Transcript Document

Labs: more data, models,
prediction, deciding with trees
Peter Fox
Data Analytics – ITWS-4963/ITWS-6965
Week 7a, March 10, 2015
1
Assignment 6 on Website
• Your term projects should fall within the scope of a data analytics
problem of the type you have worked with in class/ labs, or know of
yourself – the bigger the data the better. This means that the work must
go beyond just making lots of figures. You should develop the project to
indicate you are thinking of and exploring the relationships and
distributions within your data. Start with a hypothesis, think of a way to
model and use the hypothesis, find or collect the necessary data, and do
both preliminary analysis, detailed modeling and summary
(interpretation). Grad students must develop two types of models.
– Note: You do not have to come up with a positive result, i.e. disproving the hypothesis
is just as good.
• Introduction (2%)
•
•
•
•
•
Data Description (3%)
Analysis (5%)
Model Development (12%)
Conclusions and Discussion (3%)
Oral presentation (5%) (~5 mins)
2
Titanic – Bayes (from last week)
> data(Titanic)
> mdl <- naiveBayes(Survived ~ ., data =
Bayes Classifier for Discrete Predictors
Titanic) Naive
Call: naiveBayes.formula(formula = Survived ~ ., data = Titanic)
probabilities:
> mdl A-priori
Survived
No
Yes
0.676965 0.323035
Conditional probabilities:
Class
Survived
1st
2nd
3rd
Crew
No 0.08187919 0.11208054 0.35436242 0.45167785
Yes 0.28551336 0.16596343 0.25035162 0.29817159
Sex
Survived
Male Female
No 0.91543624 0.08456376
Yes 0.51617440 0.48382560
Age
3
Survived
Child
Adult
No 0.03489933 0.96510067
Try Lab6b_9_2014.R
Yes 0.08016878 0.91983122
Classification Bayes (last week)
• Retrieve the abalone.csv dataset
• Predicting the age of abalone from physical
measurements.
• Perform naivebayes classification to get
predictors for Age (Rings). Interpret.
• Compare to what you got from kknn (weighted
nearest neighbors) in class 4b
4
http://www.ugrad.stat.ubc.ca/R/library/mlb
ench/html/HouseVotes84.html
> require(mlbench)
> data(HouseVotes84)
> model <- naiveBayes(Class ~ ., data =
HouseVotes84)
> predict(model, HouseVotes84[1:10,-1])
[1] republican republican republican democrat
democrat democrat republican republican
republican
[10] democrat
Levels: democrat republican
5
House Votes 1984
> predict(model, HouseVotes84[1:10,-1], type = "raw")
democrat republican
[1,] 1.029209e-07 9.999999e-01
[2,] 5.820415e-08 9.999999e-01
[3,] 5.684937e-03 9.943151e-01
[4,] 9.985798e-01 1.420152e-03
[5,] 9.666720e-01 3.332802e-02
[6,] 8.121430e-01 1.878570e-01
[7,] 1.751512e-04 9.998248e-01
[8,] 8.300100e-06 9.999917e-01
[9,] 8.277705e-08 9.999999e-01
[10,] 1.000000e+00 5.029425e-11
6
House Votes 1984
> pred <- predict(model, HouseVotes84[,-1])
> table(pred, HouseVotes84$Class)
pred
democrat republican
democrat
238
13
republican
29
155
7
Hair, eye color
> data(HairEyeColor)
> mosaicplot(HairEyeColor)
> margin.table(HairEyeColor,3)
Sex
Male Female
279 313
> margin.table(HairEyeColor,c(1,3))
Sex
Hair Male Female
Black 56 52
Brown 143 143
Red 34 37
Blond 46 81
Construct a naïve Bayes classifier and test it!
8
Another example
> A = c(1, 2.5); B = c(5, 10); C = c(23, 34)
> D = c(45, 47); E = c(4, 17); F = c(18, 4)
> df <- data.frame(rbind(A,B,C,D,E,F))
> colnames(df) <- c("x","y")
> hc <- hclust(dist(df))
> plot(hc)
> df$cluster <- cutree(hc,k=2)
> plot(y~x,df,col=cluster)
# 2 clusters
9
See also
• Lab5a_ctree_1_2015.R
– Try clustergram instead
– Try hclust
• Lab3b_kmeans1_2015.R
– Try clustergram instead
– Try hclust
10
New dataset to work with trees
fitK <- rpart(Kyphosis ~ Age + Number + Start, method="class",
data=kyphosis)
printcp(fitK) # display the results
plotcp(fitK) # visualize cross-validation results
summary(fitK) # detailed summary of splits
# plot tree
plot(fitK, uniform=TRUE, main="Classification Tree for
Kyphosis")
text(fitK, use.n=TRUE, all=TRUE, cex=.8)
# create attractive postscript plot of tree
post(fitK, file = “kyphosistree.ps", title = "Classification Tree for
Kyphosis") # might need to convert to PDF (distill)
11
12
> pfitK<- prune(fitK, cp= fitK$cptable[which.min(fitK$cptable[,"xerror"]),"CP"])
> plot(pfitK, uniform=TRUE, main="Pruned Classification Tree for Kyphosis")
13
> text(pfitK, use.n=TRUE, all=TRUE, cex=.8)
> post(pfitK, file = “ptree.ps", title = "Pruned Classification Tree for Kyphosis”)
> fitK <- ctree(Kyphosis ~ Age + Number + Start, data=kyphosis)
> plot(fitK, main="Conditional Inference Tree for Kyphosis”)
14
> plot(fitK, main="Conditional Inference Tree for Kyphosis",type="simple")
15
Swiss - scatterplotMatrix
16
Hierarchical clustering
> dswiss <- dist(as.matrix(swiss))
> hs <- hclust(dswiss)
> plot(hs)
17
ctree
require(party)
swiss_ctree <- ctree(Fertility ~ Agriculture +
Education + Catholic, data = swiss)
plot(swiss_ctree)
18
How could you get this?
19
Rpart – recursive partitioning
require(rpart)
Swiss_rpart <- rpart(Fertility ~ Agriculture +
Education + Catholic, data = swiss)
plot(swiss_rpart) # try some different plot
options
text(swiss_rpart) # try some different text
options
# try other data
20
Rpart – recursive partitioning
Try this for “Rings” on the Abalone dataset
Try ctree – compare – we’ll discuss these
Friday
But if you do the ctree you may want to “try
pruning”
21
Mileage dataset.
# Regression Tree Example
require(rpart)
# build the tree
fitM <- rpart(Mileage~Price + Country + Reliability + Type,
method="anova", data=cu.summary)
printcp(fitM) # display the results
….
Root node error: 1354.6/60 = 22.576
n=60 (57 observations deleted due to missingness)
CP nsplit rel error xerror xstd
1 0.622885
0 1.00000 1.03165 0.176920
2 0.132061
1 0.37711 0.51693 0.102454
3 0.025441
2 0.24505 0.36063 0.079819
4 0.011604
3 0.21961 0.34878 0.080273
5 0.010000
4 0.20801 0.36392 0.075650
22
Mileage…
plotcp(fitM) # visualize cross-validation results
summary(fitM) # detailed summary of splits
<we will leave this for Friday to look at>
23
par(mfrow=c(1,2))
rsq.rpart(fitM) # visualize cross-validation results
24
# plot tree
plot(fitM, uniform=TRUE, main="Regression Tree for
Mileage ")
text(fitM, use.n=TRUE, all=TRUE, cex=.8)
# prune the tree
pfitM<- prune(fitM, cp=0.01160389) # from cptable
# plot the pruned tree
plot(pfitM, uniform=TRUE, main="Pruned Regression
Tree for Mileage")
text(pfitM, use.n=TRUE, all=TRUE, cex=.8)
post(pfitM, file = ”ptree2.ps", title = "Pruned
Regression Tree for Mileage”)
25
26
# Conditional Inference Tree for Mileage
fit2M <- ctree(Mileage~Price + Country +
Reliability + Type, data=na.omit(cu.summary))
27
There are many other datasets
• Try as many as you can
• Titanic?
28
Enough of trees!
29
Coming weeks
• Your project proposals (Assignment 5) are on
March 17/20. Come prepared.
• On March 20 you will likely also have a lab –
attendance will be taken.
• Spring break - March 23 – 27
• On March 31/April 3 you will have lectures on
support vector machines = SVM
• Back to ~ regular schedule in April
30