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1 Peter Fox Data Analytics – ITWS-4963/ITWS-6965 Week 7a, March 10, 2015 Labs: more data, models, prediction, deciding with trees

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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

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Titanic – Bayes (from last week) > data(Titanic) > mdl <- naiveBayes(Survived ~., data = Titanic) > mdl 3 Naive Bayes Classifier for Discrete Predictors Call: naiveBayes.formula(formula = Survived ~., data = Titanic) A-priori probabilities: 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 Survived Child Adult No 0.03489933 0.96510067 Yes 0.08016878 0.91983122 Try Lab6b_9_2014.R

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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

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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

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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

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House Votes 1984 > pred <- predict(model, HouseVotes84[,-1]) > table(pred, HouseVotes84$Class) pred democrat republican democrat 238 13 republican 29 155 7

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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

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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) # 2 clusters > plot(y~x,df,col=cluster) 9

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See also Lab5a_ctree_1_2015.R –Try clustergram instead –Try hclust Lab3b_kmeans1_2015.R –Try clustergram instead –Try hclust 10

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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

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13 > pfitK<- prune(fitK, cp= fitK$cptable[which.min(fitK$cptable[,"xerror"]),"CP"]) > plot(pfitK, uniform=TRUE, main="Pruned Classification Tree for Kyphosis") > text(pfitK, use.n=TRUE, all=TRUE, cex=.8) > post(pfitK, file = “ptree.ps", title = "Pruned Classification Tree for Kyphosis”)

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14 > fitK <- ctree(Kyphosis ~ Age + Number + Start, data=kyphosis) > plot(fitK, main="Conditional Inference Tree for Kyphosis”)

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15 > plot(fitK, main="Conditional Inference Tree for Kyphosis",type="simple")

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Swiss - scatterplotMatrix 16

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Hierarchical clustering 17 > dswiss <- dist(as.matrix(swiss)) > hs <- hclust(dswiss) > plot(hs)

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ctree 18 require(party) swiss_ctree <- ctree(Fertility ~ Agriculture + Education + Catholic, data = swiss) plot(swiss_ctree)

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19 How could you get this?

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Rpart – recursive partitioning 20 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

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Rpart – recursive partitioning 21 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”

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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

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Mileage… plotcp(fitM) # visualize cross-validation results summary(fitM) # detailed summary of splits 23

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24 par(mfrow=c(1,2)) rsq.rpart(fitM) # visualize cross-validation results

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# 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

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# Conditional Inference Tree for Mileage fit2M <- ctree(Mileage~Price + Country + Reliability + Type, data=na.omit(cu.summary)) 27

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There are many other datasets Try as many as you can Titanic? 28

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Enough of trees! 29

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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

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1 Peter Fox Data Analytics – ITWS-4963/ITWS-6965 Week 7b, March 13, 2015 Interpreting weighted kNN, decision trees, cross-validation, dimension reduction.

1 Peter Fox Data Analytics – ITWS-4963/ITWS-6965 Week 7b, March 13, 2015 Interpreting weighted kNN, decision trees, cross-validation, dimension reduction.

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