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---
title: "Lab9: Decision trees"
author: "Vladislav Litvinov <vlad@sek1ro>"
output:
pdf_document:
toc_float: TRUE
---
# Data preparation
```{r}
setwd('/home/sek1ro/git/public/lab/ds/25-1/r')
survey <- read.csv('survey.csv')
train_df = survey[1:600,]
test_df = survey[601:750,]
```
# Building classification tree
decision formula is MYDEPV ~ Price + Income + Age
Use three-fold cross-validation and the information gain splitting index
Which features were actually used to construct the tree?
Plot the tree using the “rpart.plot” package.
Three-fold cross-validation - Делают 3 прогона:
Прогон 1: обучаемся на B + C, тестируем на A
Прогон 2: обучаемся на A + C, тестируем на B
Прогон 3: обучаемся на A + B, тестируем на C
Получаем 3 значения метрики (accuracy, F1, MSE и т.п.).
Берём среднее значение — это и есть итоговая оценка качества модели.
rpart сам отбрасывает признаки, если они не улучшают разбиение по information gain.
CP-table - связь сложности дерева и ошибки
Root node error — ошибка без разбиений
nsplit — число split-ов
rel error — обучающая ошибка относительно корня
xerror — ошибка по cross-validation
xstd — стандартное отклонение xerror
type — расположение split-ов
extra — доп. информация в узлах
fallen.leaves — выравнивание листьев
H = -x\cdot\log\left(x\right)-\left(1-x\right)\log\left(1-x\right)
Gain(A) = Info(S) - Info(S_A) - максимизируем
Ранняя остановка. Ограничение грубины. Минимальное количество примеров в узле.
Отсечение ветвей.
Строительство полного дерева, в котором листья содержат примеры одного класса.
Определение двух показателей: относительную точность модели и абсолютную ошибку.
Удаление листов и узлов, потеря которых минимально скажется на точности модели и увеличении ошибки.
```{r}
library(rpart)
tree = rpart(
MYDEPV ~ Price + Income + Age,
data = train_df,
method = "class",
parms = list(split = "information"),
control = rpart.control(
xval = 3,
),
)
printcp(tree)
library(rpart.plot)
rpart.plot(
tree,
type = 1,
extra = 106,
#6 Class models: the probability of the second class only. Useful for binary responses.
#100 display the percentage of observations in the node.
fallen.leaves = TRUE,
)
```
Score the model with the training data and create the model’s confusion matrix. Which class of MYDEPV was the model better able to classify?
```{r}
pred_class = predict(tree, train_df, type="class")
conf_mat = table(
Actual = train_df$MYDEPV,
Predicted = pred_class
)
conf_mat
print(diag(conf_mat) / rowSums(conf_mat))
```
Define the resubstitution error rate, and then calculate it using the confusion matrix from the previous step. Is it a good indicator of predictive performance? Why or why not?
Resubstitution error rate — это доля неправильных предсказаний на тех же данных, на которых обучалась модель
```{r}
print(1 - sum(diag(conf_mat)) / sum(conf_mat))
```
ROC curve - Receiver Operating Characteristic
x - FPR = FP / (FP + TN)
y - TPR = TP / (TP + FN)
```{r}
pred_prob = predict(tree, train_df, type="prob")[,2]
library(ROCR)
pred = prediction(pred_prob, train_df$MYDEPV)
perf = performance(pred, "tpr", "fpr")
plot(perf)
abline(a = 0, b = 1)
auc_perf = performance(pred, measure = "auc")
auc_perf@y.values[[1]]
```
Score the model with the testing data. How accurate are the tree’s predictions?
Repeat part (a), but set the splitting index to the Gini coefficient splitting index. How does the new tree compare to the previous one?
индекс Джини показывает, как часто случайно выбранный пример обучающего множества будет распознан неправильно.
Gini(Q) = 1 - sum(p^2) - максимизируем
0 - все к 1 классу
1 - все равновероятны
1-\ x^{2}\ -\ \left(1-x\right)^{2}
```{r}
pred_test = predict(tree, test_df, type="class")
conf_mat_test = table(Actual = test_df$MYDEPV, Predicted = pred_test)
conf_mat_test
print(diag(conf_mat_test) / rowSums(conf_mat_test))
tree_gini = rpart(
MYDEPV ~ Price + Income + Age,
data = train_df,
method = "class",
parms = list(split = "gini")
)
printcp(tree_gini)
rpart.plot(
tree_gini,
type = 1,
extra = 106,
fallen.leaves = TRUE,
)
```
One way to prune a tree is according to the complexity parameter associated with the smallest cross-validation error. Prune the new tree in this way using the “prune” function. Which features were actually used in the pruned tree? Why were certain variables not used?
```{r}
best_cp <- tree_gini$cptable[which.min(tree_gini$cptable[, "xerror"]), "CP"]
best_cp
pruned_tree = prune(tree_gini, cp = best_cp)
printcp(pruned_tree)
rpart.plot(pruned_tree)
```
Create the confusion matrix for the new model, and compare the performance of the model before and after pruning.
```{r}
pruned_pred = predict(pruned_tree, test_df, type="class")
pruned_conf_mat = table(Actual = test_df$MYDEPV, Predicted = pruned_pred)
pruned_conf_mat
print(diag(pruned_conf_mat) / rowSums(pruned_conf_mat))
```

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"1",""
"1","0.43333"
"1",""
"1","
"
"1","n="
"1"," "
"1","600"
"1"," "
"1","
"
"1"," "
"1"," CP"
"1"," nsplit"
"1"," rel error"
"1"," xerror"
"1"," xstd"
"1","
1"
"1"," 0.692308"
"1"," 0"
"1"," 1.00000"
"1"," 1.00000"
"1"," 0.046685"
"1","
2"
"1"," 0.025000"
"1"," 1"
"1"," 0.30769"
"1"," 0.31154"
"1"," 0.032194"
"1","
3"
"1"," 0.011538"
"1"," 3"
"1"," 0.25769"
"1"," 0.26538"
"1"," 0.030055"
"1","
"
"0","rpart.plot(pruned_tree)"
1 0 best_cp <- tree_gini$cptable[which.min(tree_gini$cptable[, "xerror"]), "CP"]
2 0 best_cp
3 1 [1]
4 1 0.01153846
5 1
6 0 pruned_tree = prune(tree_gini, cp = best_cp)
7 0
8 0 printcp(pruned_tree)
9 1 Classification tree:
10 1 rpart(formula = MYDEPV ~ Price + Income + Age, data = train_df,
11 1 method = "class", parms = list(split = "gini"))
12 1
13 1 Variables actually used in tree construction:
14 1 [1]
15 1 Income
16 1 Price
17 1
18 1
19 1 Root node error:
20 1
21 1 260
22 1
23 1 /
24 1
25 1 600
26 1
27 1 =
28 1
29 1 0.43333
30 1
31 1
32 1 n=
33 1
34 1 600
35 1
36 1
37 1
38 1 CP
39 1 nsplit
40 1 rel error
41 1 xerror
42 1 xstd
43 1 1
44 1 0.692308
45 1 0
46 1 1.00000
47 1 1.00000
48 1 0.046685
49 1 2
50 1 0.025000
51 1 1
52 1 0.30769
53 1 0.31154
54 1 0.032194
55 1 3
56 1 0.011538
57 1 3
58 1 0.25769
59 1 0.26538
60 1 0.030055
61 1
62 0 rpart.plot(pruned_tree)

1
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@ -0,0 +1,125 @@
"0","pred_test = predict(tree, test_df, type=""class"")"
"0","conf_mat_test = table(Actual = test_df$MYDEPV, Predicted = pred_test)"
"0","conf_mat_test"
"1"," Predicted
"
"1","Actual"
"1"," 0"
"1"," 1"
"1","
0"
"1"," 76"
"1"," 10"
"1","
1"
"1"," 6"
"1"," 58"
"1","
"
"0","print(diag(conf_mat_test) / rowSums(conf_mat_test))"
"1"," 0 "
"1"," 1 "
"1","
"
"1","0.8837209 "
"1","0.9062500 "
"1","
"
"0","tree_gini = rpart("
"0"," MYDEPV ~ Price + Income + Age,"
"0"," data = train_df,"
"0"," method = ""class"","
"0"," parms = list(split = ""gini"")"
"0",")"
"0",""
"0","printcp(tree_gini)"
"1","
Classification tree:
"
"1","rpart(formula = MYDEPV ~ Price + Income + Age, data = train_df,
"
"1"," method = ""class"", parms = list(split = ""gini""))
"
"1","
"
"1","Variables actually used in tree construction:
"
"1","[1]"
"1"," Age "
"1"," Income"
"1"," Price "
"1","
"
"1","
"
"1","Root node error: "
"1",""
"1","260"
"1",""
"1","/"
"1",""
"1","600"
"1",""
"1"," = "
"1",""
"1","0.43333"
"1",""
"1","
"
"1","n="
"1"," "
"1","600"
"1"," "
"1","
"
"1"," "
"1"," CP"
"1"," nsplit"
"1"," rel error"
"1"," xerror"
"1"," xstd"
"1","
1"
"1"," 0.692308"
"1"," 0"
"1"," 1.00000"
"1"," 1.00000"
"1"," 0.046685"
"1","
2"
"1"," 0.025000"
"1"," 1"
"1"," 0.30769"
"1"," 0.31154"
"1"," 0.032194"
"1","
3"
"1"," 0.011538"
"1"," 3"
"1"," 0.25769"
"1"," 0.26538"
"1"," 0.030055"
"1","
4"
"1"," 0.010256"
"1"," 5"
"1"," 0.23462"
"1"," 0.28846"
"1"," 0.031157"
"1","
5"
"1"," 0.010000"
"1"," 11"
"1"," 0.17308"
"1"," 0.28462"
"1"," 0.030978"
"1","
"
"0","rpart.plot("
"0"," tree_gini,"
"0"," type = 1,"
"0"," extra = 106,"
"0"," fallen.leaves = TRUE,"
"0",")"
1 0 pred_test = predict(tree, test_df, type="class")
2 0 conf_mat_test = table(Actual = test_df$MYDEPV, Predicted = pred_test)
3 0 conf_mat_test
4 1 Predicted
5 1 Actual
6 1 0
7 1 1
8 1 0
9 1 76
10 1 10
11 1 1
12 1 6
13 1 58
14 1
15 0 print(diag(conf_mat_test) / rowSums(conf_mat_test))
16 1 0
17 1 1
18 1
19 1 0.8837209
20 1 0.9062500
21 1
22 0 tree_gini = rpart(
23 0 MYDEPV ~ Price + Income + Age,
24 0 data = train_df,
25 0 method = "class",
26 0 parms = list(split = "gini")
27 0 )
28 0
29 0 printcp(tree_gini)
30 1 Classification tree:
31 1 rpart(formula = MYDEPV ~ Price + Income + Age, data = train_df,
32 1 method = "class", parms = list(split = "gini"))
33 1
34 1 Variables actually used in tree construction:
35 1 [1]
36 1 Age
37 1 Income
38 1 Price
39 1
40 1
41 1 Root node error:
42 1
43 1 260
44 1
45 1 /
46 1
47 1 600
48 1
49 1 =
50 1
51 1 0.43333
52 1
53 1
54 1 n=
55 1
56 1 600
57 1
58 1
59 1
60 1 CP
61 1 nsplit
62 1 rel error
63 1 xerror
64 1 xstd
65 1 1
66 1 0.692308
67 1 0
68 1 1.00000
69 1 1.00000
70 1 0.046685
71 1 2
72 1 0.025000
73 1 1
74 1 0.30769
75 1 0.31154
76 1 0.032194
77 1 3
78 1 0.011538
79 1 3
80 1 0.25769
81 1 0.26538
82 1 0.030055
83 1 4
84 1 0.010256
85 1 5
86 1 0.23462
87 1 0.28846
88 1 0.031157
89 1 5
90 1 0.010000
91 1 11
92 1 0.17308
93 1 0.28462
94 1 0.030978
95 1
96 0 rpart.plot(
97 0 tree_gini,
98 0 type = 1,
99 0 extra = 106,
100 0 fallen.leaves = TRUE,
101 0 )

1
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"0","pred_prob = predict(tree, train_df, type=""prob"")[,2]"
"0",""
"0","library(ROCR)"
"0","pred = prediction(pred_prob, train_df$MYDEPV)"
"0","perf = performance(pred, ""tpr"", ""fpr"")"
"0",""
"0","plot(perf)"
1 0 pred_prob = predict(tree, train_df, type="prob")[,2]
2 0
3 0 library(ROCR)
4 0 pred = prediction(pred_prob, train_df$MYDEPV)
5 0 perf = performance(pred, "tpr", "fpr")
6 0
7 0 plot(perf)

1
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"0","abline(a = 0, b = 1)"
1 0 abline(a = 0, b = 1)

1
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"0",""
"0","auc_perf = performance(pred, measure = ""auc"")"
"0","auc_perf@y.values[[1]]"
"1","[1]"
"1"," 0.9720645"
"1","
"
1 0
2 0 auc_perf = performance(pred, measure = "auc")
3 0 auc_perf@y.values[[1]]
4 1 [1]
5 1 0.9720645
6 1

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"0","setwd('/home/sek1ro/git/public/lab/ds/25-1/r')"
"0","survey <- read.csv('survey.csv')"
"0",""
"0","train_df = survey[1:600,]"
"0","test_df = survey[601:750,]"
1 0 setwd('/home/sek1ro/git/public/lab/ds/25-1/r')
2 0 survey <- read.csv('survey.csv')
3 0
4 0 train_df = survey[1:600,]
5 0 test_df = survey[601:750,]

0
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/home/sek1ro/git/public/lab/ds/25-1/r/9.Rmd="EB7B11F9"