
#end of model selection 1

#model evaluation section 1a
rfx <- randomForest(Survived ~.,data=forSurf,nodesize=3,mtry=7,ntree=1000)
pp <- predict(rfx,type='prob')
cuts <- seq(.20,.7,.001)
plot(y=sapply(cuts,function(cc){
decide=factor(as.numeric(pp[,1]<cc))
sum(decide==forSurf\$Survived)
}),
x=cuts)
#end  of model evaluation section 1a

cuts <- seq(.25,.65,.001)
# model evaluation 1b
eval2 <- expand.grid(nodesize=seq(4,100,8),mtry=seq(2,8,2),count=1:10)
sach <- lapply( 1:nrow(eval2),function(i) {
rfx <- randomForest(Survived ~.,
data=forSurf,
nodesize=eval2\$nodesize[i],
mtry=eval2\$mtry[i],
ntree=1000)
pp <- predict(rfx,type='prob')
nerr=sapply(cuts,function(cc){
decide=factor(as.numeric(pp[,1]<cc))
sum(decide==forSurf\$Survived)})
data.frame(
nerr=nerr,
cuts=cuts,
mtry=eval2\$mtry[i],
nodesize=eval2\$nodesize[i],
i=rep(i,length(cuts)))
})
sach <- do.call(rbind,sach)
xyplot(nerr ~ cuts | nodesize + mtry ,group=i, data=sach,auto.key=FALSE,type='l')
##############
# # chose cuts at .55
##############

#biased prediction
twpred <- function(object,newdata=NULL) {
preds <- predict(object,newdata,type='prob')
factor(as.numeric(preds[,1]<0.55),levels=c('0','1'))
}
totest2 <- expand.grid(mtry=seq(2,8,2),nodesize=seq(2,30,4),count=1:10)

la2 <- lapply(1:nrow(totest2),function(ii) {
ee <-    errorest(Survived ~.,
mtry=totest2\$mtry[ii],
nodesize=totest2\$nodesize[ii],
model=randomForest,
data=forSurf,
ntree=500,
predict=twpred,
est.para=control.errorest(k=10)
)
cc <- c(mtry=totest2\$mtry[ii],
nodesize=totest2\$nodesize[ii],
i=totest2\$count[ii],
error=ee\$error)
print(cc)
cc
})
sla2 <- do.call(rbind,la2)
sla2 <- as.data.frame(sla2)
xyplot(error ~ factor(mtry) | factor(nodesize),
groups= i, data=sla2,auto.key=FALSE,type='l')
##
#let select mtry=6, nodesize=6
rf2 <-randomForest(Survived ~ .,
data=forSurf,
replace=TRUE,
ntree=2000,
nodesize=6,
mtry=6)

pp <- predict(rf2,test)
out <- data.frame(
PassengerId=test\$PassengerId,
Survived=pp,row.names=NULL)
write.csv(x=out,
file='rf.16.aug.csv',
row.names=FALSE,
quote=FALSE)

# get a result

## Sunday, August 9, 2015

### Predicting Titanic deaths on Kaggle III: Bagging

This is the third post on prediction the deaths. The first one used randomforest, the second boosting (gbm). The aim of the third post was to use bagging. In contrast to the former posts I abandoned dplyr in this post. It gave some now you see now you don't errors.

### Data

The data is supposed to be the same as previous.
library(ipred)
library(rpart)
library(lattice)

train\$status <- 'train'
test\$status <- 'test'
test\$Survived <- NA
tt <- rbind(test,train)

# generate variables
tt\$Pclass <- factor(tt\$Pclass)
tt\$Survived <- factor(tt\$Survived)
tt\$age <- tt\$Age
tt\$age[is.na(tt\$age)] <- 35
tt\$age <- cut(tt\$age,c(0,2,5,9,12,15,21,55,65,100))
tt\$Title <- sapply(tt\$Name,function(x) strsplit(as.character(x),'[.,]')[[1]][2])
tt\$Title <- gsub(' ','',tt\$Title)
tt\$Title[tt\$Title %in% c('Capt','Col','Don','Sir','Jonkheer','Major')] <- 'Mr'
tt\$Title <- factor(tt\$Title)
tt\$A <- factor(grepl('A',tt\$Cabin))
tt\$B <- factor(grepl('B',tt\$Cabin))
tt\$C <- factor(grepl('C',tt\$Cabin))
tt\$D <- factor(grepl('D',tt\$Cabin))
tt\$E <- factor(grepl('E',tt\$Cabin))
tt\$F <- factor(grepl('F',tt\$Cabin))
tt\$ncabin <- nchar(as.character(tt\$Cabin))
tt\$PC <- factor(grepl('PC',tt\$Ticket))
tt\$STON <- factor(grepl('STON',tt\$Ticket))
tt\$cn <- as.numeric(gsub('[[:space:][:alpha:]]','',tt\$Cabin))
tt\$oe <- factor(ifelse(!is.na(tt\$cn),tt\$cn%%2,-1))
tt\$Fare[is.na(tt\$Fare)]<- median(tt\$Fare,na.rm=TRUE)

### Age

The first step is again to predict the missing ages. Even though we have I have all data available in one data.frame, I still think the correct approach is to create the age model using only the training data. Note that I am not too impressed with the age model. Perhaps this should also be optimized.
forage <- tt[!is.na(tt\$Age) & tt\$status=='train',names(tt) %in%
c('Age','Sex','Pclass','SibSP',
'Parch','Fare','Title','Embarked','A','B','C','D','E','F',
'ncabin','PC','STON','oe')]

ipbag1 <- bagging(Age ~.,data=forage)
ipbag1
Bagging regression trees with 25 bootstrap replications

Call: bagging.data.frame(formula = Age ~ ., data = forage)
plot(tt\$Age~predict(ipbag1,tt))
tt\$AGE <- tt\$Age
tt\$AGE[is.na(tt\$AGE)] <- predict(ipbag1,tt[is.na(tt\$AGE),])

### Selecting the survival model

ipred, the package in which bagging resides, comes with a nice general purpose cross validation utility. In the end, I decided the two parameters to be optimized are ns; the size of the bags and minsplit: the minimum number of observations that must exist in a node in order for a split to be attempted. Nbagg, the number of bootstrap evaluations, just needs to be big enough. Regarding nbagg, I have the feeling that this particular problem, with relatively few records, it may be needed to have relatively high nbagg in order to have reproducible models.
di1 <- subset(titanic,select=c(
age,SibSp,Parch,Fare,Sex,Pclass,
Title,Embarked,A,B,C,D,E,F,ncabin,PC,STON,oe,AGE,Survived))
dso <- expand.grid(ns=seq(100,300,25),nbagg=c(500),minsplit=1:6)
la <- lapply(1:nrow(dso),function(ii) {
ee <-    errorest(Survived ~ .,
ns=dso\$ns[ii],
control=rpart.control(minsplit=dso\$minsplit[ii], cp=0,
xval=0,maxsurrogate=0),
nbagg=dso\$nbagg[ii],
model=bagging,
data=di1,
est.para=control.errorest(k=20)
)
cc <- c(ns=dso\$ns[ii],minsplit=dso\$minsplit[ii],nbagg=dso\$nbagg[ii],error=ee\$error)
print(cc)
cc
})
las <- do.call(rbind,la)
las <- as.data.frame(las)
xyplot(error ~ ns, groups= minsplit, data=las,auto.key=TRUE,type='l')

#### Predictions

Based on the plot I have chosen for ns=275 and minsplit=5. But, to be honest, in a previous run I had chosen ns=150 and minsplit=2. Obviously from this plot a silly choice. But, given the high variability in this plot between parameters which are relatively similar and the totally different result, I actually think there is relatively much noise in the validation. Thus what is actually seen is that there is relatively little difference between the settings.
Having said that, these new settings got me just over 0.8 in the Kaggle score, while the previous settings were just below.
bagmod <- bagging(Survived ~.,ns=275,nbagg=500,
control=rpart.control(minsplit=5, cp=0, xval=0,maxsurrogate=0),
data=di1)

pp <- predict(bagmod,test)

out <- data.frame(
PassengerId=test\$PassengerId,
Survived=pp,row.names=NULL)
write.csv(x=out,
file='bag8aug.csv',
row.names=FALSE,
quote=FALSE)