1. Package
Berikut ini adalah package yang dipakai dalam analisa week 5 ini.
library(gbm)## Loaded gbm 2.1.8library(mlr3tuning)## Loading required package: mlr3## Loading required package: paradoxlibrary(gam)## Loading required package: splines## Loading required package: foreach## Loaded gam 1.20library(rpart)
library(pROC)## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, varlibrary(tidyverse)## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.3 v dplyr 1.0.7
## v tidyr 1.1.3 v stringr 1.4.0
## v readr 2.0.1 v forcats 0.5.1## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x purrr::accumulate() masks foreach::accumulate()
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
## x purrr::when() masks foreach::when()library(mlr3verse)
library(mlr3extralearners)##
## Attaching package: 'mlr3extralearners'## The following objects are masked from 'package:mlr3':
##
## lrn, lrnslibrary(precrec)##
## Attaching package: 'precrec'## The following object is masked from 'package:pROC':
##
## auclibrary(adabag)## Loading required package: caret## Loading required package: lattice##
## Attaching package: 'caret'## The following object is masked from 'package:purrr':
##
## lift## Loading required package: doParallel## Loading required package: iterators## Loading required package: parallellibrary(ROCR)
library(ROCit)
library(magrittr)##
## Attaching package: 'magrittr'## The following object is masked from 'package:purrr':
##
## set_names## The following object is masked from 'package:tidyr':
##
## extractlibrary(visdat)
library(naniar)
library(UpSetR)##
## Attaching package: 'UpSetR'## The following object is masked from 'package:lattice':
##
## histogramlibrary(laeken)
library(vcd)## Loading required package: gridlibrary(VIM)## Loading required package: colorspace##
## Attaching package: 'colorspace'## The following object is masked from 'package:pROC':
##
## coords## VIM is ready to use.## Suggestions and bug-reports can be submitted at: https://github.com/statistikat/VIM/issues##
## Attaching package: 'VIM'## The following object is masked from 'package:datasets':
##
## sleeplibrary(sm)## Package 'sm', version 2.2-5.7: type help(sm) for summary informationlibrary(ggplot2)
library(dplyr)
library(mlbench)
library(caret)
library(mlr3verse)
library(mlr3fselect)
library(DataExplorer)
library(skimr)##
## Attaching package: 'skimr'## The following object is masked from 'package:naniar':
##
## n_complete## The following object is masked from 'package:mlr3':
##
## partitionlibrary(corrplot)## corrplot 0.92 loadedlibrary(leaps)
library(olsrr)##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riverslibrary(kableExtra) #Tampilan Tabel##
## Attaching package: 'kableExtra'## The following object is masked from 'package:dplyr':
##
## group_rowslibrary(agricolae) #Pemeriksaan Asumsi
library(lmtest) #Untuk pengecekan asumsi## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(car) #Untuk pengecekan asumsi## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:ROCit':
##
## logit## The following object is masked from 'package:dplyr':
##
## recode## The following object is masked from 'package:purrr':
##
## somelibrary(tseries) #Untuk pengecekan asumsi## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(glmnet)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loaded glmnet 4.1-2library(glmnetUtils)##
## Attaching package: 'glmnetUtils'## The following objects are masked from 'package:glmnet':
##
## cv.glmnet, glmnetlibrary(broom)
library(ggpubr)
library(modelr)##
## Attaching package: 'modelr'## The following object is masked from 'package:broom':
##
## bootstrap## The following object is masked from 'package:mlr3':
##
## resamplelibrary(precrec)
library(adabag)
library(rpart.plot)
library(mice)##
## Attaching package: 'mice'## The following object is masked from 'package:stats':
##
## filter## The following objects are masked from 'package:base':
##
## cbind, rbindlibrary(caret)
library(randomForest)## randomForest 4.6-14## Type rfNews() to see new features/changes/bug fixes.##
## Attaching package: 'randomForest'## The following object is masked from 'package:dplyr':
##
## combine## The following object is masked from 'package:ggplot2':
##
## marginlibrary(ROSE)## Loaded ROSE 0.0-42. Data Training
Data training yang dipakai adalah data training hasil pre-processing pada week sebelumnya dengan sedikit ada perubahan yaitu merubah variabel factor menjadi variabel dummy.
data2 <- read.csv2("D:/Magister IPB/Kuliah/Semester 2/STA582_Pembelajaran_Mesin_Statistika/Praktikum/Tugas_UTS/Problem 2/datatrainnew.csv",stringsAsFactors = TRUE)
dim(data2)## [1] 49692 13data2$bed_type <- ifelse(data2$bed_type == "Airbed", 1, ifelse(data2$bed_type == "Couch", 2, ifelse(data2$bed_type == "Futon", 3, ifelse(data2$bed_type == "Pull-out Sofa", 4,5))))
data2$cancellation_policy <- ifelse(data2$cancellation_policy == "flexible", 1, ifelse(data2$cancellation_policy == "moderate", 2, ifelse(data2$cancellation_policy == "strict", 3, ifelse(data2$cancellation_policy == "Psuper_strict_30", 4,5))))
data2$city <- ifelse(data2$city == "Boston", 1, ifelse(data2$city == "Chicago", 2, ifelse(data2$city == "DC", 3, ifelse(data2$city == "LA", 4,ifelse(data2$city == "NYC", 5,6)))))
data2$property_type <- ifelse(data2$property_type == "Apartment", 1,
ifelse(data2$property_type == "Bed & Breakfast", 2,
ifelse(data2$property_type == "Boat", 3,
ifelse(data2$property_type == "Boutique hotel", 4,
ifelse(data2$property_type == "Bungalow", 5,
ifelse(data2$property_type == "Cabin", 6,
ifelse(data2$property_type == "Camper/RV", 7,
ifelse(data2$property_type == "Castle", 8,
ifelse(data2$property_type == "Cave", 9,
ifelse(data2$property_type == "Chalet", 10,
ifelse(data2$property_type == "Condominium", 11,
ifelse(data2$property_type == "Dorm", 12,
ifelse(data2$property_type == "Earth House", 13,
ifelse(data2$property_type == "Guest suite", 14,
ifelse(data2$property_type == "Guesthouse", 15,
ifelse(data2$property_type == "Hostel", 16,
ifelse(data2$property_type == "House", 17,
ifelse(data2$property_type == "Hut", 18,
ifelse(data2$property_type == "In-law", 19,
ifelse(data2$property_type == "Loft", 20,
ifelse(data2$property_type == "Other", 21,
ifelse(data2$property_type == "Serviced apartment", 22,
ifelse(data2$property_type == "Tent", 23,
ifelse(data2$property_type == "Timeshare", 24,
ifelse(data2$property_type == "Townhouse", 25,
ifelse(data2$property_type == "Train", 26,
ifelse(data2$property_type == "Treehouse", 27,
ifelse(data2$property_type == "Vacation home", 28,
ifelse(data2$property_type == "Villa", 29,
30)))))))))))))))))))))))))))))
str(data2)## 'data.frame': 49692 obs. of 13 variables:
## $ property_type : num 1 1 1 1 1 1 11 17 17 1 ...
## $ room_type : Factor w/ 3 levels "Entire home/apt",..: 1 1 1 1 2 1 1 2 2 2 ...
## $ accommodates : int 3 7 5 2 2 3 2 2 2 2 ...
## $ bathrooms : int 1 1 1 1 1 1 1 1 1 1 ...
## $ bed_type : num 5 5 5 5 5 5 5 5 5 5 ...
## $ cancellation_policy: num 3 3 2 2 3 2 2 2 2 3 ...
## $ cleaning_fee : logi TRUE TRUE TRUE TRUE TRUE TRUE ...
## $ city : num 5 5 5 3 6 4 4 6 4 5 ...
## $ instant_bookable : Factor w/ 2 levels "f","t": 1 2 2 2 2 2 1 1 2 1 ...
## $ bedrooms : int 1 3 1 0 1 1 1 1 1 1 ...
## $ beds : int 1 3 3 1 1 1 1 1 1 1 ...
## $ price : num 5.01 5.13 4.98 4.74 4.44 ...
## $ sum_amenities : int 9 15 19 12 10 21 26 21 13 15 ...anyNA(data2)## [1] FALSEdata2$cleaning_fee<- as.factor(data2$cleaning_fee)
glimpse(data2)## Rows: 49,692
## Columns: 13
## $ property_type <dbl> 1, 1, 1, 1, 1, 1, 11, 17, 17, 1, 1, 1, 1, 20, 25, ~
## $ room_type <fct> Entire home/apt, Entire home/apt, Entire home/apt,~
## $ accommodates <int> 3, 7, 5, 2, 2, 3, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 8,~
## $ bathrooms <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,~
## $ bed_type <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,~
## $ cancellation_policy <dbl> 3, 3, 2, 2, 3, 2, 2, 2, 2, 3, 1, 3, 3, 3, 3, 3, 3,~
## $ cleaning_fee <fct> TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TR~
## $ city <dbl> 5, 5, 5, 3, 6, 4, 4, 6, 4, 5, 4, 3, 4, 2, 1, 5, 5,~
## $ instant_bookable <fct> f, t, t, t, t, t, f, f, t, f, f, t, f, f, f, f, t,~
## $ bedrooms <int> 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3,~
## $ beds <int> 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 3,~
## $ price <dbl> 5.010635, 5.129899, 4.976734, 4.744932, 4.442651, ~
## $ sum_amenities <int> 9, 15, 19, 12, 10, 21, 26, 21, 13, 15, 17, 25, 7, ~3. Data Testing
Data testing tetap menggunakan data test awal, namun ada sedikit modifkasi yaitu adanya proses imputasi data hilang agar bisa dieksekuis prediksinya dalam model yang sudah dibangun. Metode dalam imputasi menggunakan random forest.
data_test <- read.csv2("D:/Magister IPB/Kuliah/Semester 2/STA582_Pembelajaran_Mesin_Statistika/Praktikum/Tugas_UTS/Problem 2/test2.csv",stringsAsFactors = TRUE)
data_test<- data_test[,c(2,3,5,6,7,8,9,10,17,27,28,29)]
data_test$bed_type <- ifelse(data_test$bed_type == "Airbed", 1, ifelse(data_test$bed_type == "Couch", 2, ifelse(data_test$bed_type == "Futon", 3, ifelse(data_test$bed_type == "Pull-out Sofa", 4,5))))
data_test$cancellation_policy <- ifelse(data_test$cancellation_policy == "flexible", 1, ifelse(data_test$cancellation_policy == "moderate", 2, ifelse(data_test$cancellation_policy == "strict", 3, ifelse(data_test$cancellation_policy == "Psuper_strict_30", 4,5))))
data_test$city <- ifelse(data_test$city == "Boston", 1, ifelse(data_test$city == "Chicago", 2, ifelse(data_test$city == "DC", 3, ifelse(data_test$city == "LA", 4,ifelse(data_test$city == "NYC", 5,6)))))
data_test$property_type <- ifelse(data_test$property_type == "Apartment", 1,
ifelse(data_test$property_type == "Bed & Breakfast", 2,
ifelse(data_test$property_type == "Boat", 3,
ifelse(data_test$property_type == "Boutique hotel", 4,
ifelse(data_test$property_type == "Bungalow", 5,
ifelse(data_test$property_type == "Cabin", 6,
ifelse(data_test$property_type == "Camper/RV", 7,
ifelse(data_test$property_type == "Castle", 8,
ifelse(data_test$property_type == "Cave", 9,
ifelse(data_test$property_type == "Chalet", 10,
ifelse(data_test$property_type == "Condominium", 11,
ifelse(data_test$property_type == "Dorm", 12,
ifelse(data_test$property_type == "Earth House", 13,
ifelse(data_test$property_type == "Guest suite", 14,
ifelse(data_test$property_type == "Guesthouse", 15,
ifelse(data_test$property_type == "Hostel", 16,
ifelse(data_test$property_type == "House", 17,
ifelse(data_test$property_type == "Hut", 18,
ifelse(data_test$property_type == "In-law", 19,
ifelse(data_test$property_type == "Loft", 20,
ifelse(data_test$property_type == "Other", 21,
ifelse(data_test$property_type == "Serviced apartment", 22,
ifelse(data_test$property_type == "Tent", 23,
ifelse(data_test$property_type == "Timeshare", 24,
ifelse(data_test$property_type == "Townhouse", 25,
ifelse(data_test$property_type == "Train", 26,
ifelse(data_test$property_type == "Treehouse", 27,
ifelse(data_test$property_type == "Vacation home", 28,
ifelse(data_test$property_type == "Villa", 29,
30)))))))))))))))))))))))))))))
data_test$cleaning_fee <- as.factor(data_test$cleaning_fee)
glimpse(data_test)## Rows: 22,232
## Columns: 12
## $ property_type <dbl> 17, 1, 1, 17, 1, 1, 1, 1, 1, 1, 17, 17, 1, 1, 1, 1~
## $ room_type <fct> Entire home/apt, Private room, Entire home/apt, Pr~
## $ accommodates <int> 4, 2, 4, 2, 4, 6, 4, 8, 2, 1, 2, 2, 2, 5, 6, 1, 3,~
## $ bathrooms <dbl> 1.5, 1.5, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, ~
## $ bed_type <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,~
## $ cancellation_policy <dbl> 3, 2, 2, 2, 2, 3, 3, 2, 1, 1, 3, 3, 1, 3, 3, 1, 2,~
## $ cleaning_fee <fct> TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FA~
## $ city <dbl> 4, 2, 4, 4, 3, 5, 4, 4, 5, 5, 5, 2, 4, 5, 1, 5, 4,~
## $ instant_bookable <fct> f, f, t, f, f, f, f, t, f, f, t, f, f, f, f, f, f,~
## $ bedrooms <int> 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1,~
## $ beds <int> 2, 1, 1, 1, 2, 3, 3, 7, 1, 1, 1, 1, 1, 2, 4, 1, 1,~
## $ sum_amenities <int> 22, 12, 29, 16, 14, 44, 27, 15, 14, 16, 22, 20, 15~str(data_test)## 'data.frame': 22232 obs. of 12 variables:
## $ property_type : num 17 1 1 17 1 1 1 1 1 1 ...
## $ room_type : Factor w/ 3 levels "Entire home/apt",..: 1 2 1 2 1 1 1 2 1 2 ...
## $ accommodates : int 4 2 4 2 4 6 4 8 2 1 ...
## $ bathrooms : num 1.5 1.5 1 1 1 1 1 1 1 1 ...
## $ bed_type : num 5 5 5 5 5 5 5 5 5 5 ...
## $ cancellation_policy: num 3 2 2 2 2 3 3 2 1 1 ...
## $ cleaning_fee : Factor w/ 2 levels "FALSE","TRUE": 2 2 2 2 2 2 2 2 1 1 ...
## $ city : num 4 2 4 4 3 5 4 4 5 5 ...
## $ instant_bookable : Factor w/ 2 levels "f","t": 1 1 2 1 1 1 1 2 1 1 ...
## $ bedrooms : int 2 1 1 1 1 3 2 1 1 1 ...
## $ beds : int 2 1 1 1 2 3 3 7 1 1 ...
## $ sum_amenities : int 22 12 29 16 14 44 27 15 14 16 ...Cek data hilang
sum_mis2<-miss_var_summary(data_test)
sum_mis_plot2<-head(sum_mis2,7)
sum_mis_plot2Imputasi data hilang
my_imptest<- mice(data_test, m = 2, method = "rf", maxit = 10, seed = 52500)##
## iter imp variable
## 1 1 bathrooms bedrooms beds
## 1 2 bathrooms bedrooms beds
## 2 1 bathrooms bedrooms beds
## 2 2 bathrooms bedrooms beds
## 3 1 bathrooms bedrooms beds
## 3 2 bathrooms bedrooms beds
## 4 1 bathrooms bedrooms beds
## 4 2 bathrooms bedrooms beds
## 5 1 bathrooms bedrooms beds
## 5 2 bathrooms bedrooms beds
## 6 1 bathrooms bedrooms beds
## 6 2 bathrooms bedrooms beds
## 7 1 bathrooms bedrooms beds
## 7 2 bathrooms bedrooms beds
## 8 1 bathrooms bedrooms beds
## 8 2 bathrooms bedrooms beds
## 9 1 bathrooms bedrooms beds
## 9 2 bathrooms bedrooms beds
## 10 1 bathrooms bedrooms beds
## 10 2 bathrooms bedrooms bedssummary(my_imptest)## Class: mids
## Number of multiple imputations: 2
## Imputation methods:
## property_type room_type accommodates bathrooms
## "" "" "" "rf"
## bed_type cancellation_policy cleaning_fee city
## "" "" "" ""
## instant_bookable bedrooms beds sum_amenities
## "" "rf" "rf" ""
## PredictorMatrix:
## property_type room_type accommodates bathrooms bed_type
## property_type 0 1 1 1 1
## room_type 1 0 1 1 1
## accommodates 1 1 0 1 1
## bathrooms 1 1 1 0 1
## bed_type 1 1 1 1 0
## cancellation_policy 1 1 1 1 1
## cancellation_policy cleaning_fee city instant_bookable
## property_type 1 1 1 1
## room_type 1 1 1 1
## accommodates 1 1 1 1
## bathrooms 1 1 1 1
## bed_type 1 1 1 1
## cancellation_policy 0 1 1 1
## bedrooms beds sum_amenities
## property_type 1 1 1
## room_type 1 1 1
## accommodates 1 1 1
## bathrooms 1 1 1
## bed_type 1 1 1
## cancellation_policy 1 1 1data_test_final = complete(my_imptest,2)Cek kembali data hilang
anyNA(data_test_final)## [1] FALSEsum_mis3<-miss_var_summary(data_test_final)
sum_mis_plot3<-head(sum_mis3,7)
sum_mis_plot3Data hilang sudah berhasil diselesaikan.
4. Eksplorasi Korelasi Data
Berikut ini adalah pola hubungan setiap variabel prediktor dengan variabel respon.
DataExplorer::plot_scatterplot(data = data2,
by = "price",nrow = 3,ncol = 3,geom_point_args = list(color="Steelblue"))
plot_intro(data2)
5. Pemodelan
Pada pertemuan ini metode yang akan digunakan dalam pomodelan adalah regresi gradient boost.
Gradient Boosting
Pertama kita akan bangun dengan menggunakan model gradient boosting, untuk kemudian akan kita uji akurasinya dengan menggunakan fungsi predict yang mengacu pada nilai RMSE dan MAE.
Memprediksi respon pada data baru
Berikut ini kita definisikan dahulu fungsi untuk membangun regresi gradient boosting.
gbm <- gbm(formula = price ~ .,
distribution = "gaussian",
data =data2,
n.trees = 500,
interaction.depth = 12,
cv.folds = 5,
n.cores = NULL, # will use all cores by default
verbose = FALSE)
print(gbm)## gbm(formula = price ~ ., distribution = "gaussian", data = data2,
## n.trees = 500, interaction.depth = 12, cv.folds = 5, verbose = FALSE,
## n.cores = NULL)
## A gradient boosted model with gaussian loss function.
## 500 iterations were performed.
## The best cross-validation iteration was 305.
## There were 12 predictors of which 12 had non-zero influence.Variabel Importance
Berikut ini akan ditampilkan urutan variabel yang paling berpengaruh terhadap variabel respon secara terurut tersusun menurun.
sqrt(min(gbm$cv.error))## [1] 0.3777056summary(gbm)
Tuning Hyperparameter
Untuk mendapatkan model terbaik, perlu dilakukan tuning hyperparameter sebagai berikut.
hyper_grid <- expand.grid(
interaction.depth = c(2,5,7,9,12), #Maximum depth of each tree
optimal_trees = 0,
min_mae = 0,
n.minobsinnode = c(1000, 500, 100,50,25)# minimum number of observations in the terminal nodes of the trees
)
nrow(hyper_grid) ## [1] 25Berikutnya kita siapkan random data baru sebagai data uji bagi model yang sudah terbentuk.
# data dummy
set.seed(123)
data_house_baru <- data2 %>% slice_sample(n=100)
head(data_house_baru)Sekarang kita siapkan, parameter-parameter yang akan kita tuning.
for(i in 1:nrow(hyper_grid)) {
set.seed(123)
gbm.tune <- gbm(
formula = price ~ .,
distribution = "gaussian",
data = data2,
n.trees = 1000,
interaction.depth = hyper_grid$interaction.depth[i],
n.minobsinnode = hyper_grid$n.minobsinnode[i],
train.fraction = 0.75,
n.cores = NULL,
verbose = FALSE
)
hyper_grid$optimal_trees[i] <- which.min(gbm.tune$valid.error)
hyper_grid$min_mae[i] <- sqrt(min(gbm.tune$valid.error))
}
hyper_grid %>%
dplyr::arrange(min_mae) %>%
head(10)min(hyper_grid$min_mae)## [1] 0.3791272Berdasarkan output di atas, dapat disimpulkan bahwa model ini akan menghasilkan nilai RMSE minimum saat kita menggunakan interaction.depth = 12, n-trees = 316, dan n.minobsinnode = 25. Hal ini terlihat dari nilai RMSE nya adalah yang paling kecil.
Final Model
Sekarang kita bangun ulang model dengan menggunakan model yang terbaik di atas.
# train GBM model
gbm.fit.final <- gbm(
formula = price ~ .,
distribution = "gaussian",
data = data2,
n.trees = 316,
interaction.depth = 12,
n.minobsinnode = 25,
n.cores = NULL,
verbose = FALSE
)
summary(gbm.fit.final, cBars = 10,
method = relative.influence, las = 2)
Didapatkan secara terurut variabel importance dari model tsb.
Predict data test
Selanjutnya kita prediksi variabel respon dengan menggunakan datatest.
gbm_pred <- predict(object=gbm.fit.final, newdata=data_test_final)## Using 316 trees...gbm_pred<-as.data.frame(gbm_pred)
a<-gbm_pred$gbm_predKemudian kita simulasikan dengan data test yang sebelumnya kita siapkan. Data test kita kembalikan ke bentuk asalnya karena data test yang kita gunakan sudah ditransformasi ke bentuk logaritma natural.
#Mengembalikan fungsi log natural
pred_gbm<- 2.718282^(a)
pred_gbm<-as.data.frame(pred_gbm)7. Kesimpulan
Adapun yang dapat disimpulkan dari simulasi di atas adalah sbb:
- Model terbaik adalah regresi gradient boosting dengan hyperparameter tertentu.
- Metode ini dapat sangat baik dalam menjelaskan hubungan antara variabel respon dan predictor.
- Tuning hyperparameter adalah hal yang sangat penting untuk dilakukan.
- Semakin presisi model pada data training, maka berpeluang akan overfit pada data test.
- Model regresi gradient boosting ini lebih baik dibanding model random forest.
Referensi
Breheny P. (n.d.). Getting started with grpreg. GitHub Pages. https://pbreheny.github.io/grpreg/articles/getting-started.html
Hastie T. (2013, May 9). glmnet: Lasso and elastic-net regularization in R. Revolutions. https://blog.revolutionanalytics.com/2013/05/hastie-glmnet.html
Post J. (2014, September 29). LASSO, Ridge, and Elastic Net. https://www4.stat.ncsu.edu/~post/josh/LASSO_Ridge_Elastic_Net_-_Examples.html
Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., & Knight, K. (2005). Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(1), 91-108. https://doi.org/10.1111/j.1467-9868.2005.00490.x
Tripathy A. (2013, July 14). Regularization – Predictive Modeling Beyond Ordinary Least Squares Fit. ShatterLine Blog. https://shatterline.com/blog/2013/07/
Xiaotong C., Chen G., & Chong W. (n.d.). Statistical Learning and Data Mining Codes. Biostatistics - Academic Divisions - School of Public Health - University of Minnesota. https://www.biostat.umn.edu/~weip/course/dm/examples/