## Sunday, July 26, 2015

### Predicting Titanic deaths on Kaggle II: gbm

Following my previous post I have decided to try and use a different method: generalized boosted regression models (gbm). I have read the background in Elements of Statistical Learning and arthur charpentier's nice post on it. This data is a nice occasion to get my hands dirty.

#### Data

Data as before. However, I have added some more variables. In addition, during the analysis it appeared that gbm does not like to have logical variables in the x-variables. One missing value of Fare in the test set gets the median value in order to avoid having missing values in the data. I must say I like using dplyr for this data handing. It allows me to use the same code for training and test with minimum effort.
library(dplyr)
library(gbm)

set.seed(4321)
mutate(.,Pclass=factor(Pclass),
Survived=factor(Survived),
age=ifelse(is.na(Age),35,Age),
age = cut(age,c(0,2,5,9,12,15,21,55,65,100)),
Title=sapply(Name,function(x) strsplit(as.character(x),'[.,]')[[1]][2]),
Title=gsub(' ','',Title),
Title =ifelse(Title %in% c('Capt','Col','Don','Sir','Jonkheer','Major'),'Mr',Title),
Title = factor(Title),
A=factor(grepl('A',Cabin)),
B=factor(grepl('B',Cabin)),
C=factor(grepl('C',Cabin)),
D=factor(grepl('D',Cabin)),
E=factor(grepl('E',Cabin)),
F=factor(grepl('F',Cabin)),
ncabin=nchar(as.character(Cabin)),
PC=factor(grepl('PC',Ticket)),
STON=factor(grepl('STON',Ticket)),
cn = as.numeric(gsub('[[:space:][:alpha:]]','',Cabin)),
oe=factor(ifelse(!is.na(cn),cn%%2,-1)),
train = sample(c(TRUE,FALSE),
size=891,
replace=TRUE,
prob=c(.9,.1)   ) )

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

### Age

Age has missing values, thus the first task is to fill those. Since gbm is the method used for the main analysis, I will be used it for age too. This has the added advantage that I can exercise with both a numerical and a categorical variable as response.
One of the things with boosting is that it opens itself to over fitting. Boosting consists of adding trees which are structured to improve fit. At some point the trees will just start boost the noise rather than the structure. Gbm comes with a cross validation (cv) option, which is the preferred way to get the predictive qualities of models, and cv is used to determine the optimum number of trees. But, there is catch, it throws an error if there are variables in the data.frame which are not used in the model. Hence in the code below first the data is selected, and subsequently the model run.
The model parameters, interaction.depth=4, shrinkage=0.0005 come from a bit of experimenting. n.trees has to be high enough that it is clear the optimum number of trees is lower than the number estimated. It seems n.cores=2 works under both windows and linux.
forage <- filter(titanic,!is.na(titanic\$Age)) %>%
select(.,Age,SibSp,Parch,Fare,Sex,Pclass,Title,Embarked,A,B,C,D,E,F,ncabin,PC,STON,oe)

rfa1 <- gbm(Age ~ .,
data=forage,
interaction.depth=4,
cv.folds=10,
n.trees=8000,
shrinkage=0.0005,
n.cores=2)

gbm.perf(rfa1)
Using cv method...
[1] 6824
It is time here to confess that I have been working on this over several sessions. It appears that when I created the code, 7118 trees were optimum, while I stored that data for a session with 6824 trees. Thus is the way of these methods, unlike traditional statistical methods, they have a different result any time. But, as can be seen from the plot, the difference should be minimal.
titanic\$AGE<- titanic\$Age
titanic\$AGE[is.na(titanic\$AGE)] <- predict(rfa1,titanic,n.trees=7118)[is.na(titanic\$Age)]
test\$AGE<- test\$Age
test\$AGE[is.na(test\$AGE)] <- predict(rfa1,test,n.trees=7118)[is.na(test\$Age)]

### Survival

During the calculations I learned that the response should be a float containing 0 and 1. With two categories there are various distributions to be used: bernoulli, huberized and adaboost. Using the 10% test data I had set apart, it seemed adaboost worked best for these data.
gb1 <- filter(titanic,train) %>%
select(.,age,SibSp,Parch,Fare,Sex,Pclass,
Title,Embarked,A,B,C,D,E,F,ncabin,PC,STON,oe,AGE,Survived)%>%
mutate(Survived=c(0,1)[Survived]) # not integer or factor but float
#table(gb1\$Survived)
gb1m <-      gbm(Survived ~ .,
cv.folds=11,
n.cores=2,
interaction.depth=5,
shrinkage = 0.0005,
data=gb1,
n.trees=10000)
gbm.perf(gb1m)
Using cv method...
[1] 6355

In my code I have used 6000 trees.
One thing about gbm is that it does not respond with categories. It is a proportion answers for either category.
preds <- predict(gb1m,titanic,
n.trees=6000,type='response')
density(preds) %>% plot
Thus there is a need or opportunity to determine the cut off point. For this my test set comes in somewhat handy.
preds2<- preds[!titanic\$train]
target <- c(0,1)[titanic\$Survived[!titanic\$train]]
sapply(seq(.3,.7,.01),function(step)
c(step,sum(ifelse(preds2<step,0,1)!=target)))
[,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10] [,11] [,12]
[1,]  0.3  0.31  0.32  0.33  0.34  0.35  0.36  0.37  0.38  0.39   0.4  0.41
[2,] 17.0 17.00 17.00 17.00 17.00 17.00 17.00 17.00 18.00 17.00  16.0 16.00
[,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
[1,]  0.42  0.43  0.44  0.45  0.46  0.47  0.48  0.49   0.5  0.51  0.52  0.53
[2,] 16.00 16.00 15.00 14.00 14.00 14.00 13.00 15.00  15.0 15.00 16.00 16.00
[,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36]
[1,]  0.54  0.55  0.56  0.57  0.58  0.59   0.6  0.61  0.62  0.63  0.64  0.65
[2,] 16.00 17.00 17.00 17.00 17.00 18.00  18.0 18.00 18.00 19.00 20.00 20.00
[,37] [,38] [,39] [,40] [,41]
[1,]  0.66  0.67  0.68  0.69   0.7
[2,] 20.00 21.00 21.00 21.00  21.0
It is a bit messy output, but at 0.48 the least errors are found.

### Predictions

This is fairly straightforward. I am not unhappy to report an improvement, bringing me from tail to middle region of the peloton.
pp <- predict(gb1m,test,n.trees=6000,type='response')
pp <- ifelse(pp<0.48,0,1)
out <- data.frame(
PassengerId=test\$PassengerId,
Survived=pp,row.names=NULL)
write.csv(x=out,
file='gbm.csv',
row.names=FALSE,
quote=FALSE)

## Sunday, July 19, 2015

### Predicting Titanic deaths on Kaggle

Kaggle has a competition to predict who will die on the famous Titanic 'Machine Learning from Disaster''. It is placed as knowledge competition. Just up there to learn. I am late to the party, it has been been for 1 1/2 year, to end by end 2015. It is a small data set, hence interesting to learn from. It is also a competition with a number of entries which have perfect predictions.
Just for fun, I have been trying to see what I would achieve with simple attempt with randomforest. For those in the competition, this randomforest got me 0.74163, placing me 2781 out of 3064 entries. An acceptable spot, since this is using off the shelf approach. An improvement may follow in a subsequent post.

#### Data

Data downloaded from Kaggle. It is real world data, hence has the odd missing (in passenger age) and a number of columns with messy data, which might be employed to create additional variables. For the purpose of validation about 90% of the data gets flagged to be training set. test will be the test, set, results of which to be passed back to Kaggle.
PassengerId Survived Pclass                                                Name
1           1        0      3                             Braund, Mr. Owen Harris
2           2        1      1 Cumings, Mrs. John Bradley (Florence Briggs Thayer)
3           3        1      3                              Heikkinen, Miss. Laina
4           4        1      1        Futrelle, Mrs. Jacques Heath (Lily May Peel)
5           5        0      3                            Allen, Mr. William Henry
6           6        0      3                                    Moran, Mr. James
Sex Age SibSp Parch           Ticket    Fare Cabin Embarked
1   male  22     1     0        A/5 21171  7.2500              S
2 female  38     1     0         PC 17599 71.2833   C85        C
3 female  26     0     0 STON/O2. 3101282  7.9250              S
4 female  35     1     0           113803 53.1000  C123        S
5   male  35     0     0           373450  8.0500              S
6   male  NA     0     0           330877  8.4583              Q
library(dplyr)
library(randomForest)
library(lattice)
options(width=85)

mutate(.,Pclass=factor(Pclass),
Survived=factor(Survived),
age=ifelse(is.na(Age),35,Age),
age = cut(age,c(0,2,5,9,12,15,21,55,65,100)),
A=grepl('A',Cabin),
B=grepl('B',Cabin),
C=grepl('C',Cabin),
D=grepl('D',Cabin),
cn = as.numeric(gsub('[[:space:][:alpha:]]','',Cabin)),
oe=factor(ifelse(!is.na(cn),cn%%2,-1)),
train = sample(c(TRUE,FALSE),
size=891,
replace=TRUE,
prob=c(.9,.1)   ) )
mutate(.,Pclass=factor(Pclass),
age=ifelse(is.na(Age),35,Age),
age = cut(age,c(0,2,5,9,12,15,21,55,65,100)),
A=grepl('A',Cabin),
B=grepl('B',Cabin),
C=grepl('C',Cabin),
D=grepl('D',Cabin),
cn = as.numeric(gsub('[[:space:][:alpha:]]','',Cabin)),
oe=factor(ifelse(!is.na(cn),cn%%2,-1)),
Embarked=factor(Embarked,levels=levels(titanic\$Embarked))
)
test\$Fare[is.na(test\$Fare)]<- median(titanic\$Fare)
Age has missing values, hence the first step is to fill those in. In the code above, an age factor has been made, where missings are imputed the largest category.

#### Model building

A simple prediction using randomForest.
rf1 <- randomForest(Survived ~
Sex+Pclass + SibSp +
Parch + Fare +
Embarked + age +
A+B+C+D +oe,
data=titanic,
subset=train,
replace=FALSE,
ntree=1000)
Call:
randomForest(formula = Survived ~ Sex + Pclass + SibSp + Parch +      Fare + Embarked + age + A + B + C + D + oe, data = titanic,      replace = FALSE, ntree = 1000, subset = train)
Type of random forest: classification
Number of trees: 1000
No. of variables tried at each split: 3

OOB estimate of  error rate: 16.94%
Confusion matrix:
0   1 class.error
0 454  40  0.08097166
1  95 208  0.31353135

This shows some bias in the predictions. Class one gets predicted as class 0 far too often. Hence I will optimize not only the normal variables nodesize (Minimum size of terminal nodes) and mtry (Number of variables randomly sampled as candidates at each split) but also classwt (Priors of the classes).

titanic\$pred <- predict(rf1,titanic)
with(titanic[!titanic\$train,],sum(pred!=Survived)/length(pred))

mygrid <- expand.grid(nodesize=c(2,4,6),
mtry=2:5,
wt=seq(.5,.7,.05))
sa <- sapply(1:nrow(mygrid), function(i) {
rfx <- randomForest(Survived ~
Sex+Pclass + SibSp +
Parch + Fare +
Embarked + age +
A+B+C+D +oe,
data=titanic,
subset=train,
replace=TRUE,
ntree=4000,
nodesize=mygrid\$nodesize[i],
mtry=mygrid\$mtry[i],
classwt=c(1-mygrid\$wt[i],mygrid\$wt[i]))
preds <- predict(rfx,titanic[!titanic\$train,])
nwrong <- sum(preds!=titanic\$Survived[!titanic\$train])
c(nodesize=mygrid\$nodesize[i],mtry=mygrid\$mtry[i],wt=mygrid\$wt[i],pw=nwrong/length(preds))
})
tsa <- as.data.frame(t(sa))
xyplot(pw ~ wt | mtry,group=factor(nodesize), data=tsa,auto.key=TRUE,type='l')

What is less visible from this plot is the amount of variation I had in the results. One prediction better or worse really makes a difference in the figure. This is the reason I have increased the number of trees in the model.

#### Final predictions

Using the best settings from above, gets you to the bottom of the ranking. The script makes the model, writes predictions in the format required by kaggle.
rf2 <- randomForest(Survived ~
Sex+Pclass + SibSp +
Parch + Fare +
Embarked + age +
A+B+C+D +oe,
data=titanic,
replace=TRUE,
ntree=5000,
nodesize=4,
mtry=3,
classwt=c(1-.6,.6))

pp <- predict(rf2,test)
out <- data.frame(
PassengerId=test\$PassengerId,
Survived=pp,row.names=NULL)
write.csv(x=out,
file='rf1.csv',
row.names=FALSE,
quote=FALSE)

## Sunday, July 5, 2015

### More on causes of death in Netherlands over the years

Last week I had a post 'Deaths in the Netherlands by cause and age'. During creation of that post I made one plot which I had not shown. It shows something odd. There is a vertical striping. Hence mortality varies by year across age.
To examine this phenomenon further here is a plot of some underlying causes. I would say the striping is present for at least three categories; "Diseases of the circulatory system", "Diseases of the respiratory organs" and "Sympt., Abnormal clinical Observations". This is odd, since these do not seem to be contagious. I suspect therefore that something like harsh weather (heat or cold) makes life more difficult, but does not get to be the final cause in the administration.
In addition there is something which I did not realize before regarding "Mental and behavioral disorders". They are age related. But it also seems that somewhere in the nineties of last century they became acceptable to register. And suddenly they are present, across several age categories.
This plot, same data, differently organized, shows that the years with these causes are similar, especially "Diseases of the circulatory system" and "Diseases of the respiratory organs"

### Can it statistically be seen?

It is very nice that I can see that, but how about measuring it? Hence for age 90 to 95, after detrending, correlation between the two most visually correlated causes of death.
Pearson's product-moment correlation

data:  xx\$`Diseases of the respiratory organs` and xx\$`Diseases of the circulatory system`
t = 2.4997, df = 62, p-value = 0.01509
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.06133681 0.51042863
sample estimates:
cor
0.302584

### Code

library(dplyr)
library(ggplot2)
txtlines <- grep('Centraal',txtlines,value=TRUE,invert=TRUE)
#txtlines[1:5]
#cat(txtlines[4])
col.names=c('Causes','Causes2','Age','year','aantal','count'),
na.strings='-',text=txtlines[3:length(txtlines)]) %>%
select(.,-aantal,-Causes2)
transcauses <- c(
"Infectious and parasitic diseases",
"Diseases of skin and subcutaneous",
"Diseases musculoskeletal system and connective ",
"Diseases of the genitourinary system",
"Pregnancy, childbirth",
"Conditions of perinatal period",
"Congenital abnormalities",
"Sympt., Abnormal clinical Observations",
"External causes of death",
"Neoplasms",
"Illness of blood, blood-forming organs",
"Endocrine, nutritional, metabolic illness",
"Mental and behavioral disorders",
"Diseases of the nervous system and sense organs",
"Diseases of the circulatory system",
"Diseases of the respiratory organs",
"Diseases of the digestive organs",
"Population",
"Total all causes of death")
#cc <-
cbind(transcauses,levels(r1\$Causes))
options(width=100)
levels(r1\$Causes) <- transcauses
levels(r1\$Age) <-
gsub('jaar','year',levels(r1\$Age)) %>%
gsub('tot','to',.) %>%
gsub('of ouder','+',.)
r1 <- mutate(r1,age=as.numeric(sub(' .*\$','',Age)))

Deaths <- filter(r1,Causes=='Total all causes of death') %>%
mutate(.,Total=count) %>%
select(.,-count,-Causes) %>%
merge(.,r1) %>%
filter(.,Causes %in% transcauses[18]) %>%
mutate(.,Population=count,
Percentage=100*Total/Population,
year = as.numeric(gsub('*','',year,fixed=TRUE))) %>%
select(.,-Causes,-count)

png('deathall.png')
v <- ggplot(Deaths[Deaths\$age>60,], aes( year,Age, fill = Percentage))
v + geom_raster() +
colours=c('white','black'))+
theme(legend.position="bottom")+
ggtitle('Total all causes of death')
dev.off()

v3 <- filter(r1,Causes %in% transcauses[18],
age>65) %>%
mutate(.,Population=count) %>%
select(.,-count,-Causes) %>%
merge(.,r1) %>%
filter(.,Causes %in% transcauses[c(8,15,9,10,13,16)]) %>%
mutate(.,Total=count,
Percentage=100*Total/Population,
year = as.numeric(gsub('*','',year,fixed=TRUE))) %>%
select(.,-count)
png('bycause.png')
ggplot(v3, aes( year,Age, fill = Percentage))+
geom_raster() +
colours=c('white','black'))+
theme(legend.position="bottom")+
facet_wrap( ~ Causes,nrow=3)
dev.off()

png('byage.png')
ggplot(v3[v3\$age>75,], aes( year,Causes, fill = Percentage))+
geom_raster() +
colours=c('white','black'))+
theme(legend.position="bottom")+
facet_wrap( ~ Age,nrow=3)
dev.off()

xx <- filter(r1,Causes %in% transcauses[18],
age==90) %>%
mutate(.,Population=count) %>%
select(.,-count,-Causes) %>%
merge(.,r1) %>%
filter(.,Causes %in% transcauses[c(8,15,9,16)]) %>%
mutate(.,Total=count,
Percentage=100*Total/Population,
year = as.numeric(gsub('*','',year,fixed=TRUE)),
Causes=factor(Causes)) %>%
select(.,-count,-Age,-age,-Population,-Total) %>%
reshape(.,direction='wide',timevar='Causes',idvar='year')

names(xx) <- gsub('Percentage.','',names(xx))
for (i in 2:ncol(xx)) xx[,i]<- xx[,i] - predict(loess(xx[,i] ~ year,data=xx))

cor.test(xx\$`Diseases of the respiratory organs`,
xx\$`Diseases of the circulatory system`)