The document describes using bootstrap aggregation (bagging) with naive Bayes classification on a heart disease dataset. It performs 100 bootstrap iterations, training a naive Bayes model on each resampled dataset and making predictions on the out-of-bag data. Performance is evaluated using mean and variance of accuracy, kappa, and other metrics across the 100 models. Leave-one-out cross-validation is also used to directly evaluate the naive Bayes model on each observation.

1. Bootstrap Aggregation-LooCV-naiveBayes file:///E:/users/rkannan/cuny/fall2020/fall2020/m11-bagging-loocv/baggi...
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2. library('e1071')
file<-'c://Users/rk215/Data/heart.csv'
heart<-read.csv(file,head=T,sep=',',stringsAsFactors=F)
head(heart)
## age sex cp trestbps chol fbs restecg thalach exang oldpeak slope ca tha
l
## 1 63 1 3 145 233 1 0 150 0 2.3 0 0
1
## 2 37 1 2 130 250 0 1 187 0 3.5 0 0
2
## 3 41 0 1 130 204 0 0 172 0 1.4 2 0
2
## 4 56 1 1 120 236 0 1 178 0 0.8 2 0
2
## 5 57 0 0 120 354 0 1 163 1 0.6 2 0
2
## 6 57 1 0 140 192 0 1 148 0 0.4 1 0
1
## target
## 1 1
## 2 1
## 3 1
## 4 1
## 5 1
## 6 1
catheart<-heart[,c(2,3,6,7,9,11,12,13,14)]
set.seed(43)
trdidx<-sample(1:nrow(catheart),0.7*nrow(catheart),replace=F)
trcatheart<-catheart[trdidx,]
tstcatheart<-catheart[-trdidx,]
nb.model<-naiveBayes(target~.,data=trcatheart)
#str(nb.model)
object.size(nb.model) #11096
## 11096 bytes
nb.tstpred<-predict(nb.model,tstcatheart[,-c(9)],type='raw')
nb.tstclass<-unlist(apply(round(nb.tstpred),1,which.max))-1
nb.tbl<-table(tstcatheart[[9]], nb.tstclass)
nb.cfm<-caret::confusionMatrix(nb.tbl)
nb.cfm
Bootstrap Aggregation-LooCV-naiveBayes file:///E:/users/rkannan/cuny/fall2020/fall2020/m11-bagging-loocv/baggi...
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3. ## Confusion Matrix and Statistics
##
## nb.tstclass
## 0 1
## 0 28 12
## 1 3 48
##
## Accuracy : 0.8352
## 95% CI : (0.7427, 0.9047)
## No Information Rate : 0.6593
## P-Value [Acc > NIR] : 0.0001482
##
## Kappa : 0.6571
##
## Mcnemar's Test P-Value : 0.0388671
##
## Sensitivity : 0.9032
## Specificity : 0.8000
## Pos Pred Value : 0.7000
## Neg Pred Value : 0.9412
## Prevalence : 0.3407
## Detection Rate : 0.3077
## Detection Prevalence : 0.4396
## Balanced Accuracy : 0.8516
##
## 'Positive' Class : 0
##
start_tm <- proc.time()
df<-trcatheart
runModel<-function(df) {naiveBayes(target~.,data=df[sample(1:nrow(df),nrow(d
f),replace=T),])}
lapplyrunmodel<-function(x)runModel(df)
system.time(models<-lapply(1:100,lapplyrunmodel))
## user system elapsed
## 0.32 0.02 0.33
object.size(models)
## 1110448 bytes
end_tm<-proc.time()
print(paste("time taken to run 100 bootstrapps",(end_tm-start_tm),sep=":"))
Bootstrap Aggregation-LooCV-naiveBayes file:///E:/users/rkannan/cuny/fall2020/fall2020/m11-bagging-loocv/baggi...
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4. ## [1] "time taken to run 100 bootstrapps:0.46"
## [2] "time taken to run 100 bootstrapps:0.02"
## [3] "time taken to run 100 bootstrapps:0.47"
## [4] "time taken to run 100 bootstrapps:NA"
## [5] "time taken to run 100 bootstrapps:NA"
bagging_preds<-lapply(models,FUN=function(M,D=tstcatheart[,-c(9)])predict(M,
D,type='raw'))
bagging_cfm<-lapply(bagging_preds,FUN=function(P,A=tstcatheart[[9]])
{pred_class<-unlist(apply(round(P),1,which.max))-1
pred_tbl<-table(A,pred_class)
pred_cfm<-caret::confusionMatrix(pred_tbl)
pred_cfm
})
bagging.perf<-as.data.frame(do.call('rbind',lapply(bagging_cfm,FUN=function
(cfm)c(cfm$overall,cfm$byClass))))
bagging.perf.mean<-apply(bagging.perf[bagging.perf$AccuracyPValue<0.01,-c(6:
7)],2,mean)
bagging.perf.var<-apply(bagging.perf[bagging.perf$AccuracyPValue<0.01,-c(6:
7)],2,sd)
bagging.perf.var
## Accuracy Kappa AccuracyLower
## 0.01618750 0.03355331 0.01846838
## AccuracyUpper AccuracyNull Sensitivity
## 0.01273569 0.01795716 0.03073122
## Specificity Pos Pred Value Neg Pred Value
## 0.01470108 0.02693220 0.02200582
## Precision Recall F1
## 0.02693220 0.03073122 0.02087685
## Prevalence Detection Rate Detection Prevalence
## 0.01795716 0.01183833 0.00000000
## Balanced Accuracy
## 0.01875328
bagging.perf.mean
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5. ## Accuracy Kappa AccuracyLower
## 0.8323565 0.6521225 0.7396540
## AccuracyUpper AccuracyNull Sensitivity
## 0.9023711 0.6496947 0.8891540
## Specificity Pos Pred Value Neg Pred Value
## 0.8025070 0.7077778 0.9300654
## Precision Recall F1
## 0.7077778 0.8891540 0.7876655
## Prevalence Detection Rate Detection Prevalence
## 0.3503053 0.3111111 0.4395604
## Balanced Accuracy
## 0.8458305
(bagging_tm<-proc.time()-start_tm)
## user system elapsed
## 2.35 0.02 2.36
N<-nrow(trcatheart)
cv_df<-do.call('rbind',lapply(1:N,FUN=function(idx,data=trcatheart) { # For
each observation
m<-naiveBayes(target~.,data=data[-idx,]) # train with ALL other observatio
ns
p<-predict(m,data[idx,-c(9)],type='raw') # predict that one observation
# NB returns the probabilities of the classes, as per Bayesian Classifie
r,we take the classs with the higher probability
pc<-unlist(apply(round(p),1,which.max))-1 # -1 to make class to be 0 or
1, which.max returns 1 or 2
#pred_tbl<-table(data[idx,c(9)],pc)
#pred_cfm<-caret::confusionMatrix(pred_tbl)
list(fold=idx,m=m,predicted=pc,actual=data[idx,c(9)]) # store the idx, mod
el, predicted class and actual class
}
))
cv_df<-as.data.frame(cv_df)
head(cv_df)
Bootstrap Aggregation-LooCV-naiveBayes file:///E:/users/rkannan/cuny/fall2020/fall2020/m11-bagging-loocv/baggi...
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6. ## fold
## 1 1
## 2 2
## 3 3
## 4 4
## 5 5
## 6 6
##
m
## 1 98, 113, 0.8061224, 0.5840708, 0.3973667, 0.4950769, 0.4387755, 1.35398
2, 0.8623431, 0.9535681, 0.1428571, 0.1327434, 0.3517262, 0.3408085, 0.43877
55, 0.6106195, 0.5385419, 0.5076843, 0.5510204, 0.1769912, 0.4999474, 0.3833
613, 1.132653, 1.530973, 0.5493718, 0.6277909, 1.285714, 0.3539823, 1.03545
4, 0.8856026, 2.581633, 2.123894, 0.6568194, 0.4842657, TRUE, TRUE, TRUE, TR
UE, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = lapla
ce)
## 2 97, 114, 0.8041237, 0.5789474, 0.3989354, 0.4959078, 0.443299, 1.
342105, 0.8656533, 0.9577716, 0.1443299, 0.1315789, 0.3532495, 0.3395249, 0.
443299, 0.6052632, 0.5394649, 0.5086582, 0.5463918, 0.1754386, 0.5004294, 0.
382021, 1.123711, 1.526316, 0.5450102, 0.6269822, 1.278351, 0.3508772, 1.038
25, 0.8822984, 2.57732, 2.122807, 0.658835, 0.4822578, TRUE, TRUE, TRUE, TRU
E, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = laplac
e)
## 3 97, 114, 0.8041237, 0.5789474, 0.3989354, 0.4959078, 0.443299, 1.
342105, 0.8656533, 0.9577716, 0.1443299, 0.1315789, 0.3532495, 0.3395249, 0.
443299, 0.6052632, 0.5394649, 0.5086582, 0.5463918, 0.1754386, 0.5004294, 0.
382021, 1.14433, 1.526316, 0.5398628, 0.6269822, 1.298969, 0.3508772, 1.0324
42, 0.8822984, 2.57732, 2.122807, 0.658835, 0.4822578, TRUE, TRUE, TRUE, TRU
E, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = laplac
e)
## 4 98, 113, 0.8061224, 0.5752212, 0.3973667, 0.4965112, 0.4387755, 1.33628
3, 0.8623431, 0.9600095, 0.1428571, 0.1327434, 0.3517262, 0.3408085, 0.43877
55, 0.6017699, 0.5385419, 0.5095485, 0.5510204, 0.1769912, 0.4999474, 0.3833
613, 1.132653, 1.522124, 0.5493718, 0.6281683, 1.285714, 0.3539823, 1.03545
4, 0.8856026, 2.581633, 2.123894, 0.6568194, 0.4842657, TRUE, TRUE, TRUE, TR
UE, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = lapla
ce)
## 5 98, 113, 0.8061224, 0.5840708, 0.3973667, 0.4950769, 0.4387755, 1.35398
2, 0.8623431, 0.9535681, 0.1428571, 0.1327434, 0.3517262, 0.3408085, 0.43877
55, 0.6017699, 0.5385419, 0.5095485, 0.5510204, 0.1769912, 0.4999474, 0.3833
613, 1.132653, 1.522124, 0.5493718, 0.6281683, 1.285714, 0.3539823, 1.03545
4, 0.8856026, 2.581633, 2.123894, 0.6568194, 0.4842657, TRUE, TRUE, TRUE, TR
UE, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = lapla
ce)
## 6 97, 114, 0.814433, 0.5789474, 0.3907764, 0.4959078, 0.443299, 1.
342105, 0.8656533, 0.9577716, 0.1340206, 0.1315789, 0.3424442, 0.3395249, 0.
4329897, 0.6052632, 0.5382691, 0.5086582, 0.5463918, 0.1754386, 0.5004294,
0.382021, 1.134021, 1.526316, 0.552058, 0.6269822, 1.278351, 0.3508772, 1.03
825, 0.8822984, 2.57732, 2.122807, 0.658835, 0.4822578, TRUE, TRUE, TRUE, TR
UE, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = lapla
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7. ce)
## predicted actual
## 1 1 1
## 2 0 0
## 3 0 0
## 4 1 1
## 5 1 1
## 6 0 0
tail(cv_df)
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8. ## fold
## 207 207
## 208 208
## 209 209
## 210 210
## 211 211
## 212 212
##
m
## 207 98, 113, 0.8061224, 0.5840708, 0.3973667, 0.4950769, 0.4387755, 1.336
283, 0.8623431, 0.9600095, 0.1428571, 0.1238938, 0.3517262, 0.3309279, 0.438
7755, 0.6017699, 0.5385419, 0.5095485, 0.5510204, 0.1769912, 0.4999474, 0.38
33613, 1.132653, 1.522124, 0.5493718, 0.6281683, 1.285714, 0.3539823, 1.0354
54, 0.8856026, 2.581633, 2.123894, 0.6568194, 0.4842657, TRUE, TRUE, TRUE, T
RUE, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = lapl
ace)
## 208 98, 113, 0.8061224, 0.5752212, 0.3973667, 0.4965112, 0.4387755, 1.345
133, 0.8623431, 0.9614898, 0.1428571, 0.1238938, 0.3517262, 0.3309279, 0.438
7755, 0.6106195, 0.5385419, 0.5076843, 0.5510204, 0.1769912, 0.4999474, 0.38
33613, 1.132653, 1.522124, 0.5493718, 0.6281683, 1.285714, 0.3539823, 1.0354
54, 0.8856026, 2.581633, 2.123894, 0.6568194, 0.4842657, TRUE, TRUE, TRUE, T
RUE, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = lapl
ace)
## 209 98, 113, 0.8061224, 0.5752212, 0.3973667, 0.4965112, 0.4387755, 1.353
982, 0.8623431, 0.9535681, 0.1428571, 0.1327434, 0.3517262, 0.3408085, 0.438
7755, 0.6017699, 0.5385419, 0.5095485, 0.5510204, 0.1769912, 0.4999474, 0.38
33613, 1.132653, 1.522124, 0.5493718, 0.6281683, 1.285714, 0.3539823, 1.0354
54, 0.8856026, 2.581633, 2.123894, 0.6568194, 0.4842657, TRUE, TRUE, TRUE, T
RUE, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = lapl
ace)
## 210 98, 113, 0.8061224, 0.5840708, 0.3973667, 0.4950769, 0.4387755, 1.345
133, 0.8623431, 0.9614898, 0.1428571, 0.1238938, 0.3517262, 0.3309279, 0.438
7755, 0.6106195, 0.5385419, 0.5076843, 0.5510204, 0.1681416, 0.4999474, 0.37
56579, 1.132653, 1.522124, 0.5493718, 0.6281683, 1.285714, 0.3451327, 1.0354
54, 0.8840846, 2.581633, 2.123894, 0.6568194, 0.4842657, TRUE, TRUE, TRUE, T
RUE, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = lapl
ace)
## 211 97, 114, 0.8041237, 0.5789474, 0.3989354, 0.4959078, 0.443299,
1.342105, 0.8656533, 0.9577716, 0.1443299, 0.1315789, 0.3532495, 0.3395249,
0.4329897, 0.6052632, 0.5382691, 0.5086582, 0.5463918, 0.1754386, 0.5004294,
0.382021, 1.134021, 1.526316, 0.552058, 0.6269822, 1.28866, 0.3508772, 1.040
42, 0.8822984, 2.57732, 2.122807, 0.658835, 0.4822578, TRUE, TRUE, TRUE, TRU
E, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = laplac
e)
## 212 98, 113, 0.8061224, 0.5840708, 0.3973667, 0.4950769, 0.4387755, 1.345
133, 0.8623431, 0.9614898, 0.1428571, 0.1327434, 0.3517262, 0.3408085, 0.438
7755, 0.6106195, 0.5385419, 0.5076843, 0.5510204, 0.1769912, 0.4999474, 0.38
33613, 1.132653, 1.522124, 0.5493718, 0.6281683, 1.285714, 0.3539823, 1.0354
54, 0.8856026, 2.581633, 2.123894, 0.6568194, 0.4842657, TRUE, TRUE, TRUE, T
RUE, TRUE, TRUE, TRUE, TRUE, naiveBayes.default(x = X, y = Y, laplace = lapl
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9. ace)
## predicted actual
## 207 1 1
## 208 1 1
## 209 1 1
## 210 1 1
## 211 0 0
## 212 1 1
table(as.numeric(cv_df$actual)==as.numeric(cv_df$predicted))
##
## FALSE TRUE
## 34 178
loocv_tbl<-table(as.numeric(cv_df$actual),as.numeric(cv_df$predicted))
sum(diag(loocv_tbl))/sum(loocv_tbl)
## [1] 0.8396226
(loocv_caret_cfm<-caret::confusionMatrix(loocv_tbl))
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10. ## Confusion Matrix and Statistics
##
##
## 0 1
## 0 79 19
## 1 15 99
##
## Accuracy : 0.8396
## 95% CI : (0.7832, 0.8863)
## No Information Rate : 0.5566
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.6765
##
## Mcnemar's Test P-Value : 0.6069
##
## Sensitivity : 0.8404
## Specificity : 0.8390
## Pos Pred Value : 0.8061
## Neg Pred Value : 0.8684
## Prevalence : 0.4434
## Detection Rate : 0.3726
## Detection Prevalence : 0.4623
## Balanced Accuracy : 0.8397
##
## 'Positive' Class : 0
##
# now we have to apply the training models to testdata and average them
# since this is classification we will take the majority vote
# double loop
tstcv.perf<-as.data.frame(do.call('cbind',lapply(cv_df$m,FUN=function(m,data
=tstcatheart)
{
v<-predict(m,data[,-c(9)],type='raw')
lbllist<-unlist(apply(round(v),1,which.max))-1
}
)))
np<-ncol(tstcv.perf)
predclass<-unlist(apply(tstcv.perf,1,FUN=function(v){ ifelse(sum(v[2:length
(v)])/np<0.5,0,1)}))
loocvtbl<-table(tstcatheart[,c(9)],predclass)
(loocv_cfm<-caret::confusionMatrix(loocvtbl))
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11. ## Confusion Matrix and Statistics
##
## predclass
## 0 1
## 0 28 12
## 1 3 48
##
## Accuracy : 0.8352
## 95% CI : (0.7427, 0.9047)
## No Information Rate : 0.6593
## P-Value [Acc > NIR] : 0.0001482
##
## Kappa : 0.6571
##
## Mcnemar's Test P-Value : 0.0388671
##
## Sensitivity : 0.9032
## Specificity : 0.8000
## Pos Pred Value : 0.7000
## Neg Pred Value : 0.9412
## Prevalence : 0.3407
## Detection Rate : 0.3077
## Detection Prevalence : 0.4396
## Balanced Accuracy : 0.8516
##
## 'Positive' Class : 0
##
print(paste('Bagging:',bagging.perf.mean[1]))
## [1] "Bagging: 0.832356532356532"
print(paste('LOO-CV:',loocv_cfm$overall[1]))
## [1] "LOO-CV: 0.835164835164835"
print(paste('Base NB',nb.cfm$overall[[1]]))
## [1] "Base NB 0.835164835164835"
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