pacman::p_load("data.table",
"tidyverse",
"dplyr", "tidyr",
"ggplot2", "GGally",
"caret",
"doParallel", "parallel") # For 병렬 처리
registerDoParallel(cores=detectCores()) # 사용할 Core 개수 지정
titanic <- fread("../Titanic.csv") # 데이터 불러오기
titanic %>%
as_tibble8 Ridge Regression
Ridge Regression의 장점
- 규제항을 통해 회귀계수를 “0”에 가깝게 추정한다.
- 회귀계수 추정치의 분산을 감소시켜
Training Dataset의 변화에도 회귀계수 추정치가 크게 변하지 않는다.
- 회귀계수 추정치의 분산을 감소시켜
Ridge Regression의 단점
- \(\lambda = \infty\)가 아닌 한 회귀계수를 정확하게 “0”으로 추정하지 못한다.
- 변수 선택을 수행할 수 없다.
- 예측변수가 많을 경우 해석이 어렵다.
실습 자료 : 1912년 4월 15일 타이타닉호 침몰 당시 탑승객들의 정보를 기록한 데이터셋이며, 총 11개의 변수를 포함하고 있다. 이 자료에서 Target은
Survived이다.
8.1 데이터 불러오기
# A tibble: 891 × 11
Survived Pclass Name Sex Age SibSp Parch Ticket Fare Cabin Embarked
<int> <int> <chr> <chr> <dbl> <int> <int> <chr> <dbl> <chr> <chr>
1 0 3 Braund, Mr. Owen Harris male 22 1 0 A/5 21171 7.25 "" S
2 1 1 Cumings, Mrs. John Bradley (Florence Briggs Thayer) female 38 1 0 PC 17599 71.3 "C85" C
3 1 3 Heikkinen, Miss. Laina female 26 0 0 STON/O2. 3101282 7.92 "" S
4 1 1 Futrelle, Mrs. Jacques Heath (Lily May Peel) female 35 1 0 113803 53.1 "C123" S
5 0 3 Allen, Mr. William Henry male 35 0 0 373450 8.05 "" S
6 0 3 Moran, Mr. James male NA 0 0 330877 8.46 "" Q
7 0 1 McCarthy, Mr. Timothy J male 54 0 0 17463 51.9 "E46" S
8 0 3 Palsson, Master. Gosta Leonard male 2 3 1 349909 21.1 "" S
9 1 3 Johnson, Mrs. Oscar W (Elisabeth Vilhelmina Berg) female 27 0 2 347742 11.1 "" S
10 1 2 Nasser, Mrs. Nicholas (Adele Achem) female 14 1 0 237736 30.1 "" C
# ℹ 881 more rows8.2 데이터 전처리 I
titanic %<>%
data.frame() %>% # Data Frame 형태로 변환
mutate(Survived = ifelse(Survived == 1, "yes", "no")) # Target을 문자형 변수로 변환
# 1. Convert to Factor
fac.col <- c("Pclass", "Sex",
# Target
"Survived")
titanic <- titanic %>%
mutate_at(fac.col, as.factor) # 범주형으로 변환
glimpse(titanic) # 데이터 구조 확인Rows: 891
Columns: 11
$ Survived <fct> no, yes, yes, yes, no, no, no, no, yes, yes, yes, yes, no, no, no, yes, no, yes, no, yes, no, yes, yes, yes, no, yes, no, no, yes, no, no, yes, yes, no, no, no, yes, no, no, yes, no…
$ Pclass <fct> 3, 1, 3, 1, 3, 3, 1, 3, 3, 2, 3, 1, 3, 3, 3, 2, 3, 2, 3, 3, 2, 2, 3, 1, 3, 3, 3, 1, 3, 3, 1, 1, 3, 2, 1, 1, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 1, 1, 2, 3, 2, 3, 3…
$ Name <chr> "Braund, Mr. Owen Harris", "Cumings, Mrs. John Bradley (Florence Briggs Thayer)", "Heikkinen, Miss. Laina", "Futrelle, Mrs. Jacques Heath (Lily May Peel)", "Allen, Mr. William Henry…
$ Sex <fct> male, female, female, female, male, male, male, male, female, female, female, female, male, male, female, female, male, male, female, female, male, male, female, male, female, femal…
$ Age <dbl> 22.0, 38.0, 26.0, 35.0, 35.0, NA, 54.0, 2.0, 27.0, 14.0, 4.0, 58.0, 20.0, 39.0, 14.0, 55.0, 2.0, NA, 31.0, NA, 35.0, 34.0, 15.0, 28.0, 8.0, 38.0, NA, 19.0, NA, NA, 40.0, NA, NA, 66.…
$ SibSp <int> 1, 1, 0, 1, 0, 0, 0, 3, 0, 1, 1, 0, 0, 1, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 3, 1, 0, 3, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 1, 4, 0, 1, 1, 0, 0, 0, 0, 1, 5, 0…
$ Parch <int> 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 5, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 5, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0…
$ Ticket <chr> "A/5 21171", "PC 17599", "STON/O2. 3101282", "113803", "373450", "330877", "17463", "349909", "347742", "237736", "PP 9549", "113783", "A/5. 2151", "347082", "350406", "248706", "38…
$ Fare <dbl> 7.2500, 71.2833, 7.9250, 53.1000, 8.0500, 8.4583, 51.8625, 21.0750, 11.1333, 30.0708, 16.7000, 26.5500, 8.0500, 31.2750, 7.8542, 16.0000, 29.1250, 13.0000, 18.0000, 7.2250, 26.0000,…
$ Cabin <chr> "", "C85", "", "C123", "", "", "E46", "", "", "", "G6", "C103", "", "", "", "", "", "", "", "", "", "D56", "", "A6", "", "", "", "C23 C25 C27", "", "", "", "B78", "", "", "", "", ""…
$ Embarked <chr> "S", "C", "S", "S", "S", "Q", "S", "S", "S", "C", "S", "S", "S", "S", "S", "S", "Q", "S", "S", "C", "S", "S", "Q", "S", "S", "S", "C", "S", "Q", "S", "C", "C", "Q", "S", "C", "S", "…# 2. Generate New Variable
titanic <- titanic %>%
mutate(FamSize = SibSp + Parch) # "FamSize = 형제 및 배우자 수 + 부모님 및 자녀 수"로 가족 수를 의미하는 새로운 변수
glimpse(titanic) # 데이터 구조 확인Rows: 891
Columns: 12
$ Survived <fct> no, yes, yes, yes, no, no, no, no, yes, yes, yes, yes, no, no, no, yes, no, yes, no, yes, no, yes, yes, yes, no, yes, no, no, yes, no, no, yes, yes, no, no, no, yes, no, no, yes, no…
$ Pclass <fct> 3, 1, 3, 1, 3, 3, 1, 3, 3, 2, 3, 1, 3, 3, 3, 2, 3, 2, 3, 3, 2, 2, 3, 1, 3, 3, 3, 1, 3, 3, 1, 1, 3, 2, 1, 1, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 1, 1, 2, 3, 2, 3, 3…
$ Name <chr> "Braund, Mr. Owen Harris", "Cumings, Mrs. John Bradley (Florence Briggs Thayer)", "Heikkinen, Miss. Laina", "Futrelle, Mrs. Jacques Heath (Lily May Peel)", "Allen, Mr. William Henry…
$ Sex <fct> male, female, female, female, male, male, male, male, female, female, female, female, male, male, female, female, male, male, female, female, male, male, female, male, female, femal…
$ Age <dbl> 22.0, 38.0, 26.0, 35.0, 35.0, NA, 54.0, 2.0, 27.0, 14.0, 4.0, 58.0, 20.0, 39.0, 14.0, 55.0, 2.0, NA, 31.0, NA, 35.0, 34.0, 15.0, 28.0, 8.0, 38.0, NA, 19.0, NA, NA, 40.0, NA, NA, 66.…
$ SibSp <int> 1, 1, 0, 1, 0, 0, 0, 3, 0, 1, 1, 0, 0, 1, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 3, 1, 0, 3, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 1, 4, 0, 1, 1, 0, 0, 0, 0, 1, 5, 0…
$ Parch <int> 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 5, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 5, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0…
$ Ticket <chr> "A/5 21171", "PC 17599", "STON/O2. 3101282", "113803", "373450", "330877", "17463", "349909", "347742", "237736", "PP 9549", "113783", "A/5. 2151", "347082", "350406", "248706", "38…
$ Fare <dbl> 7.2500, 71.2833, 7.9250, 53.1000, 8.0500, 8.4583, 51.8625, 21.0750, 11.1333, 30.0708, 16.7000, 26.5500, 8.0500, 31.2750, 7.8542, 16.0000, 29.1250, 13.0000, 18.0000, 7.2250, 26.0000,…
$ Cabin <chr> "", "C85", "", "C123", "", "", "E46", "", "", "", "G6", "C103", "", "", "", "", "", "", "", "", "", "D56", "", "A6", "", "", "", "C23 C25 C27", "", "", "", "B78", "", "", "", "", ""…
$ Embarked <chr> "S", "C", "S", "S", "S", "Q", "S", "S", "S", "C", "S", "S", "S", "S", "S", "S", "Q", "S", "S", "C", "S", "S", "Q", "S", "S", "S", "C", "S", "Q", "S", "C", "C", "Q", "S", "C", "S", "…
$ FamSize <int> 1, 1, 0, 1, 0, 0, 0, 4, 2, 1, 2, 0, 0, 6, 0, 0, 5, 0, 1, 0, 0, 0, 0, 0, 4, 6, 0, 5, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 1, 0, 3, 0, 0, 1, 0, 2, 1, 5, 0, 1, 1, 1, 0, 0, 0, 3, 7, 0…# 3. Select Variables used for Analysis
titanic1 <- titanic %>%
select(Survived, Pclass, Sex, Age, Fare, FamSize) # 분석에 사용할 변수 선택
titanic1 %>%
as_tibble# A tibble: 891 × 6
Survived Pclass Sex Age Fare FamSize
<fct> <fct> <fct> <dbl> <dbl> <int>
1 no 3 male 22 7.25 1
2 yes 1 female 38 71.3 1
3 yes 3 female 26 7.92 0
4 yes 1 female 35 53.1 1
5 no 3 male 35 8.05 0
6 no 3 male NA 8.46 0
7 no 1 male 54 51.9 0
8 no 3 male 2 21.1 4
9 yes 3 female 27 11.1 2
10 yes 2 female 14 30.1 1
# ℹ 881 more rows8.3 데이터 탐색
ggpairs(titanic1,
aes(colour = Survived)) + # Target의 범주에 따라 색깔을 다르게 표현
theme_bw()
ggpairs(titanic1,
aes(colour = Survived, alpha = 0.8)) + # Target의 범주에 따라 색깔을 다르게 표현
scale_colour_manual(values = c("#00798c", "#d1495b")) + # 특정 색깔 지정
scale_fill_manual(values = c("#00798c", "#d1495b")) + # 특정 색깔 지정
theme_bw()
8.4 데이터 분할
# Partition (Training Dataset : Test Dataset = 7:3)
y <- titanic1$Survived # Target
set.seed(200)
ind <- createDataPartition(y, p = 0.7, list =T) # Index를 이용하여 7:3으로 분할
titanic.trd <- titanic1[ind$Resample1,] # Training Dataset
titanic.ted <- titanic1[-ind$Resample1,] # Test Dataset8.5 데이터 전처리 II
# Imputation
titanic.trd.Imp <- titanic.trd %>%
mutate(Age = replace_na(Age, mean(Age, na.rm = TRUE))) # 평균으로 결측값 대체
titanic.ted.Imp <- titanic.ted %>%
mutate(Age = replace_na(Age, mean(titanic.trd$Age, na.rm = TRUE))) # Training Dataset을 이용하여 결측값 대체
glimpse(titanic.trd.Imp) # 데이터 구조 확인Rows: 625
Columns: 6
$ Survived <fct> no, yes, yes, no, no, no, yes, yes, yes, yes, no, no, yes, no, yes, no, yes, no, no, no, yes, no, no, yes, yes, no, no, no, no, no, yes, no, no, no, yes, no, yes, no, no, no, yes, n…
$ Pclass <fct> 3, 3, 1, 3, 3, 3, 3, 2, 3, 1, 3, 3, 2, 3, 3, 2, 1, 3, 3, 1, 3, 3, 1, 1, 3, 2, 1, 1, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 3, 3, 1, 3, 1, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 1, 2, 3…
$ Sex <fct> male, female, female, male, male, male, female, female, female, female, male, female, male, female, female, male, male, female, male, male, female, male, male, female, female, male,…
$ Age <dbl> 22.00000, 26.00000, 35.00000, 35.00000, 29.93737, 2.00000, 27.00000, 14.00000, 4.00000, 58.00000, 39.00000, 14.00000, 29.93737, 31.00000, 29.93737, 35.00000, 28.00000, 8.00000, 29.9…
$ Fare <dbl> 7.2500, 7.9250, 53.1000, 8.0500, 8.4583, 21.0750, 11.1333, 30.0708, 16.7000, 26.5500, 31.2750, 7.8542, 13.0000, 18.0000, 7.2250, 26.0000, 35.5000, 21.0750, 7.2250, 263.0000, 7.8792,…
$ FamSize <int> 1, 0, 1, 0, 0, 4, 2, 1, 2, 0, 6, 0, 0, 1, 0, 0, 0, 4, 0, 5, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 1, 0, 2, 1, 5, 1, 1, 0, 7, 0, 0, 5, 0, 2, 7, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3…glimpse(titanic.ted.Imp) # 데이터 구조 확인Rows: 266
Columns: 6
$ Survived <fct> yes, no, no, yes, no, yes, yes, yes, yes, yes, no, no, yes, yes, no, yes, no, yes, yes, no, yes, no, no, no, no, no, no, yes, yes, no, no, no, no, no, no, no, no, no, no, yes, no, n…
$ Pclass <fct> 1, 1, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 2, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 3, 3, 3, 3, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 2, 3, 3, 2, 1, 3, 1, 3, 2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 1, 3…
$ Sex <fct> female, male, male, female, male, male, female, female, male, female, male, male, female, female, male, female, male, male, female, male, female, male, male, male, male, male, male,…
$ Age <dbl> 38.00000, 54.00000, 20.00000, 55.00000, 2.00000, 34.00000, 15.00000, 38.00000, 29.93737, 3.00000, 29.93737, 21.00000, 29.00000, 21.00000, 28.50000, 5.00000, 45.00000, 29.93737, 29.0…
$ Fare <dbl> 71.2833, 51.8625, 8.0500, 16.0000, 29.1250, 13.0000, 8.0292, 31.3875, 7.2292, 41.5792, 8.0500, 7.8000, 26.0000, 10.5000, 7.2292, 27.7500, 83.4750, 15.2458, 10.5000, 8.1583, 7.9250, …
$ FamSize <int> 1, 0, 0, 0, 5, 0, 0, 6, 0, 3, 0, 0, 1, 0, 0, 3, 1, 2, 0, 0, 6, 0, 0, 0, 0, 4, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 6, 2, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 1, 5, 2, 5, 0, 5, 0, 4, 0, 6…8.6 모형 훈련
Package "caret"은 통합 API를 통해 R로 기계 학습을 실행할 수 있는 매우 실용적인 방법을 제공한다. Package "caret"를 통해 Ridge Regression을 수행하기 위해 옵션 method에 다양한 방법(Ex: "ridge", "foba" 등)을 입력할 수 있지만, 대부분 회귀 문제에 대해서만 분석이 가능하다. 분류와 회귀 문제 모두 가능한 "glmnet"을 이용하려면 옵션 tuneGrid = expand.grid()을 통해 탐색하고자 하는 초모수 lambda의 범위를 직접 지정해줘야 한다.
fitControl <- trainControl(method = "cv", number = 5, # 5-Fold Cross Validation (5-Fold CV)
allowParallel = TRUE) # 병렬 처리
set.seed(200) # For CV
ridge.fit <- train(Survived ~ ., data = titanic.trd.Imp,
trControl = fitControl ,
method = "glmnet",
tuneGrid = expand.grid(alpha = 0, # For Ridge Regression
lambda = seq(0, 1, 0.001)), # lambda의 탐색 범위
preProc = c("center", "scale")) # Standardization for 예측 변수
ridge.fitglmnet
625 samples
5 predictor
2 classes: 'no', 'yes'
Pre-processing: centered (6), scaled (6)
Resampling: Cross-Validated (5 fold)
Summary of sample sizes: 500, 500, 500, 500, 500
Resampling results across tuning parameters:
lambda Accuracy Kappa
0.000 0.7920 0.5477147
0.001 0.7920 0.5477147
0.002 0.7920 0.5477147
0.003 0.7920 0.5477147
0.004 0.7920 0.5477147
0.005 0.7920 0.5477147
0.006 0.7920 0.5477147
0.007 0.7920 0.5477147
0.008 0.7920 0.5477147
0.009 0.7920 0.5477147
0.010 0.7920 0.5477147
0.011 0.7920 0.5477147
0.012 0.7920 0.5477147
0.013 0.7920 0.5477147
0.014 0.7920 0.5477147
0.015 0.7920 0.5477147
0.016 0.7920 0.5477147
0.017 0.7920 0.5477147
0.018 0.7920 0.5477147
0.019 0.7920 0.5477147
0.020 0.7920 0.5477147
0.021 0.7920 0.5477147
0.022 0.7920 0.5477147
0.023 0.7920 0.5477147
0.024 0.7920 0.5477147
0.025 0.7920 0.5477147
0.026 0.7920 0.5477147
0.027 0.7904 0.5439323
0.028 0.7904 0.5439323
0.029 0.7904 0.5439323
0.030 0.7904 0.5439323
0.031 0.7888 0.5408846
0.032 0.7888 0.5408846
0.033 0.7904 0.5439795
0.034 0.7904 0.5439795
0.035 0.7904 0.5439795
0.036 0.7904 0.5439795
0.037 0.7904 0.5439795
0.038 0.7904 0.5439795
0.039 0.7888 0.5401998
0.040 0.7888 0.5401998
0.041 0.7888 0.5401998
0.042 0.7888 0.5401998
0.043 0.7888 0.5401998
0.044 0.7888 0.5401998
0.045 0.7888 0.5401998
0.046 0.7904 0.5432476
0.047 0.7904 0.5432476
0.048 0.7904 0.5432476
0.049 0.7936 0.5495496
0.050 0.7952 0.5526223
0.051 0.7952 0.5526223
0.052 0.7952 0.5526223
0.053 0.7984 0.5588816
0.054 0.7984 0.5588816
0.055 0.7968 0.5550660
0.056 0.7968 0.5550660
0.057 0.7968 0.5550660
0.058 0.7984 0.5582310
0.059 0.7984 0.5582310
0.060 0.7952 0.5503013
0.061 0.7952 0.5494856
0.062 0.7952 0.5494856
0.063 0.7952 0.5494856
0.064 0.7952 0.5494856
0.065 0.7952 0.5494856
0.066 0.7952 0.5494856
0.067 0.7952 0.5494856
0.068 0.7936 0.5456362
0.069 0.7936 0.5456362
0.070 0.7936 0.5456362
0.071 0.7920 0.5418538
0.072 0.7920 0.5418538
0.073 0.7904 0.5380410
0.074 0.7904 0.5380410
0.075 0.7920 0.5411832
0.076 0.7920 0.5411832
0.077 0.7920 0.5411832
0.078 0.7920 0.5411832
0.079 0.7920 0.5411832
0.080 0.7920 0.5411832
0.081 0.7920 0.5411832
0.082 0.7904 0.5373676
0.083 0.7904 0.5373676
0.084 0.7904 0.5373676
0.085 0.7904 0.5373676
0.086 0.7920 0.5405558
0.087 0.7920 0.5405558
0.088 0.7920 0.5405558
0.089 0.7920 0.5405558
0.090 0.7920 0.5405558
0.091 0.7920 0.5392003
0.092 0.7936 0.5424629
0.093 0.7920 0.5384109
0.094 0.7920 0.5384109
0.095 0.7920 0.5384109
0.096 0.7920 0.5384109
0.097 0.7920 0.5384109
0.098 0.7920 0.5384109
0.099 0.7904 0.5345671
0.100 0.7904 0.5345671
0.101 0.7920 0.5378571
0.102 0.7920 0.5378571
0.103 0.7936 0.5410796
0.104 0.7936 0.5410796
0.105 0.7936 0.5410796
0.106 0.7936 0.5410796
0.107 0.7936 0.5410796
0.108 0.7936 0.5410796
0.109 0.7936 0.5410796
0.110 0.7904 0.5322904
0.111 0.7920 0.5355403
0.112 0.7904 0.5316909
0.113 0.7904 0.5309466
0.114 0.7888 0.5256137
0.115 0.7888 0.5256137
0.116 0.7904 0.5288914
0.117 0.7904 0.5288914
0.118 0.7904 0.5288914
0.119 0.7904 0.5288914
0.120 0.7904 0.5288914
0.121 0.7904 0.5288914
0.122 0.7904 0.5288914
0.123 0.7904 0.5288914
0.124 0.7904 0.5288914
0.125 0.7888 0.5240297
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0.710 0.7600 0.4307502
0.711 0.7600 0.4307502
0.712 0.7584 0.4263125
0.713 0.7584 0.4263125
0.714 0.7584 0.4263125
0.715 0.7584 0.4263125
0.716 0.7584 0.4263125
0.717 0.7584 0.4263125
0.718 0.7584 0.4263125
0.719 0.7568 0.4221040
0.720 0.7568 0.4221040
0.721 0.7568 0.4221040
0.722 0.7568 0.4221040
0.723 0.7568 0.4221040
0.724 0.7568 0.4221040
0.725 0.7568 0.4221040
0.726 0.7568 0.4221040
0.727 0.7568 0.4221040
0.728 0.7568 0.4221040
0.729 0.7552 0.4177832
0.730 0.7552 0.4177832
0.731 0.7568 0.4210756
0.732 0.7568 0.4210756
0.733 0.7568 0.4210756
0.734 0.7568 0.4210756
0.735 0.7568 0.4210756
0.736 0.7568 0.4210756
0.737 0.7568 0.4210756
0.738 0.7568 0.4210756
0.739 0.7568 0.4210756
0.740 0.7568 0.4210756
0.741 0.7568 0.4210756
0.742 0.7568 0.4210756
0.743 0.7568 0.4210756
0.744 0.7568 0.4210756
0.745 0.7568 0.4210756
0.746 0.7568 0.4210756
0.747 0.7552 0.4167164
0.748 0.7552 0.4167164
0.749 0.7552 0.4167164
0.750 0.7552 0.4167164
0.751 0.7536 0.4122335
0.752 0.7536 0.4122335
0.753 0.7536 0.4122335
0.754 0.7536 0.4122335
0.755 0.7520 0.4078353
0.756 0.7520 0.4078353
0.757 0.7520 0.4078353
0.758 0.7520 0.4078353
0.759 0.7520 0.4078353
0.760 0.7520 0.4078353
0.761 0.7488 0.3991522
0.762 0.7488 0.3991522
0.763 0.7488 0.3991522
0.764 0.7472 0.3946285
0.765 0.7472 0.3946285
0.766 0.7456 0.3903123
0.767 0.7440 0.3860294
0.768 0.7440 0.3860294
0.769 0.7440 0.3860294
0.770 0.7440 0.3860294
0.771 0.7440 0.3860294
0.772 0.7408 0.3768573
0.773 0.7408 0.3768573
0.774 0.7392 0.3725366
0.775 0.7392 0.3725366
0.776 0.7392 0.3725366
0.777 0.7392 0.3725366
0.778 0.7376 0.3678871
0.779 0.7376 0.3678871
0.780 0.7376 0.3678871
0.781 0.7376 0.3678871
0.782 0.7376 0.3678871
0.783 0.7360 0.3635279
0.784 0.7360 0.3635279
0.785 0.7360 0.3635279
0.786 0.7360 0.3635279
0.787 0.7360 0.3635279
0.788 0.7360 0.3635279
0.789 0.7360 0.3635279
0.790 0.7344 0.3591735
0.791 0.7344 0.3591735
0.792 0.7344 0.3591735
0.793 0.7344 0.3591735
0.794 0.7344 0.3591735
0.795 0.7344 0.3591735
0.796 0.7328 0.3546959
0.797 0.7328 0.3546959
0.798 0.7344 0.3580118
0.799 0.7344 0.3580118
0.800 0.7328 0.3536136
0.801 0.7328 0.3536136
0.802 0.7312 0.3492205
0.803 0.7312 0.3492205
0.804 0.7312 0.3492205
0.805 0.7312 0.3492205
0.806 0.7312 0.3492205
0.807 0.7312 0.3492205
0.808 0.7312 0.3492205
0.809 0.7312 0.3492205
0.810 0.7296 0.3447829
0.811 0.7296 0.3447829
0.812 0.7296 0.3447829
0.813 0.7280 0.3400903
0.814 0.7280 0.3400903
0.815 0.7280 0.3400903
0.816 0.7280 0.3400903
0.817 0.7264 0.3358032
0.818 0.7264 0.3358032
0.819 0.7264 0.3358032
0.820 0.7264 0.3358032
0.821 0.7264 0.3358032
0.822 0.7264 0.3358032
0.823 0.7248 0.3312850
0.824 0.7248 0.3312850
0.825 0.7248 0.3312850
0.826 0.7232 0.3267258
0.827 0.7232 0.3267258
0.828 0.7232 0.3267258
0.829 0.7232 0.3267258
0.830 0.7232 0.3267258
0.831 0.7216 0.3221249
0.832 0.7216 0.3221249
0.833 0.7216 0.3221249
0.834 0.7216 0.3221249
0.835 0.7216 0.3221249
0.836 0.7216 0.3221249
0.837 0.7216 0.3221249
0.838 0.7216 0.3221249
0.839 0.7216 0.3221249
0.840 0.7216 0.3221249
0.841 0.7216 0.3221249
0.842 0.7216 0.3221249
0.843 0.7184 0.3131291
0.844 0.7184 0.3131291
0.845 0.7184 0.3131291
0.846 0.7184 0.3131291
0.847 0.7152 0.3038337
0.848 0.7152 0.3038337
0.849 0.7136 0.2994013
0.850 0.7120 0.2950760
0.851 0.7120 0.2950760
0.852 0.7120 0.2950760
0.853 0.7120 0.2950760
0.854 0.7120 0.2950760
0.855 0.7120 0.2950760
0.856 0.7120 0.2950760
0.857 0.7120 0.2950760
0.858 0.7104 0.2906038
0.859 0.7104 0.2906038
0.860 0.7104 0.2906038
0.861 0.7104 0.2906038
0.862 0.7104 0.2906038
0.863 0.7088 0.2858233
0.864 0.7088 0.2858233
0.865 0.7088 0.2858233
0.866 0.7072 0.2813109
0.867 0.7072 0.2813109
0.868 0.7072 0.2813109
0.869 0.7072 0.2813109
0.870 0.7072 0.2813109
0.871 0.7072 0.2813109
0.872 0.7072 0.2813109
0.873 0.7072 0.2813109
0.874 0.7072 0.2813109
0.875 0.7072 0.2813109
0.876 0.7072 0.2813109
0.877 0.7072 0.2813109
0.878 0.7056 0.2769470
0.879 0.7056 0.2769470
0.880 0.7056 0.2769470
0.881 0.7056 0.2769470
0.882 0.7056 0.2769470
0.883 0.7056 0.2769470
0.884 0.7040 0.2723038
0.885 0.7040 0.2723038
0.886 0.7040 0.2723038
0.887 0.7040 0.2723038
0.888 0.7040 0.2723038
0.889 0.7040 0.2723038
0.890 0.7040 0.2723038
0.891 0.7040 0.2723038
0.892 0.7040 0.2723038
0.893 0.7056 0.2755557
0.894 0.7072 0.2788371
0.895 0.7040 0.2695861
0.896 0.7040 0.2695861
0.897 0.7040 0.2695861
0.898 0.7024 0.2651830
0.899 0.7024 0.2651830
0.900 0.7024 0.2651830
0.901 0.7024 0.2651830
0.902 0.7024 0.2651830
0.903 0.7024 0.2651830
0.904 0.7024 0.2651830
0.905 0.7008 0.2607403
0.906 0.7008 0.2607403
0.907 0.7008 0.2607403
0.908 0.6992 0.2561394
0.909 0.6992 0.2561394
0.910 0.6976 0.2515324
0.911 0.6976 0.2515324
0.912 0.6976 0.2515324
0.913 0.6976 0.2515324
0.914 0.6960 0.2468030
0.915 0.6960 0.2468030
0.916 0.6960 0.2468030
0.917 0.6960 0.2468030
0.918 0.6960 0.2468030
0.919 0.6960 0.2468030
0.920 0.6960 0.2468030
0.921 0.6960 0.2468030
0.922 0.6944 0.2419776
0.923 0.6944 0.2419776
0.924 0.6944 0.2419776
0.925 0.6944 0.2419776
0.926 0.6944 0.2419776
0.927 0.6944 0.2419776
0.928 0.6928 0.2374946
0.929 0.6912 0.2328515
0.930 0.6896 0.2281656
0.931 0.6896 0.2281656
0.932 0.6896 0.2281656
0.933 0.6896 0.2281656
0.934 0.6896 0.2281656
0.935 0.6896 0.2281656
0.936 0.6896 0.2281656
0.937 0.6896 0.2281656
0.938 0.6896 0.2281656
0.939 0.6896 0.2281656
0.940 0.6896 0.2281656
0.941 0.6880 0.2233922
0.942 0.6880 0.2233922
0.943 0.6880 0.2233922
0.944 0.6880 0.2233922
0.945 0.6880 0.2233922
0.946 0.6880 0.2233922
0.947 0.6880 0.2233922
0.948 0.6864 0.2186628
0.949 0.6864 0.2186628
0.950 0.6848 0.2141391
0.951 0.6848 0.2141391
0.952 0.6832 0.2093211
0.953 0.6832 0.2093211
0.954 0.6832 0.2093211
0.955 0.6832 0.2093211
0.956 0.6832 0.2093211
0.957 0.6832 0.2093211
0.958 0.6832 0.2093211
0.959 0.6832 0.2093211
0.960 0.6832 0.2093211
0.961 0.6832 0.2093211
0.962 0.6832 0.2093211
0.963 0.6832 0.2093211
0.964 0.6816 0.2046716
0.965 0.6816 0.2046716
0.966 0.6816 0.2046716
0.967 0.6816 0.2046716
0.968 0.6816 0.2046716
0.969 0.6816 0.2046716
0.970 0.6816 0.2046716
0.971 0.6816 0.2046716
0.972 0.6816 0.2046716
0.973 0.6800 0.1998983
0.974 0.6784 0.1953332
0.975 0.6784 0.1953332
0.976 0.6768 0.1906406
0.977 0.6768 0.1906406
0.978 0.6768 0.1906406
0.979 0.6768 0.1906406
0.980 0.6768 0.1906406
0.981 0.6768 0.1906406
0.982 0.6768 0.1906406
0.983 0.6768 0.1906406
0.984 0.6768 0.1906406
0.985 0.6752 0.1857774
0.986 0.6752 0.1857774
0.987 0.6752 0.1857774
0.988 0.6752 0.1857774
0.989 0.6752 0.1857774
0.990 0.6752 0.1857774
0.991 0.6720 0.1762612
0.992 0.6720 0.1762612
0.993 0.6720 0.1762612
0.994 0.6720 0.1762612
0.995 0.6720 0.1762612
0.996 0.6720 0.1762612
0.997 0.6720 0.1762612
0.998 0.6704 0.1715250
0.999 0.6688 0.1668755
1.000 0.6688 0.1668755
Tuning parameter 'alpha' was held constant at a value of 0
Accuracy was used to select the optimal model using the largest value.
The final values used for the model were alpha = 0 and lambda = 0.059.plot(ridge.fit) # Plot
ridge.fit$bestTune # lambda의 최적값 alpha lambda
60 0 0.059Result! lambda = 0.059일 때 정확도가 가장 높은 것을 알 수 있으며, lambda = 0.059를 가지는 모형을 최적의 훈련된 모형으로 선택한다.
round(coef(ridge.fit$finalModel, ridge.fit$bestTune$lambda), 3) # lambda의 최적값에 대한 회귀계수 추정치7 x 1 sparse Matrix of class "dgCMatrix"
s1
(Intercept) -0.566
Pclass2 -0.072
Pclass3 -0.569
Sexmale -0.871
Age -0.251
Fare 0.247
FamSize -0.204Result! 데이터 “titanic.trd.Imp”의 Target “Survived”은 “no”와 “yes” 2개의 클래스를 가지며, “Factor” 변환하면 알파벳순으로 수준을 부여하기 때문에 “yes”가 두 번째 클래스가 된다. 즉, “yes”에 속할 확률(= 탑승객이 생존할 확률)을 \(p\)라고 할 때, 추정된 회귀계수를 이용하여 다음과 같은 모형식을 얻을 수 있다. \[
\begin{align*}
\log{\frac{p}{1-p}} = &-0.566 - 0.072 Z_{\text{Pclass2}} - 0.569 Z_{\text{Pclass3}} -0.871 Z_{\text{Sexmale}} \\
&-0.251 Z_{\text{Age}} +0.247 Z_{\text{Fare}} - 0.204 Z_{\text{FamSize}}
\end{align*}
\] 여기서, \(Z_{\text{예측 변수}}\)는 표준화한 예측 변수를 의미한다.
범주형 예측 변수(“Pclass”, “Sex”)는 더미 변환이 수행되었는데, 예를 들어, Pclass2는 탑승객의 티켓 등급이 2등급인 경우 “1”값을 가지고 2등급이 아니면 “0”값을 가진다.
8.7 모형 평가
Caution! 모형 평가를 위해 Test Dataset에 대한 예측 class/확률 이 필요하며, 함수 predict()를 이용하여 생성한다.
# 예측 class 생성
test.ridge.class <- predict(ridge.fit,
newdata = titanic.ted.Imp[,-1]) # Test Dataset including Only 예측 변수
test.ridge.class %>%
as_tibble# A tibble: 266 × 1
value
<fct>
1 yes
2 no
3 no
4 yes
5 no
6 no
7 yes
8 no
9 no
10 yes
# ℹ 256 more rows8.7.1 ConfusionMatrix
CM <- caret::confusionMatrix(test.ridge.class, titanic.ted.Imp$Survived,
positive = "yes") # confusionMatrix(예측 class, 실제 class, positive = "관심 class")
CMConfusion Matrix and Statistics
Reference
Prediction no yes
no 152 36
yes 12 66
Accuracy : 0.8195
95% CI : (0.768, 0.8638)
No Information Rate : 0.6165
P-Value [Acc > NIR] : 5.675e-13
Kappa : 0.6006
Mcnemar's Test P-Value : 0.0009009
Sensitivity : 0.6471
Specificity : 0.9268
Pos Pred Value : 0.8462
Neg Pred Value : 0.8085
Prevalence : 0.3835
Detection Rate : 0.2481
Detection Prevalence : 0.2932
Balanced Accuracy : 0.7869
'Positive' Class : yes
8.7.2 ROC 곡선
# 예측 확률 생성
test.ridge.prob <- predict(ridge.fit,
newdata = titanic.ted.Imp[,-1],# Test Dataset including Only 예측 변수
type = "prob") # 예측 확률 생성
test.ridge.prob %>%
as_tibble# A tibble: 266 × 2
no yes
<dbl> <dbl>
1 0.219 0.781
2 0.694 0.306
3 0.820 0.180
4 0.352 0.648
5 0.842 0.158
6 0.691 0.309
7 0.404 0.596
8 0.663 0.337
9 0.847 0.153
10 0.202 0.798
# ℹ 256 more rowstest.ridge.prob <- test.ridge.prob[,2] # "Survived = yes"에 대한 예측 확률
ac <- titanic.ted.Imp$Survived # Test Dataset의 실제 class
pp <- as.numeric(test.ridge.prob) # 예측 확률을 수치형으로 변환8.7.2.1 Package “pROC”
pacman::p_load("pROC")
ridge.roc <- roc(ac, pp, plot = T, col = "gray") # roc(실제 class, 예측 확률)
auc <- round(auc(ridge.roc), 3)
legend("bottomright", legend = auc, bty = "n")
Caution! Package "pROC"를 통해 출력한 ROC 곡선은 다양한 함수를 이용해서 그래프를 수정할 수 있다.
# 함수 plot.roc() 이용
plot.roc(ridge.roc,
col="gray", # Line Color
print.auc = TRUE, # AUC 출력 여부
print.auc.col = "red", # AUC 글씨 색깔
print.thres = TRUE, # Cutoff Value 출력 여부
print.thres.pch = 19, # Cutoff Value를 표시하는 도형 모양
print.thres.col = "red", # Cutoff Value를 표시하는 도형의 색깔
auc.polygon = TRUE, # 곡선 아래 면적에 대한 여부
auc.polygon.col = "gray90") # 곡선 아래 면적의 색깔
# 함수 ggroc() 이용
ggroc(ridge.roc) +
annotate(geom = "text", x = 0.9, y = 1.0,
label = paste("AUC = ", auc),
size = 5,
color="red") +
theme_bw()
8.7.2.2 Package “Epi”
pacman::p_load("Epi")
# install_version("etm", version = "1.1", repos = "http://cran.us.r-project.org")
ROC(pp, ac, plot = "ROC") # ROC(예측 확률, 실제 class) 
8.7.2.3 Package “ROCR”
pacman::p_load("ROCR")
ridge.pred <- prediction(pp, ac) # prediction(예측 확률, 실제 class)
ridge.perf <- performance(ridge.pred, "tpr", "fpr") # performance(, "민감도", "1-특이도")
plot(ridge.perf, col = "gray") # ROC Curve
perf.auc <- performance(ridge.pred, "auc") # AUC
auc <- attributes(perf.auc)$y.values
legend("bottomright", legend = auc, bty = "n")
8.7.3 향상 차트
8.7.3.1 Package “ROCR”
ridge.perf <- performance(ridge.pred, "lift", "rpp") # Lift Chart
plot(ridge.perf, main = "lift curve",
colorize = T, # Coloring according to cutoff
lwd = 2) 