Example is retrieved from the book Machine Learning with R (Brett Lantz).
The dataset retrieved UCI Machine Learning Data Repository (http://archive.ics.uci.edu/ml) and contains information on loans obtained from a credit agency in Germany.
The data set includes 1000 observations with 1 nominal variable about loan outcome (default) and 16 other nominal and numeric variables.
credit <- read.csv("credit.csv")
str(credit)## 'data.frame': 1000 obs. of 17 variables:
## $ checking_balance : Factor w/ 4 levels "< 0 DM","> 200 DM",..: 1 3 4 1 1 4 4 3 4 3 ...
## $ months_loan_duration: int 6 48 12 42 24 36 24 36 12 30 ...
## $ credit_history : Factor w/ 5 levels "critical","good",..: 1 2 1 2 4 2 2 2 2 1 ...
## $ purpose : Factor w/ 6 levels "business","car",..: 5 5 4 5 2 4 5 2 5 2 ...
## $ amount : int 1169 5951 2096 7882 4870 9055 2835 6948 3059 5234 ...
## $ savings_balance : Factor w/ 5 levels "< 100 DM","> 1000 DM",..: 5 1 1 1 1 5 4 1 2 1 ...
## $ employment_duration : Factor w/ 5 levels "< 1 year","> 7 years",..: 2 3 4 4 3 3 2 3 4 5 ...
## $ percent_of_income : int 4 2 2 2 3 2 3 2 2 4 ...
## $ years_at_residence : int 4 2 3 4 4 4 4 2 4 2 ...
## $ age : int 67 22 49 45 53 35 53 35 61 28 ...
## $ other_credit : Factor w/ 3 levels "bank","none",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ housing : Factor w/ 3 levels "other","own",..: 2 2 2 1 1 1 2 3 2 2 ...
## $ existing_loans_count: int 2 1 1 1 2 1 1 1 1 2 ...
## $ job : Factor w/ 4 levels "management","skilled",..: 2 2 4 2 2 4 2 1 4 1 ...
## $ dependents : int 1 1 2 2 2 2 1 1 1 1 ...
## $ phone : Factor w/ 2 levels "no","yes": 2 1 1 1 1 2 1 2 1 1 ...
## $ default : Factor w/ 2 levels "no","yes": 1 2 1 1 2 1 1 1 1 2 ...# look at two characteristics of the applicant
table(credit$checking_balance)##
## < 0 DM > 200 DM 1 - 200 DM unknown
## 274 63 269 394table(credit$savings_balance)##
## < 100 DM > 1000 DM 100 - 500 DM 500 - 1000 DM unknown
## 603 48 103 63 183# look at two characteristics of the loan
summary(credit$months_loan_duration)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.0 12.0 18.0 20.9 24.0 72.0summary(credit$amount)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 250 1366 2320 3271 3972 18420# look at the class variable
table(credit$default)##
## no yes
## 700 300# create a random sample for training and test data
# use set.seed to use the same random number sequence as the tutorial
set.seed(123)
train_sample <- sample(1000, 900)
str(train_sample)## int [1:900] 288 788 409 881 937 46 525 887 548 453 ...# split the data frames
credit_train <- credit[train_sample, ]
credit_test <- credit[-train_sample, ]
# check the proportion of class variable
prop.table(table(credit_train$default))##
## no yes
## 0.7033333 0.2966667prop.table(table(credit_test$default))##
## no yes
## 0.67 0.33In model training, we remove the 17th column since it is the outcome variable that we want to predict.
# build the simplest decision tree
library(C50)
credit_model <- C5.0(credit_train[-17], credit_train$default)Tree size is 57 which represents that the tree is 57 decision deep.
# display simple facts about the tree
credit_model##
## Call:
## C5.0.default(x = credit_train[-17], y = credit_train$default)
##
## Classification Tree
## Number of samples: 900
## Number of predictors: 16
##
## Tree size: 57
##
## Non-standard options: attempt to group attributesThe summary shows the first branches of the decision tree. First number in the parentheses indicates the total number of observations classified with that branch and the second shows the number of observations which are incorrectly labeled. At the bottom, we see that 133 observations out of 900 in the training dataset are incorrectly labeled.
# build the simplest decision tree
# display detailed information about the tree
summary(credit_model)##
## Call:
## C5.0.default(x = credit_train[-17], y = credit_train$default)
##
##
## C5.0 [Release 2.07 GPL Edition] Fri Apr 21 21:41:51 2017
## -------------------------------
##
## Class specified by attribute `outcome'
##
## Read 900 cases (17 attributes) from undefined.data
##
## Decision tree:
##
## checking_balance in {> 200 DM,unknown}: no (412/50)
## checking_balance in {< 0 DM,1 - 200 DM}:
## :...credit_history in {perfect,very good}: yes (59/18)
## credit_history in {critical,good,poor}:
## :...months_loan_duration <= 22:
## :...credit_history = critical: no (72/14)
## : credit_history = poor:
## : :...dependents > 1: no (5)
## : : dependents <= 1:
## : : :...years_at_residence <= 3: yes (4/1)
## : : years_at_residence > 3: no (5/1)
## : credit_history = good:
## : :...savings_balance in {> 1000 DM,500 - 1000 DM}: no (15/1)
## : savings_balance = 100 - 500 DM:
## : :...other_credit = bank: yes (3)
## : : other_credit in {none,store}: no (9/2)
## : savings_balance = unknown:
## : :...other_credit = bank: yes (1)
## : : other_credit in {none,store}: no (21/8)
## : savings_balance = < 100 DM:
## : :...purpose in {business,car0,renovations}: no (8/2)
## : purpose = education:
## : :...checking_balance = < 0 DM: yes (4)
## : : checking_balance = 1 - 200 DM: no (1)
## : purpose = car:
## : :...employment_duration = > 7 years: yes (5)
## : : employment_duration = unemployed: no (4/1)
## : : employment_duration = < 1 year:
## : : :...years_at_residence <= 2: yes (5)
## : : : years_at_residence > 2: no (3/1)
## : : employment_duration = 1 - 4 years:
## : : :...years_at_residence <= 2: yes (2)
## : : : years_at_residence > 2: no (6/1)
## : : employment_duration = 4 - 7 years:
## : : :...amount <= 1680: yes (2)
## : : amount > 1680: no (3)
## : purpose = furniture/appliances:
## : :...job in {management,unskilled}: no (23/3)
## : job = unemployed: yes (1)
## : job = skilled:
## : :...months_loan_duration > 13: [S1]
## : months_loan_duration <= 13:
## : :...housing in {other,own}: no (23/4)
## : housing = rent:
## : :...percent_of_income <= 3: yes (3)
## : percent_of_income > 3: no (2)
## months_loan_duration > 22:
## :...savings_balance = > 1000 DM: no (2)
## savings_balance = 500 - 1000 DM: yes (4/1)
## savings_balance = 100 - 500 DM:
## :...credit_history in {critical,poor}: no (14/3)
## : credit_history = good:
## : :...other_credit = bank: no (1)
## : other_credit in {none,store}: yes (12/2)
## savings_balance = unknown:
## :...checking_balance = 1 - 200 DM: no (17)
## : checking_balance = < 0 DM:
## : :...credit_history = critical: no (1)
## : credit_history in {good,poor}: yes (12/3)
## savings_balance = < 100 DM:
## :...months_loan_duration > 47: yes (21/2)
## months_loan_duration <= 47:
## :...housing = other:
## :...percent_of_income <= 2: no (6)
## : percent_of_income > 2: yes (9/3)
## housing = rent:
## :...other_credit = bank: no (1)
## : other_credit in {none,store}: yes (16/3)
## housing = own:
## :...employment_duration = > 7 years: no (13/4)
## employment_duration = 4 - 7 years:
## :...job in {management,skilled,
## : : unemployed}: yes (9/1)
## : job = unskilled: no (1)
## employment_duration = unemployed:
## :...years_at_residence <= 2: yes (4)
## : years_at_residence > 2: no (3)
## employment_duration = 1 - 4 years:
## :...purpose in {business,car0,education}: yes (7/1)
## : purpose in {furniture/appliances,
## : : renovations}: no (7)
## : purpose = car:
## : :...years_at_residence <= 3: yes (3)
## : years_at_residence > 3: no (3)
## employment_duration = < 1 year:
## :...years_at_residence > 3: yes (5)
## years_at_residence <= 3:
## :...other_credit = bank: no (0)
## other_credit = store: yes (1)
## other_credit = none:
## :...checking_balance = 1 - 200 DM: no (8/2)
## checking_balance = < 0 DM:
## :...job in {management,skilled,
## : unemployed}: yes (2)
## job = unskilled: no (3/1)
##
## SubTree [S1]
##
## employment_duration in {< 1 year,4 - 7 years}: no (4)
## employment_duration in {> 7 years,1 - 4 years,unemployed}: yes (10)
##
##
## Evaluation on training data (900 cases):
##
## Decision Tree
## ----------------
## Size Errors
##
## 56 133(14.8%) <<
##
##
## (a) (b) <-classified as
## ---- ----
## 598 35 (a): class no
## 98 169 (b): class yes
##
##
## Attribute usage:
##
## 100.00% checking_balance
## 54.22% credit_history
## 47.67% months_loan_duration
## 38.11% savings_balance
## 14.33% purpose
## 14.33% housing
## 12.56% employment_duration
## 9.00% job
## 8.67% other_credit
## 6.33% years_at_residence
## 2.22% percent_of_income
## 1.56% dependents
## 0.56% amount
##
##
## Time: 0.0 secs# create a factor vector of predictions on test data
credit_pred <- predict(credit_model, credit_test)
# cross tabulation of predicted versus actual classes
library(gmodels)
CrossTable(credit_test$default, credit_pred,
prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
dnn = c('actual default', 'predicted default'))##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 100
##
##
## | predicted default
## actual default | no | yes | Row Total |
## ---------------|-----------|-----------|-----------|
## no | 59 | 8 | 67 |
## | 0.590 | 0.080 | |
## ---------------|-----------|-----------|-----------|
## yes | 19 | 14 | 33 |
## | 0.190 | 0.140 | |
## ---------------|-----------|-----------|-----------|
## Column Total | 78 | 22 | 100 |
## ---------------|-----------|-----------|-----------|
##
## The overall accuracy rate of the model is 73%. 19% of the actual default loans in the test dataset are labeled as not default by the decision tree. This result is risky for the bank since it loses money on each default. Furthermore, 8% of the loans that are not default are labeled as default which cause bank to lose customers.
By adaptive boosting we can increase the model accuracy. In this process, many trees are built and vote on each observation’s label.
## Boosting the accuracy of decision trees
# boosted decision tree with 10 trials
credit_boost10 <- C5.0(credit_train[-17], credit_train$default,
trials = 10)
credit_boost10##
## Call:
## C5.0.default(x = credit_train[-17], y = credit_train$default, trials = 10)
##
## Classification Tree
## Number of samples: 900
## Number of predictors: 16
##
## Number of boosting iterations: 10
## Average tree size: 47.5
##
## Non-standard options: attempt to group attributessummary(credit_boost10)##
## Call:
## C5.0.default(x = credit_train[-17], y = credit_train$default, trials = 10)
##
##
## C5.0 [Release 2.07 GPL Edition] Fri Apr 21 21:41:51 2017
## -------------------------------
##
## Class specified by attribute `outcome'
##
## Read 900 cases (17 attributes) from undefined.data
##
## ----- Trial 0: -----
##
## Decision tree:
##
## checking_balance in {> 200 DM,unknown}: no (412/50)
## checking_balance in {< 0 DM,1 - 200 DM}:
## :...credit_history in {perfect,very good}: yes (59/18)
## credit_history in {critical,good,poor}:
## :...months_loan_duration <= 22:
## :...credit_history = critical: no (72/14)
## : credit_history = poor:
## : :...dependents > 1: no (5)
## : : dependents <= 1:
## : : :...years_at_residence <= 3: yes (4/1)
## : : years_at_residence > 3: no (5/1)
## : credit_history = good:
## : :...savings_balance in {> 1000 DM,500 - 1000 DM}: no (15/1)
## : savings_balance = 100 - 500 DM:
## : :...other_credit = bank: yes (3)
## : : other_credit in {none,store}: no (9/2)
## : savings_balance = unknown:
## : :...other_credit = bank: yes (1)
## : : other_credit in {none,store}: no (21/8)
## : savings_balance = < 100 DM:
## : :...purpose in {business,car0,renovations}: no (8/2)
## : purpose = education:
## : :...checking_balance = < 0 DM: yes (4)
## : : checking_balance = 1 - 200 DM: no (1)
## : purpose = car:
## : :...employment_duration = > 7 years: yes (5)
## : : employment_duration = unemployed: no (4/1)
## : : employment_duration = < 1 year:
## : : :...years_at_residence <= 2: yes (5)
## : : : years_at_residence > 2: no (3/1)
## : : employment_duration = 1 - 4 years:
## : : :...years_at_residence <= 2: yes (2)
## : : : years_at_residence > 2: no (6/1)
## : : employment_duration = 4 - 7 years:
## : : :...amount <= 1680: yes (2)
## : : amount > 1680: no (3)
## : purpose = furniture/appliances:
## : :...job in {management,unskilled}: no (23/3)
## : job = unemployed: yes (1)
## : job = skilled:
## : :...months_loan_duration > 13: [S1]
## : months_loan_duration <= 13:
## : :...housing in {other,own}: no (23/4)
## : housing = rent:
## : :...percent_of_income <= 3: yes (3)
## : percent_of_income > 3: no (2)
## months_loan_duration > 22:
## :...savings_balance = > 1000 DM: no (2)
## savings_balance = 500 - 1000 DM: yes (4/1)
## savings_balance = 100 - 500 DM:
## :...credit_history in {critical,poor}: no (14/3)
## : credit_history = good:
## : :...other_credit = bank: no (1)
## : other_credit in {none,store}: yes (12/2)
## savings_balance = unknown:
## :...checking_balance = 1 - 200 DM: no (17)
## : checking_balance = < 0 DM:
## : :...credit_history = critical: no (1)
## : credit_history in {good,poor}: yes (12/3)
## savings_balance = < 100 DM:
## :...months_loan_duration > 47: yes (21/2)
## months_loan_duration <= 47:
## :...housing = other:
## :...percent_of_income <= 2: no (6)
## : percent_of_income > 2: yes (9/3)
## housing = rent:
## :...other_credit = bank: no (1)
## : other_credit in {none,store}: yes (16/3)
## housing = own:
## :...employment_duration = > 7 years: no (13/4)
## employment_duration = 4 - 7 years:
## :...job in {management,skilled,
## : : unemployed}: yes (9/1)
## : job = unskilled: no (1)
## employment_duration = unemployed:
## :...years_at_residence <= 2: yes (4)
## : years_at_residence > 2: no (3)
## employment_duration = 1 - 4 years:
## :...purpose in {business,car0,education}: yes (7/1)
## : purpose in {furniture/appliances,
## : : renovations}: no (7)
## : purpose = car:
## : :...years_at_residence <= 3: yes (3)
## : years_at_residence > 3: no (3)
## employment_duration = < 1 year:
## :...years_at_residence > 3: yes (5)
## years_at_residence <= 3:
## :...other_credit = bank: no (0)
## other_credit = store: yes (1)
## other_credit = none:
## :...checking_balance = 1 - 200 DM: no (8/2)
## checking_balance = < 0 DM:
## :...job in {management,skilled,
## : unemployed}: yes (2)
## job = unskilled: no (3/1)
##
## SubTree [S1]
##
## employment_duration in {< 1 year,4 - 7 years}: no (4)
## employment_duration in {> 7 years,1 - 4 years,unemployed}: yes (10)
##
## ----- Trial 1: -----
##
## Decision tree:
##
## checking_balance = unknown:
## :...other_credit in {bank,store}:
## : :...purpose in {business,education,renovations}: yes (19.5/6.3)
## : : purpose in {car0,furniture/appliances}: no (24.8/6.6)
## : : purpose = car:
## : : :...dependents <= 1: yes (20.1/4.8)
## : : dependents > 1: no (2.4)
## : other_credit = none:
## : :...credit_history in {critical,perfect,very good}: no (102.8/4.4)
## : credit_history = good:
## : :...existing_loans_count <= 1: no (112.7/17.5)
## : : existing_loans_count > 1: yes (18.9/7.9)
## : credit_history = poor:
## : :...years_at_residence <= 1: yes (4.4)
## : years_at_residence > 1:
## : :...percent_of_income <= 3: no (11.9)
## : percent_of_income > 3: yes (14.3/5.6)
## checking_balance in {< 0 DM,> 200 DM,1 - 200 DM}:
## :...savings_balance in {> 1000 DM,500 - 1000 DM}: no (42.9/11.3)
## savings_balance = unknown:
## :...credit_history in {perfect,poor}: no (8.5)
## : credit_history in {critical,good,very good}:
## : :...employment_duration in {< 1 year,> 7 years,4 - 7 years,
## : : unemployed}: no (52.3/17.3)
## : employment_duration = 1 - 4 years: yes (19.7/5.6)
## savings_balance = 100 - 500 DM:
## :...existing_loans_count > 3: yes (3)
## : existing_loans_count <= 3:
## : :...credit_history in {critical,poor,very good}: no (24.6/7.6)
## : credit_history = perfect: yes (2.4)
## : credit_history = good:
## : :...months_loan_duration <= 27: no (23.7/10.5)
## : months_loan_duration > 27: yes (5.6)
## savings_balance = < 100 DM:
## :...months_loan_duration > 42: yes (28/5.2)
## months_loan_duration <= 42:
## :...percent_of_income <= 2:
## :...employment_duration in {1 - 4 years,4 - 7 years,
## : : unemployed}: no (86.2/23.8)
## : employment_duration in {< 1 year,> 7 years}:
## : :...housing = other: no (4.8/1.6)
## : housing = rent: yes (10.7/2.4)
## : housing = own:
## : :...phone = yes: yes (12.9/4)
## : phone = no:
## : :...percent_of_income <= 1: no (7.1/0.8)
## : percent_of_income > 1: yes (17.5/7.1)
## percent_of_income > 2:
## :...years_at_residence <= 1: no (31.6/8.5)
## years_at_residence > 1:
## :...credit_history in {perfect,poor}: yes (20.9/1.6)
## credit_history in {critical,good,very good}:
## :...job = skilled: yes (95/34.7)
## job = unemployed: no (1.6)
## job = management:
## :...amount <= 11590: no (23.8/7)
## : amount > 11590: yes (3.8)
## job = unskilled:
## :...checking_balance in {< 0 DM,
## : > 200 DM}: yes (23.8/9.5)
## checking_balance = 1 - 200 DM: no (17.9/6.2)
##
## ----- Trial 2: -----
##
## Decision tree:
##
## checking_balance = unknown:
## :...other_credit = bank:
## : :...existing_loans_count > 2: no (3.3)
## : : existing_loans_count <= 2:
## : : :...months_loan_duration <= 8: no (4)
## : : months_loan_duration > 8: yes (43/16.6)
## : other_credit in {none,store}:
## : :...employment_duration in {< 1 year,unemployed}:
## : :...purpose in {business,renovations}: yes (6.4)
## : : purpose in {car,car0,education}: no (13.2)
## : : purpose = furniture/appliances:
## : : :...amount <= 4594: no (22.5/7.3)
## : : amount > 4594: yes (9.1)
## : employment_duration in {> 7 years,1 - 4 years,4 - 7 years}:
## : :...percent_of_income <= 3: no (92.7/3.6)
## : percent_of_income > 3:
## : :...age > 30: no (73.6/5.5)
## : age <= 30:
## : :...job in {management,unemployed,unskilled}: yes (14/4)
## : job = skilled:
## : :...credit_history = very good: no (0)
## : credit_history = poor: yes (3.6)
## : credit_history in {critical,good,perfect}:
## : :...age <= 29: no (20.4/4.6)
## : age > 29: yes (2.7)
## checking_balance in {< 0 DM,> 200 DM,1 - 200 DM}:
## :...housing = other:
## :...dependents > 1: yes (28.3/7.6)
## : dependents <= 1:
## : :...employment_duration in {< 1 year,4 - 7 years,
## : : unemployed}: no (22.9/4.5)
## : employment_duration in {> 7 years,1 - 4 years}: yes (29.6/10.5)
## housing = rent:
## :...credit_history = perfect: yes (5.3)
## : credit_history = poor: no (7.1/0.7)
## : credit_history in {critical,good,very good}:
## : :...employment_duration = < 1 year: yes (28.3/9.3)
## : employment_duration in {> 7 years,4 - 7 years,
## : : unemployed}: no (33.9/12.3)
## : employment_duration = 1 - 4 years:
## : :...checking_balance = > 200 DM: no (2)
## : checking_balance in {< 0 DM,1 - 200 DM}:
## : :...years_at_residence <= 3: no (10.3/3.8)
## : years_at_residence > 3: yes (20.4/3.1)
## housing = own:
## :...job in {management,unemployed}: yes (55.8/19.8)
## job in {skilled,unskilled}:
## :...months_loan_duration <= 7: no (25.3/2)
## months_loan_duration > 7:
## :...years_at_residence > 3: no (92.2/29.6)
## years_at_residence <= 3:
## :...purpose = renovations: yes (7/1.3)
## purpose in {business,car0,education}: no (32.2/5.3)
## purpose = car:
## :...months_loan_duration > 40: no (7.2/0.7)
## : months_loan_duration <= 40:
## : :...amount <= 947: yes (12.9)
## : amount > 947:
## : :...months_loan_duration <= 16: no (23.2/8.5)
## : months_loan_duration > 16: [S1]
## purpose = furniture/appliances:
## :...savings_balance in {> 1000 DM,unknown}: no (15.4/3.2)
## savings_balance in {100 - 500 DM,
## : 500 - 1000 DM}: yes (14.6/4.5)
## savings_balance = < 100 DM:
## :...months_loan_duration > 36: yes (7.1)
## months_loan_duration <= 36:
## :...existing_loans_count > 1: no (14.1/4.3)
## existing_loans_count <= 1: [S2]
##
## SubTree [S1]
##
## savings_balance in {< 100 DM,> 1000 DM,500 - 1000 DM,unknown}: yes (22.5/2.7)
## savings_balance = 100 - 500 DM: no (4.5/0.7)
##
## SubTree [S2]
##
## checking_balance = < 0 DM: no (22.4/9.1)
## checking_balance in {> 200 DM,1 - 200 DM}: yes (46.7/20)
##
## ----- Trial 3: -----
##
## Decision tree:
##
## checking_balance in {> 200 DM,unknown}:
## :...employment_duration = > 7 years: no (98.9/17.1)
## : employment_duration = unemployed: yes (16/6.7)
## : employment_duration = < 1 year:
## : :...amount <= 1333: no (11.7)
## : : amount > 1333:
## : : :...amount <= 6681: no (38.2/16.3)
## : : amount > 6681: yes (5.3)
## : employment_duration = 4 - 7 years:
## : :...checking_balance = > 200 DM: yes (9.6/3.6)
## : : checking_balance = unknown:
## : : :...age <= 22: yes (6.5/1.6)
## : : age > 22: no (42.6/1.5)
## : employment_duration = 1 - 4 years:
## : :...percent_of_income <= 1: no (20.6/1.5)
## : percent_of_income > 1:
## : :...job in {skilled,unemployed}: no (64.9/17.6)
## : job in {management,unskilled}:
## : :...existing_loans_count > 2: yes (2.4)
## : existing_loans_count <= 2:
## : :...age <= 34: yes (26.4/10.7)
## : age > 34: no (10.5)
## checking_balance in {< 0 DM,1 - 200 DM}:
## :...savings_balance in {> 1000 DM,500 - 1000 DM}: no (35.8/12)
## savings_balance = 100 - 500 DM:
## :...amount <= 1285: yes (12.8/0.5)
## : amount > 1285:
## : :...existing_loans_count <= 1: no (27/9.2)
## : existing_loans_count > 1: yes (15.8/4.9)
## savings_balance = unknown:
## :...credit_history in {critical,perfect,poor}: no (15.5)
## : credit_history in {good,very good}:
## : :...age > 56: no (4.5)
## : age <= 56:
## : :...months_loan_duration <= 18: yes (24.5/5.6)
## : months_loan_duration > 18: no (28.4/12.3)
## savings_balance = < 100 DM:
## :...months_loan_duration <= 11:
## :...job = management: yes (13.7/4.9)
## : job in {skilled,unemployed,unskilled}: no (45.9/10)
## months_loan_duration > 11:
## :...percent_of_income <= 1:
## :...credit_history in {critical,poor,very good}: no (11.1)
## : credit_history in {good,perfect}: yes (24.4/11)
## percent_of_income > 1:
## :...job = unemployed: yes (7/3.1)
## job = management:
## :...years_at_residence <= 1: no (6.6)
## : years_at_residence > 1:
## : :...checking_balance = < 0 DM: no (23.1/7)
## : checking_balance = 1 - 200 DM: yes (15.8/4)
## job = unskilled:
## :...housing in {other,rent}: yes (12.2/2.2)
## : housing = own:
## : :...purpose = car: yes (18.1/3.9)
## : purpose in {business,car0,education,
## : furniture/appliances,
## : renovations}: no (32.1/11.1)
## job = skilled:
## :...checking_balance = < 0 DM:
## :...credit_history in {poor,very good}: yes (16.6)
## : credit_history in {critical,good,perfect}:
## : :...purpose in {business,car0,education,
## : : renovations}: yes (10.2/1.5)
## : purpose = car:
## : :...age <= 51: yes (34.6/8.1)
## : : age > 51: no (4.4)
## : purpose = furniture/appliances:
## : :...years_at_residence <= 1: no (4.4)
## : years_at_residence > 1:
## : :...other_credit = bank: yes (2.4)
## : other_credit = store: no (0.5)
## : other_credit = none:
## : :...amount <= 1743: no (11.5/2.4)
## : amount > 1743: yes (29/6.6)
## checking_balance = 1 - 200 DM:
## :...months_loan_duration > 36: yes (6.5)
## months_loan_duration <= 36:
## :...other_credit in {bank,store}: yes (8/1.5)
## other_credit = none:
## :...dependents > 1: yes (7.4/3.1)
## dependents <= 1:
## :...percent_of_income <= 2: no (12.7/1.1)
## percent_of_income > 2: [S1]
##
## SubTree [S1]
##
## purpose in {business,renovations}: yes (3.9)
## purpose in {car,car0,education,furniture/appliances}: no (19.8/6.1)
##
## ----- Trial 4: -----
##
## Decision tree:
##
## checking_balance in {> 200 DM,unknown}:
## :...other_credit = store: no (20.6/9.6)
## : other_credit = none:
## : :...employment_duration in {> 7 years,1 - 4 years,4 - 7 years,
## : : : unemployed}: no (211.3/45.7)
## : : employment_duration = < 1 year:
## : : :...amount <= 1333: no (8.8)
## : : amount > 1333:
## : : :...purpose in {business,car0,education,furniture/appliances,
## : : : renovations}: yes (32.9/8.1)
## : : purpose = car: no (4.9)
## : other_credit = bank:
## : :...age > 44: no (14.4/1.2)
## : age <= 44:
## : :...years_at_residence <= 1: no (5)
## : years_at_residence > 1:
## : :...housing = rent: yes (4.3)
## : housing in {other,own}:
## : :...job = unemployed: yes (0)
## : job = management: no (4)
## : job in {skilled,unskilled}:
## : :...age <= 26: no (3.7)
## : age > 26:
## : :...savings_balance in {< 100 DM,500 - 1000 DM,
## : : unknown}: yes (30.6/7.4)
## : savings_balance in {> 1000 DM,
## : 100 - 500 DM}: no (4)
## checking_balance in {< 0 DM,1 - 200 DM}:
## :...credit_history = perfect:
## :...housing in {other,rent}: yes (7.8)
## : housing = own: no (20.5/9)
## credit_history = poor:
## :...checking_balance = < 0 DM: yes (10.4/2.2)
## : checking_balance = 1 - 200 DM:
## : :...other_credit in {bank,none}: no (24/4.3)
## : other_credit = store: yes (5.8/1.2)
## credit_history = very good:
## :...age <= 23: no (5.7)
## : age > 23:
## : :...months_loan_duration <= 27: yes (28.4/3.7)
## : months_loan_duration > 27: no (6.9/2)
## credit_history = critical:
## :...years_at_residence <= 1: no (6.7)
## : years_at_residence > 1:
## : :...purpose in {business,car,car0,renovations}: no (62.2/21.9)
## : purpose = education: yes (7.9/0.9)
## : purpose = furniture/appliances:
## : :...phone = yes: no (14.5/2.8)
## : phone = no:
## : :...amount <= 1175: no (5.2)
## : amount > 1175: yes (30.1/7.6)
## credit_history = good:
## :...savings_balance in {> 1000 DM,500 - 1000 DM}: no (15.7/4.7)
## savings_balance = 100 - 500 DM: yes (32.1/11.7)
## savings_balance = unknown:
## :...job = unskilled: no (4.4)
## : job in {management,skilled,unemployed}:
## : :...checking_balance = < 0 DM: yes (27.8/6)
## : checking_balance = 1 - 200 DM: no (26.8/10.4)
## savings_balance = < 100 DM:
## :...dependents > 1:
## :...existing_loans_count > 1: no (2.6/0.4)
## : existing_loans_count <= 1:
## : :...years_at_residence <= 2: yes (10.2/2.9)
## : years_at_residence > 2: no (20.4/5.9)
## dependents <= 1:
## :...purpose in {business,car0}: no (9.7/2.5)
## purpose in {education,renovations}: yes (13/5.1)
## purpose = car:
## :...employment_duration in {< 1 year,> 7 years,
## : : 4 - 7 years}: yes (32/8.3)
## : employment_duration in {1 - 4 years,
## : unemployed}: no (24.9/9)
## purpose = furniture/appliances:
## :...months_loan_duration > 39: yes (4.8)
## months_loan_duration <= 39:
## :...phone = yes: yes (21.9/9.2)
## phone = no:
## :...employment_duration in {< 1 year,> 7 years,
## : 4 - 7 years}: no (34.1/8.1)
## employment_duration = unemployed: yes (3.3/0.4)
## employment_duration = 1 - 4 years:
## :...percent_of_income <= 1: yes (3.8)
## percent_of_income > 1:
## :...months_loan_duration > 21: no (4.9/0.4)
## months_loan_duration <= 21:
## :...years_at_residence <= 3: no (20.9/8.8)
## years_at_residence > 3: yes (5.8)
##
## ----- Trial 5: -----
##
## Decision tree:
##
## checking_balance = unknown:
## :...other_credit = store: yes (16.9/7.5)
## : other_credit = bank:
## : :...housing = other: no (8.3/1.8)
## : : housing = rent: yes (4.4/0.8)
## : : housing = own:
## : : :...phone = no: no (26.9/9.7)
## : : phone = yes: yes (12.1/5)
## : other_credit = none:
## : :...credit_history in {critical,perfect,very good}: no (60.4/5.1)
## : credit_history in {good,poor}:
## : :...purpose in {business,car,car0,education}: no (53.6/12.8)
## : purpose = renovations: yes (7.3/1.1)
## : purpose = furniture/appliances:
## : :...job = unemployed: no (0)
## : job in {management,unskilled}: yes (19.2/7)
## : job = skilled:
## : :...phone = yes: no (14.6/1.8)
## : phone = no:
## : :...age > 32: no (9.2)
## : age <= 32:
## : :...employment_duration = 1 - 4 years: no (4.1)
## : employment_duration in {< 1 year,> 7 years,
## : : 4 - 7 years,unemployed}:
## : :...savings_balance in {< 100 DM,
## : : 100 - 500 DM}: yes (20.5/3)
## : savings_balance in {> 1000 DM,500 - 1000 DM,
## : unknown}: no (3.4)
## checking_balance in {< 0 DM,> 200 DM,1 - 200 DM}:
## :...percent_of_income <= 2:
## :...amount > 11054: yes (14.2/1.2)
## : amount <= 11054:
## : :...other_credit = bank: no (32.3/9.7)
## : other_credit = store: yes (8.9/2.6)
## : other_credit = none:
## : :...purpose in {business,renovations}: yes (20.3/9.1)
## : purpose in {car0,education}: no (8.4/3.7)
## : purpose = car:
## : :...savings_balance in {< 100 DM,> 1000 DM,500 - 1000 DM,
## : : : unknown}: no (46.6/7.9)
## : : savings_balance = 100 - 500 DM: yes (13.8/3.3)
## : purpose = furniture/appliances:
## : :...employment_duration in {> 7 years,
## : : 4 - 7 years}: no (18.2/2.6)
## : employment_duration in {1 - 4 years,
## : : unemployed}: yes (50.8/19.5)
## : employment_duration = < 1 year:
## : :...job in {management,skilled,unemployed}: no (16.3/2.9)
## : job = unskilled: yes (6/1.6)
## percent_of_income > 2:
## :...years_at_residence <= 1:
## :...other_credit in {bank,store}: no (7.6)
## : other_credit = none:
## : :...months_loan_duration > 42: no (2.9)
## : months_loan_duration <= 42:
## : :...age <= 36: no (26.6/8.4)
## : age > 36: yes (5.3)
## years_at_residence > 1:
## :...job = unemployed: no (5.2)
## job in {management,skilled,unskilled}:
## :...credit_history = perfect: yes (10.9)
## credit_history in {critical,good,poor,very good}:
## :...employment_duration = < 1 year:
## :...checking_balance = > 200 DM: no (2.7)
## : checking_balance in {< 0 DM,1 - 200 DM}:
## : :...months_loan_duration > 21: yes (23.4/0.7)
## : months_loan_duration <= 21:
## : :...amount <= 1928: yes (18.4/4.4)
## : amount > 1928: no (4.5)
## employment_duration in {> 7 years,1 - 4 years,4 - 7 years,
## : unemployed}:
## :...months_loan_duration <= 11:
## :...age > 47: no (12.2)
## : age <= 47:
## : :...purpose in {business,car,car0,
## : : furniture/appliances,
## : : renovations}: no (25/9.2)
## : purpose = education: yes (3.5)
## months_loan_duration > 11:
## :...savings_balance in {> 1000 DM,100 - 500 DM}:
## :...age <= 58: no (22.7/3.4)
## : age > 58: yes (4.4)
## savings_balance in {< 100 DM,500 - 1000 DM,unknown}:
## :...years_at_residence <= 2: yes (76.1/22.8)
## years_at_residence > 2:
## :...purpose in {business,car0,
## : education}: yes (24.7/7.1)
## purpose = renovations: no (1.1)
## purpose = furniture/appliances: [S1]
## purpose = car:
## :...amount <= 1388: yes (17.8/2.2)
## amount > 1388:
## :...housing = own: no (10.9)
## housing in {other,rent}: [S2]
##
## SubTree [S1]
##
## employment_duration = unemployed: no (4.4)
## employment_duration in {> 7 years,1 - 4 years,4 - 7 years}:
## :...checking_balance = < 0 DM: yes (35.6/12.4)
## checking_balance in {> 200 DM,1 - 200 DM}: no (29/10.5)
##
## SubTree [S2]
##
## savings_balance in {< 100 DM,500 - 1000 DM}: yes (21.4/6.4)
## savings_balance = unknown: no (6.8/1.5)
##
## ----- Trial 6: -----
##
## Decision tree:
##
## checking_balance in {> 200 DM,unknown}:
## :...purpose = car0: no (2.2)
## : purpose = renovations: yes (8.4/3.3)
## : purpose = education:
## : :...age <= 44: yes (19.8/7.7)
## : : age > 44: no (4.4)
## : purpose = business:
## : :...existing_loans_count > 2: yes (3.3)
## : : existing_loans_count <= 2:
## : : :...amount <= 1823: no (8.1)
## : : amount > 1823:
## : : :...percent_of_income <= 3: no (12.1/3.3)
## : : percent_of_income > 3: yes (13.2/3.4)
## : purpose = car:
## : :...job in {management,unemployed}: no (20.8/1.6)
## : : job = unskilled:
## : : :...years_at_residence <= 3: no (11/1.3)
## : : : years_at_residence > 3: yes (14.5/3.2)
## : : job = skilled:
## : : :...other_credit in {bank,store}: yes (17.6/4.9)
## : : other_credit = none:
## : : :...existing_loans_count <= 2: no (24.6)
## : : existing_loans_count > 2: yes (2.4/0.3)
## : purpose = furniture/appliances:
## : :...age > 44: no (22.7)
## : age <= 44:
## : :...job = unemployed: no (0)
## : job = unskilled:
## : :...existing_loans_count <= 1: yes (20.9/5.6)
## : : existing_loans_count > 1: no (4.5)
## : job in {management,skilled}:
## : :...dependents > 1: no (6.6)
## : dependents <= 1:
## : :...existing_loans_count <= 1:
## : :...savings_balance in {> 1000 DM,100 - 500 DM,
## : : : 500 - 1000 DM,
## : : : unknown}: no (16.9)
## : : savings_balance = < 100 DM:
## : : :...age <= 22: yes (8.5/1.3)
## : : age > 22: no (43.1/8.8)
## : existing_loans_count > 1:
## : :...housing in {other,rent}: yes (9.9/2.1)
## : housing = own:
## : :...credit_history in {critical,poor,
## : : very good}: no (18.6/1.6)
## : credit_history in {good,perfect}: yes (14.9/4.3)
## checking_balance in {< 0 DM,1 - 200 DM}:
## :...credit_history = perfect: yes (28.1/9.6)
## credit_history = very good:
## :...age <= 23: no (5.5)
## : age > 23: yes (30/8.1)
## credit_history = poor:
## :...percent_of_income <= 1: no (6.5)
## : percent_of_income > 1:
## : :...savings_balance in {500 - 1000 DM,unknown}: no (6.4)
## : savings_balance in {< 100 DM,> 1000 DM,100 - 500 DM}:
## : :...dependents <= 1: yes (25.1/8)
## : dependents > 1: no (5/0.9)
## credit_history = critical:
## :...savings_balance = unknown: no (8.4)
## : savings_balance in {< 100 DM,> 1000 DM,100 - 500 DM,500 - 1000 DM}:
## : :...other_credit = bank: yes (16.2/4.3)
## : other_credit = store: no (3.7/0.9)
## : other_credit = none:
## : :...savings_balance in {> 1000 DM,500 - 1000 DM}: yes (7.3/2.3)
## : savings_balance = 100 - 500 DM: no (5.9)
## : savings_balance = < 100 DM:
## : :...purpose = business: no (4.5/2.2)
## : purpose in {car0,education,renovations}: yes (8.5/2.2)
## : purpose = car:
## : :...age <= 29: yes (6.9)
## : : age > 29: no (25.6/6.9)
## : purpose = furniture/appliances:
## : :...months_loan_duration <= 36: no (38.4/10.9)
## : months_loan_duration > 36: yes (3.8)
## credit_history = good:
## :...amount > 8086: yes (24/3.8)
## amount <= 8086:
## :...phone = yes:
## :...age <= 28: yes (23.9/7.5)
## : age > 28: no (69.4/17.9)
## phone = no:
## :...other_credit in {bank,store}: yes (25.1/7.2)
## other_credit = none:
## :...percent_of_income <= 2:
## :...job in {management,unemployed,unskilled}: no (15.6/2.7)
## : job = skilled:
## : :...amount <= 1386: yes (9.9/1)
## : amount > 1386:
## : :...age <= 24: yes (13.4/4.6)
## : age > 24: no (27.8/3.1)
## percent_of_income > 2:
## :...checking_balance = < 0 DM: yes (62.5/21.4)
## checking_balance = 1 - 200 DM:
## :...months_loan_duration > 42: yes (4.9)
## months_loan_duration <= 42:
## :...existing_loans_count > 1: no (5)
## existing_loans_count <= 1:
## :...age <= 35: no (39.4/13.2)
## age > 35: yes (14.7/4.2)
##
## ----- Trial 7: -----
##
## Decision tree:
##
## checking_balance = unknown:
## :...employment_duration in {> 7 years,4 - 7 years}: no (101.1/20.4)
## : employment_duration = unemployed: yes (16.6/8)
## : employment_duration = < 1 year:
## : :...amount <= 4594: no (30/5.7)
## : : amount > 4594: yes (10.6/0.3)
## : employment_duration = 1 - 4 years:
## : :...dependents > 1: no (8)
## : dependents <= 1:
## : :...months_loan_duration <= 16: no (32.8/5.3)
## : months_loan_duration > 16:
## : :...existing_loans_count > 2: yes (2.7)
## : existing_loans_count <= 2:
## : :...percent_of_income <= 3: no (20.9/5.9)
## : percent_of_income > 3:
## : :...purpose in {business,car0,education}: yes (10.8)
## : purpose in {car,furniture/appliances,
## : renovations}: no (19.7/7.5)
## checking_balance in {< 0 DM,> 200 DM,1 - 200 DM}:
## :...purpose in {car0,education,renovations}: no (67.2/29.2)
## purpose = business:
## :...age > 46: yes (5.2)
## : age <= 46:
## : :...months_loan_duration <= 18: no (17.5)
## : months_loan_duration > 18:
## : :...other_credit in {bank,store}: no (10/0.5)
## : other_credit = none:
## : :...employment_duration in {> 7 years,
## : : unemployed}: yes (6.6)
## : employment_duration in {< 1 year,1 - 4 years,4 - 7 years}:
## : :...age <= 25: yes (4)
## : age > 25: no (19.2/5.6)
## purpose = car:
## :...amount <= 1297: yes (52.4/12.9)
## : amount > 1297:
## : :...percent_of_income <= 2:
## : :...phone = no: no (32.7/6.1)
## : : phone = yes:
## : : :...years_at_residence <= 3: no (20/4.9)
## : : years_at_residence > 3: yes (14.7/3.8)
## : percent_of_income > 2:
## : :...percent_of_income <= 3: yes (33.1/11.3)
## : percent_of_income > 3:
## : :...months_loan_duration <= 18: no (18.2/1.6)
## : months_loan_duration > 18:
## : :...existing_loans_count <= 1: no (19.5/7.2)
## : existing_loans_count > 1: yes (13.8/1)
## purpose = furniture/appliances:
## :...savings_balance = > 1000 DM: no (5.2)
## savings_balance = 100 - 500 DM: yes (18.6/6)
## savings_balance in {< 100 DM,500 - 1000 DM,unknown}:
## :...existing_loans_count > 1:
## :...existing_loans_count > 2: no (3.6)
## : existing_loans_count <= 2:
## : :...housing = other: yes (3.3)
## : housing in {own,rent}:
## : :...savings_balance = 500 - 1000 DM: yes (3.5/1)
## : savings_balance = unknown: no (6.9)
## : savings_balance = < 100 DM:
## : :...age > 54: yes (2.1)
## : age <= 54: [S1]
## existing_loans_count <= 1:
## :...credit_history in {critical,perfect}: yes (20.3/7.6)
## credit_history in {poor,very good}: no (20.8/9.5)
## credit_history = good:
## :...months_loan_duration <= 7: no (11.4)
## months_loan_duration > 7:
## :...other_credit = bank: no (14.2/4.6)
## other_credit = store: yes (11.7/3.9)
## other_credit = none:
## :...percent_of_income <= 1: no (20.5/5.2)
## percent_of_income > 1:
## :...amount > 6078: yes (10.9/1.1)
## amount <= 6078:
## :...dependents > 1: yes (8.7/2.5)
## dependents <= 1: [S2]
##
## SubTree [S1]
##
## employment_duration in {< 1 year,4 - 7 years}: yes (15/2.5)
## employment_duration in {> 7 years,1 - 4 years,unemployed}: no (25.7/2.9)
##
## SubTree [S2]
##
## employment_duration = > 7 years: no (17.9/2.5)
## employment_duration in {< 1 year,1 - 4 years,4 - 7 years,unemployed}:
## :...job = management: no (6.6)
## job = unemployed: yes (1.1)
## job in {skilled,unskilled}:
## :...years_at_residence <= 1: no (11.8/1.8)
## years_at_residence > 1:
## :...checking_balance = > 200 DM: no (14.7/6.3)
## checking_balance = 1 - 200 DM: yes (25.1/8.8)
## checking_balance = < 0 DM:
## :...months_loan_duration <= 16: no (13.8/3.4)
## months_loan_duration > 16: yes (19.1/5.5)
##
## ----- Trial 8: -----
##
## Decision tree:
##
## checking_balance in {< 0 DM,1 - 200 DM}:
## :...credit_history = perfect:
## : :...housing in {other,rent}: yes (8.3)
## : : housing = own:
## : : :...age <= 34: no (16.6/4.7)
## : : age > 34: yes (5.8)
## : credit_history = poor:
## : :...checking_balance = < 0 DM: yes (12/2.7)
## : : checking_balance = 1 - 200 DM:
## : : :...housing = rent: no (8.6)
## : : housing in {other,own}:
## : : :...amount <= 2279: yes (6.8/0.6)
## : : amount > 2279: no (20/5.7)
## : credit_history = very good:
## : :...existing_loans_count > 1: yes (2.5)
## : : existing_loans_count <= 1:
## : : :...age <= 23: no (3.7)
## : : age > 23:
## : : :...amount <= 8386: yes (32.9/8.1)
## : : amount > 8386: no (2.5)
## : credit_history = critical:
## : :...years_at_residence <= 1: no (8)
## : : years_at_residence > 1:
## : : :...savings_balance in {> 1000 DM,100 - 500 DM,500 - 1000 DM,
## : : : unknown}: no (25.5/5.7)
## : : savings_balance = < 100 DM:
## : : :...age > 61: no (6)
## : : age <= 61:
## : : :...existing_loans_count > 2: no (10.7/2.4)
## : : existing_loans_count <= 2:
## : : :...age > 56: yes (5.4)
## : : age <= 56:
## : : :...amount > 2483: yes (34.1/8.9)
## : : amount <= 2483:
## : : :...purpose in {business,education}: yes (4.4)
## : : purpose in {car,car0,furniture/appliances,
## : : renovations}: no (41.4/10.8)
## : credit_history = good:
## : :...amount > 8086: yes (26.6/4.8)
## : amount <= 8086:
## : :...savings_balance in {> 1000 DM,500 - 1000 DM}: no (17.5/5.1)
## : savings_balance = 100 - 500 DM:
## : :...months_loan_duration <= 27: no (21.3/7.1)
## : : months_loan_duration > 27: yes (5.1)
## : savings_balance = unknown:
## : :...age <= 56: yes (44.7/16.9)
## : : age > 56: no (4.4)
## : savings_balance = < 100 DM:
## : :...job = unemployed: yes (0.9)
## : job = management:
## : :...employment_duration in {< 1 year,1 - 4 years,4 - 7 years,
## : : : unemployed}: no (17.3/1.6)
## : : employment_duration = > 7 years: yes (8/1.2)
## : job = unskilled:
## : :...months_loan_duration <= 26: no (59/19.7)
## : : months_loan_duration > 26: yes (3.3)
## : job = skilled:
## : :...purpose in {business,car0,education,
## : : renovations}: yes (16.6/4.1)
## : purpose = car:
## : :...dependents <= 1: yes (27.7/10.6)
## : : dependents > 1: no (8.1/1.4)
## : purpose = furniture/appliances:
## : :...years_at_residence <= 1: no (18.7/6.5)
## : years_at_residence > 1:
## : :...other_credit = bank: yes (4.5)
## : other_credit = store: no (2.3)
## : other_credit = none:
## : :...percent_of_income <= 3: yes (33.5/15)
## : percent_of_income > 3: no (27.3/9.3)
## checking_balance in {> 200 DM,unknown}:
## :...years_at_residence > 2: no (135.6/32.2)
## years_at_residence <= 2:
## :...months_loan_duration <= 8: no (12.9)
## months_loan_duration > 8:
## :...months_loan_duration <= 9: yes (10.4/1.3)
## months_loan_duration > 9:
## :...months_loan_duration <= 16: no (31.3/4.2)
## months_loan_duration > 16:
## :...purpose in {business,car0,renovations}: no (21.3/8.4)
## purpose = education: yes (6.3/0.8)
## purpose = car:
## :...credit_history in {critical,very good}: yes (17.3/2.6)
## : credit_history in {good,perfect,poor}: no (9.6)
## purpose = furniture/appliances:
## :...credit_history in {critical,perfect,
## : very good}: no (5.6)
## credit_history = poor: yes (4.9)
## credit_history = good:
## :...housing in {other,rent}: no (2.6)
## housing = own:
## :...age <= 25: no (6.8)
## age > 25: yes (29.2/10.2)
##
## ----- Trial 9: -----
##
## Decision tree:
##
## checking_balance = unknown:
## :...dependents > 1: no (26)
## : dependents <= 1:
## : :...amount <= 1474: no (39.7)
## : amount > 1474:
## : :...employment_duration in {> 7 years,4 - 7 years}:
## : :...years_at_residence > 2: no (21.8)
## : : years_at_residence <= 2:
## : : :...age <= 23: yes (4.1)
## : : age > 23: no (19.7/4.2)
## : employment_duration in {< 1 year,1 - 4 years,unemployed}:
## : :...purpose in {business,renovations}: yes (23.2/3.6)
## : purpose in {car,car0,education,furniture/appliances}:
## : :...other_credit in {bank,store}: yes (29.1/10.5)
## : other_credit = none:
## : :...purpose in {car,car0}: no (12.3)
## : purpose in {education,furniture/appliances}:
## : :...amount <= 4455: no (23.7/4.4)
## : amount > 4455: yes (11.1/1.3)
## checking_balance in {< 0 DM,> 200 DM,1 - 200 DM}:
## :...percent_of_income <= 2:
## :...amount > 11054: yes (15.7/3.6)
## : amount <= 11054:
## : :...savings_balance in {> 1000 DM,500 - 1000 DM,
## : : unknown}: no (41.5/11.2)
## : savings_balance = 100 - 500 DM:
## : :...other_credit = bank: no (5.1)
## : : other_credit in {none,store}: yes (21.7/9.4)
## : savings_balance = < 100 DM:
## : :...employment_duration in {> 7 years,unemployed}: no (34.6/11.5)
## : employment_duration = 1 - 4 years:
## : :...job = management: yes (5.1/0.8)
## : : job in {skilled,unemployed,unskilled}: no (65.4/15.8)
## : employment_duration = < 1 year:
## : :...amount <= 2327:
## : : :...age <= 34: yes (20.5/1.9)
## : : : age > 34: no (3)
## : : amount > 2327:
## : : :...other_credit = bank: yes (2.8)
## : : other_credit in {none,store}: no (20.1/3.9)
## : employment_duration = 4 - 7 years:
## : :...dependents > 1: no (4.6)
## : dependents <= 1:
## : :...amount <= 6527: no (16.8/7.2)
## : amount > 6527: yes (7)
## percent_of_income > 2:
## :...housing = rent:
## :...checking_balance in {< 0 DM,1 - 200 DM}: yes (69/22.1)
## : checking_balance = > 200 DM: no (3.4)
## housing = other:
## :...existing_loans_count > 1: yes (18.7/5.3)
## : existing_loans_count <= 1:
## : :...savings_balance in {< 100 DM,> 1000 DM,
## : : 500 - 1000 DM}: yes (29.1/8.6)
## : savings_balance in {100 - 500 DM,unknown}: no (15.3/3.2)
## housing = own:
## :...credit_history in {perfect,poor}: yes (26.9/7.4)
## credit_history = very good: no (14.9/5.6)
## credit_history = critical:
## :...other_credit = bank: yes (11.7/3.4)
## : other_credit in {none,store}: no (63/20.3)
## credit_history = good:
## :...other_credit = store: yes (8.9/1.4)
## other_credit in {bank,none}:
## :...age > 54: no (9.5)
## age <= 54:
## :...existing_loans_count > 1: no (10.2/2.7)
## existing_loans_count <= 1:
## :...purpose in {business,renovations}: no (10.1/3.6)
## purpose in {car0,education}: yes (4.7)
## purpose = car:
## :...other_credit = bank: yes (4.9)
## : other_credit = none:
## : :...years_at_residence > 2: no (14.8/4.5)
## : years_at_residence <= 2:
## : :...amount <= 2150: no (14.9/6.2)
## : amount > 2150: yes (11.1)
## purpose = furniture/appliances:
## :...savings_balance = 100 - 500 DM: yes (3.8)
## savings_balance in {> 1000 DM,
## : 500 - 1000 DM}: no (2.8)
## savings_balance in {< 100 DM,unknown}:
## :...months_loan_duration > 39: yes (3.3)
## months_loan_duration <= 39:
## :...dependents <= 1: no (57.6/19.4)
## dependents > 1: yes (4.6/1.1)
##
##
## Evaluation on training data (900 cases):
##
## Trial Decision Tree
## ----- ----------------
## Size Errors
##
## 0 56 133(14.8%)
## 1 34 211(23.4%)
## 2 39 201(22.3%)
## 3 47 179(19.9%)
## 4 46 174(19.3%)
## 5 50 197(21.9%)
## 6 55 187(20.8%)
## 7 50 190(21.1%)
## 8 51 192(21.3%)
## 9 47 169(18.8%)
## boost 34( 3.8%) <<
##
##
## (a) (b) <-classified as
## ---- ----
## 629 4 (a): class no
## 30 237 (b): class yes
##
##
## Attribute usage:
##
## 100.00% checking_balance
## 100.00% purpose
## 97.11% years_at_residence
## 96.67% employment_duration
## 94.78% credit_history
## 94.67% other_credit
## 92.56% job
## 92.11% percent_of_income
## 90.33% amount
## 85.11% months_loan_duration
## 82.78% age
## 82.78% existing_loans_count
## 75.78% dependents
## 71.56% housing
## 70.78% savings_balance
## 49.22% phone
##
##
## Time: 0.1 secsIn the boosted model, accuracy improved to 82%. Furthermore, number of the actual default loans in the test dataset are labeled as not default by the decision tree decreased from 19 to 13. However, 13/33 error rate is still high for a credit risk prediction model.
credit_boost_pred10 <- predict(credit_boost10, credit_test)
CrossTable(credit_test$default, credit_boost_pred10,
prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
dnn = c('actual default', 'predicted default'))##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 100
##
##
## | predicted default
## actual default | no | yes | Row Total |
## ---------------|-----------|-----------|-----------|
## no | 62 | 5 | 67 |
## | 0.620 | 0.050 | |
## ---------------|-----------|-----------|-----------|
## yes | 13 | 20 | 33 |
## | 0.130 | 0.200 | |
## ---------------|-----------|-----------|-----------|
## Column Total | 75 | 25 | 100 |
## ---------------|-----------|-----------|-----------|
##
## Since it is more costly giving a loan out to an applicant who will default than not giving the loan to the safe customers, we can assign a penalty to different types of errors and prevent tree from making more costly mistakes.
# create dimensions for a cost matrix
matrix_dimensions <- list(c("no", "yes"), c("no", "yes"))
names(matrix_dimensions) <- c("predicted", "actual")
matrix_dimensions## $predicted
## [1] "no" "yes"
##
## $actual
## [1] "no" "yes"# build the matrix
error_cost <- matrix(c(0, 1, 4, 0), nrow = 2, dimnames = matrix_dimensions)
error_cost## actual
## predicted no yes
## no 0 4
## yes 1 0# apply the cost matrix to the tree
credit_cost <- C5.0(credit_train[-17], credit_train$default,
costs = error_cost)
credit_cost_pred <- predict(credit_cost, credit_test)Compared to our boosted model, new model’s accuracy rate is worse (63%). However, in the revised model the percentage of false negatives (7%) are far more smaller at the expense of increased false positives (30%).
CrossTable(credit_test$default, credit_cost_pred,
prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
dnn = c('actual default', 'predicted default'))##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 100
##
##
## | predicted default
## actual default | no | yes | Row Total |
## ---------------|-----------|-----------|-----------|
## no | 37 | 30 | 67 |
## | 0.370 | 0.300 | |
## ---------------|-----------|-----------|-----------|
## yes | 7 | 26 | 33 |
## | 0.070 | 0.260 | |
## ---------------|-----------|-----------|-----------|
## Column Total | 44 | 56 | 100 |
## ---------------|-----------|-----------|-----------|
##
##