This is a simple credit approval model based on decision trees. It decides whether an applicant’s credit should be approved or declined base on their collected information. Information includes pass loans and other information which will be used to predict the likelihood of a loan will go into default.
Dataset is donated by UCI Machine Learning Data Repository and can be downloaded at http://archive.ics.uci.edu/ml . The loans information is collected by a Germany credit agency. Dataset has been modified from original dataset so that it is easier to work with in R.
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 ...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 500 - 1000 DM unknown
603 48 103 63 183 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 table(credit$default) # 300 out of 1000 loans were defaulted
no yes
700 300 set.seed(123) # '123' is just some arbitary value
train_sample <- sample(1000, 900)
str(train_sample) int [1:900] 288 788 409 881 937 46 525 887 548 453 ...credit_train <- credit[train_sample, ] # create train dataset by subsetting original dataset using rows generated above
credit_test <- credit[-train_sample, ] # create test dataset using the remaining rows
# due to random splitting, there should be about 30% of defaulted loans in each train and test dataset
prop.table(table(credit_train$default))
no yes
0.7033333 0.2966667 prop.table(table(credit_test$default))
no yes
0.67 0.33 The Decision Trees model we use is from ‘C50’ package. We need to install and load it into memory.
#install.packages("C50")
library(C50)
credit_model <- C5.0(credit_train[ ,-17], credit_train$default) # train the decision tree model; exclude 17th column which contains the class labels
summary(credit_model)
Call:
C5.0.default(x = credit_train[, -17], y = credit_train$default)
C5.0 [Release 2.07 GPL Edition] Fri Dec 30 20:31:14 2016
-------------------------------
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 secscredit_pred <- predict(credit_model, credit_test[-17])
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 |
---------------|-----------|-----------|-----------|
==> As we can see, our decision tree correctly predicted 59 + 14 = 73 cases out of 100 test cases with an accuracy of 73%, and incorrectly predicted 19 + 8 = 27 (or 27%) of test cases. In the real world, this inaccuracy can be costly, our model only correctly predict 14/ 33 (42.4%) loans that will actually go into default. This will cost the banks money!!! We need to improve our decision trees model to increase its accuracy at identifying loans that will go into default.
credit_bost10 <- C5.0(credit_train[-17], credit_train$default, trial = 10)summary(credit_bost10)
Call:
C5.0.default(x = credit_train[-17], y = credit_train$default, trials = 10)
C5.0 [Release 2.07 GPL Edition] Fri Dec 30 20:31:15 2016
-------------------------------
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==> By setting trials = 10, the algorithm performed 10 boosting iterations.
credit_boost_pred10 <- predict(credit_bost10, credit_test[-17])
CrossTable(credit_test$default, credit_boost_pred10, prop.chisq = FALSE, prop.r = FALSE, prop.c = FALSE, dnn = c("Actual default", "Predicted default"))
Cell Contents
|-------------------------|
| N |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| Predicted default
Actual default | no | yes | Row Total |
---------------|-----------|-----------|-----------|
no | 62 | 5 | 67 |
| 0.620 | 0.050 | |
---------------|-----------|-----------|-----------|
yes | 13 | 20 | 33 |
| 0.130 | 0.200 | |
---------------|-----------|-----------|-----------|
Column Total | 75 | 25 | 100 |
---------------|-----------|-----------|-----------|
==> We can see that by boosting the model by setting trials = 10, our model improve quite bit. The number of defaulted loans being correctly classified as “default” went up from 14 out of 33 (= 42.4%) to 20 out of 33 (= 60%), and the number of not defaulted loans being correctly classified as “not default” went up from 59 out of 67 (= 88.1%) to 62 out of 67 (= 92.5%). This shows that our decision trees model’s accuracy with trails = 10 significantly quite a bit!
matrix_dimensions <- list(c("no", "yes"), c("no", "yes"))
names(matrix_dimensions) <- c("predicted", "actual")
matrix_dimensions$predicted
[1] "no" "yes"
$actual
[1] "no" "yes"error_cost <- matrix(c(0, 1, 4, 0), nrow = 2, dimnames = matrix_dimensions) # create an error cost matrix
error_cost actual
predicted no yes
no 0 4
yes 1 0credit_cost <- C5.0(credit_train[-17], credit_train$default, costs = error_cost)
credit_cost_pred <- predict(credit_cost, credit_test[-17])
CrossTable(credit_test$default, credit_cost_pred, prop.chisq = FALSE, prop.r = FALSE, prop.c = 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 |
---------------|-----------|-----------|-----------|
==> Compare to our boosted model, by giving our model a cost matrix which punish false positive prediction, we are able to reduce the number of actually defaulted loans misclassified as “not likely to default” ( = 78.8% accuracy for identifying defaulted loans), however, the number of not defaulted loans misclassified as “likely to default” increases from 5 to 30 cases (92.5% accuracy down to 44.8% accuracy for identifying not defaulted loans). This is a trade off that we have to deal with; the more accurate it is at identifying defaulted loans, the less accurate it is at identifying not defaulted loans and vice versa!