Identifying Risky Bank Loans
getwd()## [1] "C:/Users/Sferg/OneDrive/Desktop/JABSOM Grad School/Machine Learning/Unit 5 - Decision Trees/ML_Decision-Trees"credit <- read.csv("credit.csv", stringsAsFactors = TRUE)
str(credit)## 'data.frame': 1000 obs. of 17 variables:
## $ checking_balance : Factor w/ 4 levels "< 0 DM","> 200 DM",..: 1 3 4 1 1 4 4 3 4 3 ...
## $ months_loan_duration: int 6 48 12 42 24 36 24 36 12 30 ...
## $ credit_history : Factor w/ 5 levels "critical","good",..: 1 2 1 2 4 2 2 2 2 1 ...
## $ purpose : Factor w/ 6 levels "business","car",..: 5 5 4 5 2 4 5 2 5 2 ...
## $ amount : int 1169 5951 2096 7882 4870 9055 2835 6948 3059 5234 ...
## $ savings_balance : Factor w/ 5 levels "< 100 DM","> 1000 DM",..: 5 1 1 1 1 5 4 1 2 1 ...
## $ employment_duration : Factor w/ 5 levels "< 1 year","> 7 years",..: 2 3 4 4 3 3 2 3 4 5 ...
## $ percent_of_income : int 4 2 2 2 3 2 3 2 2 4 ...
## $ years_at_residence : int 4 2 3 4 4 4 4 2 4 2 ...
## $ age : int 67 22 49 45 53 35 53 35 61 28 ...
## $ other_credit : Factor w/ 3 levels "bank","none",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ housing : Factor w/ 3 levels "other","own",..: 2 2 2 1 1 1 2 3 2 2 ...
## $ existing_loans_count: int 2 1 1 1 2 1 1 1 1 2 ...
## $ job : Factor w/ 4 levels "management","skilled",..: 2 2 4 2 2 4 2 1 4 1 ...
## $ dependents : int 1 1 2 2 2 2 1 1 1 1 ...
## $ phone : Factor w/ 2 levels "no","yes": 2 1 1 1 1 2 1 2 1 1 ...
## $ default : Factor w/ 2 levels "no","yes": 1 2 1 1 2 1 1 1 1 2 ...# look at the applicant's account
# look at the applicant’s account
table(credit$checking_balance)##
## < 0 DM > 200 DM 1 - 200 DM unknown
## 274 63 269 394table(credit$savings_balance)##
## < 100 DM > 1000 DM 100 - 500 DM 500 - 1000 DM unknown
## 603 48 103 63 183# look at two characteristics of the loan
summary(credit$months_loan_duration)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.0 12.0 18.0 20.9 24.0 72.0summary(credit$amount)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 250 1366 2320 3271 3972 18424# look at the class variable
table(credit$default)##
## no yes
## 700 300A total of 30% of these loans went into default. Ouch.
Create a random sample for training and test data (90% and 10% of data for training and testing respectively)
RNGversion("3.5.2")## Warning in RNGkind("Mersenne-Twister", "Inversion", "Rounding"): non-uniform
## 'Rounding' sampler usedset.seed(123) # to use the same random number sequence
train_sample <- sample(1000, 900)
str(train_sample)## int [1:900] 288 788 409 881 937 46 525 887 548 453 ...# split the data frames
credit_train <- credit[train_sample, ]
credit_test <- credit[-train_sample, ]
# check the proportion of class variable
prop.table(table(credit_train$default))##
## no yes
## 0.7033333 0.2966667prop.table(table(credit_test$default))##
## no yes
## 0.67 0.33The training data and test data now have similar distributions. But if it’s random, I don’t understand how I always get the same distribution of yes/no. They should be similar, but not always identical, right?
Use the C5.0 Algorithm in the C50 package to train our decision tree model
# build the simplest decision tree
# install.packages("C50")
library(C50)
credit_model <- C5.0(credit_train[-17], credit_train$default)
# display simple facts about the tree
credit_model##
## Call:
## C5.0.default(x = credit_train[-17], y = credit_train$default)
##
## Classification Tree
## Number of samples: 900
## Number of predictors: 16
##
## Tree size: 57
##
## Non-standard options: attempt to group attributesWhy is the training data frame -17? I understand there are 17 variables, but why negative?
# display detailed information about the tree
summary(credit_model)##
## Call:
## C5.0.default(x = credit_train[-17], y = credit_train$default)
##
##
## C5.0 [Release 2.07 GPL Edition] Mon Sep 26 09:32:13 2022
## -------------------------------
##
## 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 secsUsing the “Evaluation on training data” section, we see the model correctly classified all but 133 of the 900 training instances. 35 were actual no values that were misclassified as yes (false positive). 98 were actually yes but misclassified as no (false negative) 98+35=133. 133/900= 0.0148. Therefore it had an error rate of 14.8*%
Decision trees are known for having a tendency to overfit the model to the training data.
For this reason, the error rate reported on training data may be overly optimistic, and it is especially important to evaluate decision trees on a test dataset.
To apply our decision tree to the test dataset, we use the predict()
This creates a vector of predicted class values, which we can compare to the actual class values using the CrossTable() function in the gmodels package.
# create a factor vector of predictions on test data
credit_pred <- predict(credit_model, credit_test)
# cross tabulation of predicted versus actual classes
library(gmodels)
CrossTable(credit_test$default, credit_pred,
prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
dnn = c('actual default', 'predicted default'))##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 100
##
##
## | predicted default
## actual default | no | yes | Row Total |
## ---------------|-----------|-----------|-----------|
## no | 59 | 8 | 67 |
## | 0.590 | 0.080 | |
## ---------------|-----------|-----------|-----------|
## yes | 19 | 14 | 33 |
## | 0.190 | 0.140 | |
## ---------------|-----------|-----------|-----------|
## Column Total | 78 | 22 | 100 |
## ---------------|-----------|-----------|-----------|
##
## 100 total test loan applications.
Correct calls by the model (TP, TN): 59 did not default 14 did default. Therefore, accuracy of 73%, Error Rate of 27%
Incorrect Calls by the model (FP, FN) Unfortunately, the model predicted 19 borrowers would not default, but they actually did default (FN). That’s a very costly mistake in this context. This model must be tweaked.
This error rate would be unacceptable in this context. We must adjust the C5.0 algorithm to improve the model so that we minimize unpredicted defaults.
Adaptive Boosting Process in which trees vote on best class (for example) Add trials parameter, indicating # of separate decision trees to use in boosted team Trials parameter sets upper limit algorithm stops adding trees if it sees that additional trials do not seem to be improving accuracy
# boosted decision tree with 10 trials
credit_boost10 <- C5.0(credit_train[-17], credit_train$default, trials = 10)
credit_boost10##
## Call:
## C5.0.default(x = credit_train[-17], y = credit_train$default, trials = 10)
##
## Classification Tree
## Number of samples: 900
## Number of predictors: 16
##
## Number of boosting iterations: 10
## Average tree size: 47.5
##
## Non-standard options: attempt to group attributessummary(credit_boost10)##
## Call:
## C5.0.default(x = credit_train[-17], y = credit_train$default, trials = 10)
##
##
## C5.0 [Release 2.07 GPL Edition] Mon Sep 26 09:32:13 2022
## -------------------------------
##
## 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 secsThis outputted 10 iterations of a decision tree. Tree trunk size shrunk across the 10 iterations (9 being the smallest, it starts counting at trial (tree) 0).
Okay, so collectively, the 10 trees take all of their knowledge and combine it into the boosted model. The boosted model learns from the mistakes of the 10 models before it. The boosted model had an incredible improvement in error rate: 3.8% opposed to the prior error rate of 27%!
I see this is much more computationally intensive, but this is a huge improvement.
False negatives are much more costly that false positives in this context. It’s really not a bad thing if you predict a borrower will default and it doesn’t. Well, the bank gets to keep its money, it doesn’t lose any money. Sure, it may be a missed opportunity, but the consequences here are minimal.
But what happens if the bank approves a borrower because the bank predicts the borrower will not default? And then the borrower defaults. The bank is SOL a lot of money. Perhaps we can reduce even more false positives by tweaking our model more.
I think we’re about to reduce number of false negatives at the expense of the model’s accuracy regarding false positives.
Making mistakes costlier than others Our penalty values could be defined as:
# 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 |
## ---------------|-----------|-----------|-----------|
##
## I was right. We allowed for more false positives (increased from 5% to 30% FP) in order to reduce the costly false negatives(13% to 7%). In this context, more false positives (more missed opportunities) might be acceptable in order to reduce the false negatives.