Chapter 5 - R Notebook
Chapter 5: Classification using Decision Trees and Rules
Part 1: Decision Trees
Understanding Decision Trees
Calculate entropy of a two-class segment
-0.60 * log2(0.60) - 0.40 * log2(0.40)[1] 0.9709506curve(-x * log2(x) - (1 - x) * log2(1 - x),
col = "red", xlab = "x", ylab = "Entropy", lwd = 4)
Example: Identifying Risky Bank Loans
Step 1: Download the data
Since the data has alreay been downloaded in the R Project there is no need to download again. But note that downloading a .csv can be done by using the following code.
# URL <- "http://cox.csueastbay.edu/~esuess/classes/Statistics_452/Presentations/ml07a/credit.csv"
# download.file(URL, destfile = "credit.csv", method="curl") # method="curl" may not be needed on MacStep 2: Exploring and preparing the data —-
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 two characteristics of the applicant
table(credit$checking_balance)
< 0 DM > 200 DM 1 - 200 DM unknown
274 63 269 394 table(credit$savings_balance)
< 100 DM > 1000 DM 100 - 500 DM 500 - 1000 DM unknown
603 48 103 63 183 Look at two characteristics of the loan
summary(credit$months_loan_duration) Min. 1st Qu. Median Mean 3rd Qu. Max.
4.0 12.0 18.0 20.9 24.0 72.0 summary(credit$amount) Min. 1st Qu. Median Mean 3rd Qu. Max.
250 1366 2320 3271 3972 18424 Look at the class variable
table(credit$default)
no yes
700 300 Create a random sample for training and test data Use set.seed to use the same random number sequence as the tutorial
set.seed(123)
train_sample <- sample(1000, 900)
str(train_sample) int [1:900] 288 788 409 881 937 46 525 887 548 453 ...Split the data frames
credit_train <- credit[train_sample, ]
credit_test <- credit[-train_sample, ]Check the proportion of class variable
prop.table(table(credit_train$default))
no yes
0.7033333 0.2966667 prop.table(table(credit_test$default))
no yes
0.67 0.33 Step 3: Training a model on the data
Build the simplest decision tree
library(C50)
credit_model <- C5.0(credit_train[-17], credit_train$default)Display simple facts about the tree
credit_model
Call:
C5.0.default(x = credit_train[-17], y = credit_train$default)
Classification Tree
Number of samples: 900
Number of predictors: 16
Tree size: 57
Non-standard options: attempt to group attributesDisplay detailed information about the tree
summary(credit_model)
Call:
C5.0.default(x = credit_train[-17], y = credit_train$default)
C5.0 [Release 2.07 GPL Edition] Mon Mar 9 10:08:23 2020
-------------------------------
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 secsStep 4: Evaluating model performance
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$default, credit_pred,
prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
dnn = c('actual default', 'predicted default'))
Cell Contents
|-------------------------|
| N |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| predicted default
actual default | no | yes | Row Total |
---------------|-----------|-----------|-----------|
no | 59 | 8 | 67 |
| 0.590 | 0.080 | |
---------------|-----------|-----------|-----------|
yes | 19 | 14 | 33 |
| 0.190 | 0.140 | |
---------------|-----------|-----------|-----------|
Column Total | 78 | 22 | 100 |
---------------|-----------|-----------|-----------|
Step 5: Improving model performance
Boosting the accuracy of decision trees
Boosted decision tree with 10 trials
credit_boost10 <- C5.0(credit_train[-17], credit_train$default,
trials = 10)
credit_boost10
Call:
C5.0.default(x = credit_train[-17], y = credit_train$default, trials = 10)
Classification Tree
Number of samples: 900
Number of predictors: 16
Number of boosting iterations: 10
Average tree size: 47.5
Non-standard options: attempt to group attributessummary(credit_boost10)
Call:
C5.0.default(x = credit_train[-17], y = credit_train$default, trials = 10)
C5.0 [Release 2.07 GPL Edition] Mon Mar 9 10:08:23 2020
-------------------------------
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: 0.0 secscredit_boost_pred10 <- predict(credit_boost10, credit_test)
CrossTable(credit_test$default, credit_boost_pred10,
prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
dnn = c('actual default', 'predicted default'))
Cell Contents
|-------------------------|
| N |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| predicted default
actual default | no | yes | Row Total |
---------------|-----------|-----------|-----------|
no | 62 | 5 | 67 |
| 0.620 | 0.050 | |
---------------|-----------|-----------|-----------|
yes | 13 | 20 | 33 |
| 0.130 | 0.200 | |
---------------|-----------|-----------|-----------|
Column Total | 75 | 25 | 100 |
---------------|-----------|-----------|-----------|
Making some mistakes more costly than others
Create dimensions for a cost matrix
matrix_dimensions <- list(c("no", "yes"), c("no", "yes"))
names(matrix_dimensions) <- c("predicted", "actual")
matrix_dimensions$predicted
[1] "no" "yes"
$actual
[1] "no" "yes"Build the matrix
error_cost <- matrix(c(0, 1, 4, 0), nrow = 2, dimnames = matrix_dimensions)
error_cost actual
predicted no yes
no 0 4
yes 1 0Apply the cost matrix to the tree
credit_cost <- C5.0(credit_train[-17], credit_train$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 |
---------------|-----------|-----------|-----------|
Part 2: Rule Learners
Example: Identifying Poisonous Mushrooms
Step 1: Download the data
Since the data has alreay been downloaded in the R Project there is no need to download again. But note that downloading a .csv can be done by using the following code.
# URL <- "http://cox.csueastbay.edu/~esuess/classes/Statistics_452/Presentations/ml08a/mushrooms.csv"
# download.file(URL, destfile = "./mushrooms.csv", method="curl")Step 2: Exploring and preparing the data
mushrooms <- read.csv("mushrooms.csv", stringsAsFactors = TRUE)Examine the structure of the data frame
str(mushrooms)'data.frame': 8124 obs. of 23 variables:
$ type : Factor w/ 2 levels "edible","poisonous": 2 1 1 2 1 1 1 1 2 1 ...
$ cap_shape : Factor w/ 6 levels "bell","conical",..: 3 3 1 3 3 3 1 1 3 1 ...
$ cap_surface : Factor w/ 4 levels "fibrous","grooves",..: 4 4 4 3 4 3 4 3 3 4 ...
$ cap_color : Factor w/ 10 levels "brown","buff",..: 1 10 9 9 4 10 9 9 9 10 ...
$ bruises : Factor w/ 2 levels "no","yes": 2 2 2 2 1 2 2 2 2 2 ...
$ odor : Factor w/ 9 levels "almond","anise",..: 8 1 2 8 7 1 1 2 8 1 ...
$ gill_attachment : Factor w/ 2 levels "attached","free": 2 2 2 2 2 2 2 2 2 2 ...
$ gill_spacing : Factor w/ 2 levels "close","crowded": 1 1 1 1 2 1 1 1 1 1 ...
$ gill_size : Factor w/ 2 levels "broad","narrow": 2 1 1 2 1 1 1 1 2 1 ...
$ gill_color : Factor w/ 12 levels "black","brown",..: 1 1 2 2 1 2 5 2 8 5 ...
$ stalk_shape : Factor w/ 2 levels "enlarging","tapering": 1 1 1 1 2 1 1 1 1 1 ...
$ stalk_root : Factor w/ 5 levels "bulbous","club",..: 3 2 2 3 3 2 2 2 3 2 ...
$ stalk_surface_above_ring: Factor w/ 4 levels "fibrous","scaly",..: 4 4 4 4 4 4 4 4 4 4 ...
$ stalk_surface_below_ring: Factor w/ 4 levels "fibrous","scaly",..: 4 4 4 4 4 4 4 4 4 4 ...
$ stalk_color_above_ring : Factor w/ 9 levels "brown","buff",..: 8 8 8 8 8 8 8 8 8 8 ...
$ stalk_color_below_ring : Factor w/ 9 levels "brown","buff",..: 8 8 8 8 8 8 8 8 8 8 ...
$ veil_type : Factor w/ 1 level "partial": 1 1 1 1 1 1 1 1 1 1 ...
$ veil_color : Factor w/ 4 levels "brown","orange",..: 3 3 3 3 3 3 3 3 3 3 ...
$ ring_number : Factor w/ 3 levels "none","one","two": 2 2 2 2 2 2 2 2 2 2 ...
$ ring_type : Factor w/ 5 levels "evanescent","flaring",..: 5 5 5 5 1 5 5 5 5 5 ...
$ spore_print_color : Factor w/ 9 levels "black","brown",..: 1 2 2 1 2 1 1 2 1 1 ...
$ population : Factor w/ 6 levels "abundant","clustered",..: 4 3 3 4 1 3 3 4 5 4 ...
$ habitat : Factor w/ 7 levels "grasses","leaves",..: 5 1 3 5 1 1 3 3 1 3 ...drop the veil_type feature
mushrooms$veil_type <- NULLexamine the class distribution
table(mushrooms$type)
edible poisonous
4208 3916 Randomize the Train and Test data
set.seed(123)
train_sample <- sample(8124, 7000)
str(train_sample) int [1:7000] 2337 6404 3322 7171 7637 370 4288 7244 4476 3706 ...Split the data frames
mushrooms_train <- mushrooms[train_sample, ]
mushrooms_test <- mushrooms[-train_sample, ]Step 3: Training a model on the data
library(RWeka)train OneR() on the data
mushroom_1R <- OneR(type ~ ., data = mushrooms_train)Step 4: Evaluating model performance
mushroom_1Rodor:
almond -> edible
anise -> edible
creosote -> poisonous
fishy -> poisonous
foul -> poisonous
musty -> poisonous
none -> edible
pungent -> poisonous
spicy -> poisonous
(6895/7000 instances correct)summary(mushroom_1R)
=== Summary ===
Correctly Classified Instances 6895 98.5 %
Incorrectly Classified Instances 105 1.5 %
Kappa statistic 0.9699
Mean absolute error 0.015
Root mean squared error 0.1225
Relative absolute error 3.0039 %
Root relative squared error 24.5108 %
Total Number of Instances 7000
=== Confusion Matrix ===
a b <-- classified as
3626 0 | a = edible
105 3269 | b = poisonousMake predictions
mushroom_pred <- predict(mushroom_1R, mushrooms_test)Cross tabulation of predicted versus actual classes
library(gmodels)
CrossTable(mushrooms_test$type, mushroom_pred,
prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
dnn = c('actual default', 'predicted default'))
Cell Contents
|-------------------------|
| N |
| N / Table Total |
|-------------------------|
Total Observations in Table: 1124
| predicted default
actual default | edible | poisonous | Row Total |
---------------|-----------|-----------|-----------|
edible | 582 | 0 | 582 |
| 0.518 | 0.000 | |
---------------|-----------|-----------|-----------|
poisonous | 15 | 527 | 542 |
| 0.013 | 0.469 | |
---------------|-----------|-----------|-----------|
Column Total | 597 | 527 | 1124 |
---------------|-----------|-----------|-----------|
Step 5: Improving model performance
mushroom_JRip <- JRip(type ~ ., data = mushrooms_train)
mushroom_JRipJRIP rules:
===========
(odor = foul) => type=poisonous (1860.0/0.0)
(gill_size = narrow) and (gill_color = buff) => type=poisonous (986.0/0.0)
(gill_size = narrow) and (odor = pungent) => type=poisonous (222.0/0.0)
(odor = creosote) => type=poisonous (171.0/0.0)
(spore_print_color = green) => type=poisonous (65.0/0.0)
(stalk_surface_below_ring = scaly) and (stalk_surface_above_ring = silky) => type=poisonous (58.0/0.0)
(habitat = leaves) and (cap_surface = scaly) and (population = clustered) => type=poisonous (10.0/0.0)
(cap_surface = grooves) => type=poisonous (2.0/0.0)
=> type=edible (3626.0/0.0)
Number of Rules : 9summary(mushroom_JRip)
=== Summary ===
Correctly Classified Instances 7000 100 %
Incorrectly Classified Instances 0 0 %
Kappa statistic 1
Mean absolute error 0
Root mean squared error 0
Relative absolute error 0 %
Root relative squared error 0 %
Total Number of Instances 7000
=== Confusion Matrix ===
a b <-- classified as
3626 0 | a = edible
0 3374 | b = poisonousMake predictions
mushroom_pred <- predict(mushroom_JRip, mushrooms_test)Cross tabulation of predicted versus actual classes
library(gmodels)
CrossTable(mushrooms_test$type, mushroom_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: 1124
| predicted default
actual default | edible | poisonous | Row Total |
---------------|-----------|-----------|-----------|
edible | 582 | 0 | 582 |
| 0.518 | 0.000 | |
---------------|-----------|-----------|-----------|
poisonous | 0 | 542 | 542 |
| 0.000 | 0.482 | |
---------------|-----------|-----------|-----------|
Column Total | 582 | 542 | 1124 |
---------------|-----------|-----------|-----------|
Rule Learner Using C5.0 Decision Trees (not in text)
library(C50)
mushroom_c5rules <- C5.0(type ~ odor + gill_size, data = mushrooms_train, rules = TRUE)
mushroom_c5rules
Call:
C5.0.formula(formula = type ~ odor + gill_size, data = mushrooms_train, rules = TRUE)
Rule-Based Model
Number of samples: 7000
Number of predictors: 2
Number of Rules: 2
Non-standard options: attempt to group attributessummary(mushroom_c5rules)
Call:
C5.0.formula(formula = type ~ odor + gill_size, data = mushrooms_train, rules = TRUE)
C5.0 [Release 2.07 GPL Edition] Mon Mar 9 10:08:27 2020
-------------------------------
Class specified by attribute `outcome'
Read 7000 cases (3 attributes) from undefined.data
Rules:
Rule 1: (3731/105, lift 1.9)
odor in {almond, anise, none}
-> class edible [0.972]
Rule 2: (3269, lift 2.1)
odor in {creosote, fishy, foul, musty, pungent, spicy}
-> class poisonous [1.000]
Default class: edible
Evaluation on training data (7000 cases):
Rules
----------------
No Errors
2 105( 1.5%) <<
(a) (b) <-classified as
---- ----
3626 (a): class edible
105 3269 (b): class poisonous
Attribute usage:
100.00% odor
Time: 0.0 secsmushroom_pred <- predict(mushroom_c5rules, mushrooms_test)Cross tabulation of predicted versus actual classes
library(gmodels)
CrossTable(mushrooms_test$type, mushroom_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: 1124
| predicted default
actual default | edible | poisonous | Row Total |
---------------|-----------|-----------|-----------|
edible | 582 | 0 | 582 |
| 0.518 | 0.000 | |
---------------|-----------|-----------|-----------|
poisonous | 15 | 527 | 542 |
| 0.013 | 0.469 | |
---------------|-----------|-----------|-----------|
Column Total | 597 | 527 | 1124 |
---------------|-----------|-----------|-----------|
---
title: "Chapter 5 - R Notebook"
output:
  html_notebook: default
  pdf_document: default
  word_document: default
---

# Chapter 5: Classification using Decision Trees and Rules 

## Part 1: Decision Trees 

## Understanding Decision Trees 

Calculate entropy of a two-class segment

```{r}
-0.60 * log2(0.60) - 0.40 * log2(0.40)

curve(-x * log2(x) - (1 - x) * log2(1 - x),
      col = "red", xlab = "x", ylab = "Entropy", lwd = 4)
```

## Example: Identifying Risky Bank Loans 
## Step 1: Download the data 

Since the data has alreay been downloaded in the R Project there is no need to download again.  But note that downloading a .csv can be done by using the following code.

```{r}
# URL <- "http://cox.csueastbay.edu/~esuess/classes/Statistics_452/Presentations/ml07a/credit.csv"
# download.file(URL, destfile = "credit.csv", method="curl")  # method="curl" may not be needed on Mac
```

## Step 2: Exploring and preparing the data ----

```{r}
credit <- read.csv("credit.csv", stringsAsFactors = TRUE)
str(credit)
```

Look at two characteristics of the applicant

```{r}
table(credit$checking_balance)
table(credit$savings_balance)

```

Look at two characteristics of the loan

```{r}
summary(credit$months_loan_duration)
summary(credit$amount)
```

Look at the class variable

```{r}
table(credit$default)
```

Create a random sample for training and test data
Use set.seed to use the same random number sequence as the tutorial

```{r}
set.seed(123)
train_sample <- sample(1000, 900)

str(train_sample)
```

Split the data frames

```{r}
credit_train <- credit[train_sample, ]
credit_test  <- credit[-train_sample, ]
```


Check the proportion of class variable

```{r}
prop.table(table(credit_train$default))
prop.table(table(credit_test$default))
```


## Step 3: Training a model on the data 

Build the simplest decision tree

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

Display simple facts about the tree

```{r}
credit_model

```

Display detailed information about the tree

```{r}
summary(credit_model)
```

## Step 4: Evaluating model performance 

Create a factor vector of predictions on test data

```{r}
credit_pred <- predict(credit_model, credit_test)
```

Cross tabulation of predicted versus actual classes

```{r}
library(gmodels)
CrossTable(credit_test$default, credit_pred,
           prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
           dnn = c('actual default', 'predicted default'))
```

## Step 5: Improving model performance 

## Boosting the accuracy of decision trees

Boosted decision tree with 10 trials

```{r}
credit_boost10 <- C5.0(credit_train[-17], credit_train$default,
                       trials = 10)
credit_boost10
summary(credit_boost10)
```

```{r}
credit_boost_pred10 <- predict(credit_boost10, credit_test)
CrossTable(credit_test$default, credit_boost_pred10,
           prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
           dnn = c('actual default', 'predicted default'))
```

## Making some mistakes more costly than others

Create dimensions for a cost matrix

```{r}
matrix_dimensions <- list(c("no", "yes"), c("no", "yes"))
names(matrix_dimensions) <- c("predicted", "actual")
matrix_dimensions
```

Build the matrix

```{r}
error_cost <- matrix(c(0, 1, 4, 0), nrow = 2, dimnames = matrix_dimensions)
error_cost
```

Apply the cost matrix to the tree

```{r}

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'))
```


# Part 2: Rule Learners 

## Example: Identifying Poisonous Mushrooms 
## Step 1: Download the data 

Since the data has alreay been downloaded in the R Project there is no need to download again.  But note that downloading a .csv can be done by using the following code.

```{r}
# URL <- "http://cox.csueastbay.edu/~esuess/classes/Statistics_452/Presentations/ml08a/mushrooms.csv"
# download.file(URL, destfile = "./mushrooms.csv", method="curl")
```

## Step 2: Exploring and preparing the data 

```{r}
mushrooms <- read.csv("mushrooms.csv", stringsAsFactors = TRUE)
```

Examine the structure of the data frame

```{r}
str(mushrooms)
```


# drop the veil_type feature

```{r}
mushrooms$veil_type <- NULL
```

# examine the class distribution

```{r}
table(mushrooms$type)
```

Randomize the Train and Test data

```{r}
set.seed(123)
train_sample <- sample(8124, 7000)

str(train_sample)
```

Split the data frames

```{r}
mushrooms_train <- mushrooms[train_sample, ]
mushrooms_test  <- mushrooms[-train_sample, ]
```

## Step 3: Training a model on the data 

```{r}
library(RWeka)
```

# train OneR() on the data

```{r}
mushroom_1R <- OneR(type ~ ., data = mushrooms_train)
```

## Step 4: Evaluating model performance 

```{r}
mushroom_1R
summary(mushroom_1R)
```

Make predictions

```{r}
mushroom_pred <- predict(mushroom_1R, mushrooms_test)

```

Cross tabulation of predicted versus actual classes

```{r}
library(gmodels)
CrossTable(mushrooms_test$type, mushroom_pred,
           prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
           dnn = c('actual default', 'predicted default'))
```




## Step 5: Improving model performance 

```{r}
mushroom_JRip <- JRip(type ~ ., data = mushrooms_train)
mushroom_JRip
summary(mushroom_JRip)
```

Make predictions

```{r}
mushroom_pred <- predict(mushroom_JRip, mushrooms_test)
```


Cross tabulation of predicted versus actual classes

```{r}
library(gmodels)
CrossTable(mushrooms_test$type, mushroom_pred,
           prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
           dnn = c('actual default', 'predicted default'))
```

# Rule Learner Using C5.0 Decision Trees (not in text)

```{r}
library(C50)
mushroom_c5rules <- C5.0(type ~ odor + gill_size, data = mushrooms_train, rules = TRUE)
mushroom_c5rules
summary(mushroom_c5rules)
```


```{r}
mushroom_pred <- predict(mushroom_c5rules, mushrooms_test)
```

Cross tabulation of predicted versus actual classes

```{r}
library(gmodels)
CrossTable(mushrooms_test$type, mushroom_pred,
           prop.chisq = FALSE, prop.c = FALSE, prop.r = FALSE,
           dnn = c('actual default', 'predicted default'))
```








