Step 1: Collecting the data:

The credit data is from the UCI Machine Learning Data Repository. Note that the data is from Germany and the currency is in Deutsche Marks (DM).

Step 2: Exploring and preparing the data:

credit <- read.csv(file="credit.csv")
cannot open file 'credit.csv': No such file or directoryError in file(file, "rt") : cannot open the connection

look at two characteristics of the applicant

table(credit$checking_balance)

    < 0 DM   > 200 DM 1 - 200 DM    unknown 
       274         63        269        394 
table(credit$savings_balance)

     < 100 DM     > 1000 DM  100 - 500 DM 
          603            48           103 
500 - 1000 DM       unknown 
           63           183 

look at two characteristics of the loan

summary(credit$months_loan_duration)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    4.0    12.0    18.0    20.9    24.0    72.0 
summary(credit$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 0.2966667 
prop.table(table(credit_test$default))

  no  yes 
0.67 0.33 

Step 3: Training a model on the data:

build the simplest decision tree exclude the 17th column:default

library(C50)
credit_model <- C5.0(credit_train[-17], credit_train$default)

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 attributes

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]     Mon Apr 24 17:20:43 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

Step 4: Evaluating model performance:

create a factor vector of predictions on test data

credit_pred <- predict(credit_model, credit_test)
credit_pred
  [1] no  no  no  yes no  no  no  no  yes yes yes no 
 [13] no  no  no  no  yes yes no  no  no  no  no  yes
 [25] no  yes no  no  yes no  no  no  no  no  no  yes
 [37] yes no  no  no  no  no  no  no  no  no  no  no 
 [49] no  yes no  yes no  no  no  yes no  no  no  no 
 [61] no  no  yes no  yes yes no  no  yes no  no  no 
 [73] no  no  yes no  no  no  no  no  no  no  no  yes
 [85] no  no  no  no  no  no  no  no  no  no  no  no 
 [97] no  yes yes no 
Levels: no yes

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 | 
---------------|-----------|-----------|-----------|

 

Accuracy=(59+14)/100=73%

Step 5: Improving model performance:

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 attributes
summary(credit_boost10)

Call:
C5.0.default(x = credit_train[-17], y
 = credit_train$default, trials = 10)


C5.0 [Release 2.07 GPL Edition]     Mon Apr 24 17:28:50 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 secs
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 | 
---------------|-----------|-----------|-----------|

 
credit_boost_pred10
  [1] no  no  no  yes no  no  no  no  yes no  yes no 
 [13] no  no  no  yes yes yes no  no  no  no  no  no 
 [25] no  yes no  no  yes no  no  no  no  no  no  yes
 [37] yes no  no  no  no  yes no  no  no  no  no  yes
 [49] no  yes no  yes no  yes no  yes no  no  no  no 
 [61] no  no  yes no  yes no  no  no  yes no  no  no 
 [73] no  no  yes no  yes no  no  no  no  no  yes yes
 [85] no  no  yes no  no  no  no  no  no  no  no  no 
 [97] no  yes no  no 
Levels: no yes

Accuracy after boosting=(62+20)/100=82% The performance is being improved using boosting.

Making some mistakes more costly than others

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$default,
                    costs = error_cost)
credit_cost_pred <- predict(credit_cost, credit_test)
CrossTable(credit_test$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 | 
---------------|-----------|-----------|-----------|

 
credit_cost_pred
  [1] no  no  yes yes no  yes no  yes yes yes yes yes
 [13] no  no  no  yes yes yes yes no  no  no  no  no 
 [25] yes yes no  no  yes no  no  yes no  yes no  yes
 [37] yes yes no  no  yes no  no  yes yes yes yes yes
 [49] no  no  yes yes no  yes no  yes no  yes no  no 
 [61] no  yes yes no  yes yes no  no  yes yes no  yes
 [73] yes yes yes no  yes yes yes yes yes yes yes yes
 [85] no  no  yes no  yes no  no  yes yes yes yes no 
 [97] no  yes no  no 
Levels: no yes

Accuracy after making some mistakes more costly: (37+26)/100=63%

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