R语言拉索回归

拉索回归是一种分类算法，在简单和稀疏的模型（即参数较少的模型）中使用缩减。在缩减中，数据值被缩减到一个中心点，如平均值。Lasso回归是一种正则化的回归算法，执行L1正则化，增加相当于系数大小绝对值的惩罚。

“LASSO “是最小绝对收缩和选择运算符的缩写。 拉索回归适用于显示出高水平的多重共线性的模型，或者当你想自动选择模型的某些部分，如变量选择或参数消除时。拉索回归解决方案是二次编程问题，最好用RStudio、Matlab等软件解决。它具有选择预测器的能力。

R编程中的拉索回归

该算法使有约束的平方之和最小化。一些 Beta值 被缩减为零，从而形成一个回归模型。一个调整参数 lambda 控制L1正则化惩罚的强度。

当 lambda =0时，没有参数被消除。
随着 lambda 的增加，越来越多的系数被设置为零并被消除，偏差也随之增加。
当 λ =无穷大时，所有的系数都被消除了。
随着 lambda 的减少，方差增加。

另外，如果模型中包含截距，则不作任何改变。现在让我们在R编程中实现Lasso回归。

在R中实现

# Loading data
train = fread("Train_UWu5bXk.csv")
test = fread("Test_u94Q5KV.csv")
   
# Structure
str(train)

输出

R编程中的拉索回归

对数据集进行拉索回归

在数据集上使用Lasso回归算法，该数据集包括12个特征，有1559种产品，分布在不同城市的10家商店。

# Installing Packages
install.packages("data.table")
install.packages("dplyr")
install.packages("glmnet")
install.packages("ggplot2")
install.packages("caret")
install.packages("xgboost")
install.packages("e1071")
install.packages("cowplot")
 
# load packages
library(data.table) # used for reading and manipulation of data
library(dplyr)      # used for data manipulation and joining
library(glmnet)     # used for regression
library(ggplot2)    # used for ploting
library(caret)      # used for modeling
library(xgboost)    # used for building XGBoost model
library(e1071)      # used for skewness
library(cowplot)    # used for combining multiple plots
 
# Loading datasets
train = fread("Train_UWu5bXk.csv")
test = fread("Test_u94Q5KV.csv")
 
# Setting test dataset
# Combining datasets
# add Item_Outlet_Sales to test data
test[, Item_Outlet_Sales := NA]
 
combi = rbind(train, test)
 
# Missing Value Treatment
missing_index = which(is.na(combiItem_Weight))
for(i in missing_index)
{
  item = combiItem_Identifier[i]
  combiItem_Weight[i] =
      mean(combiItem_Weight[combiItem_Identifier == item],
                                                 na.rm = T)
}
 
# Replacing 0 in Item_Visibility with mean
zero_index = which(combiItem_Visibility == 0)
for(i in zero_index)
{
  item = combiItem_Identifier[i]
  combiItem_Visibility[i] =
      mean(combiItem_Visibility[combiItem_Identifier == item],
                                                     na.rm = T)
}
 
# Label Encoding
# To convert categorical in numerical
combi[, Outlet_Size_num := ifelse(Outlet_Size == "Small", 0,
                                 ifelse(Outlet_Size == "Medium",
                                                        1, 2))]
 
combi[, Outlet_Location_Type_num :=
         ifelse(Outlet_Location_Type == "Tier 3", 0,
                ifelse(Outlet_Location_Type == "Tier 2", 1, 2))]
 
combi[, c("Outlet_Size", "Outlet_Location_Type") := NULL]
 
# One Hot Encoding
# To convert categorical in numerical
ohe_1 = dummyVars("~.", data = combi[, -c("Item_Identifier",
                                          "Outlet_Establishment_Year",
                                          "Item_Type")], fullRank = T)
ohe_df = data.table(predict(ohe_1, combi[, -c("Item_Identifier",
                                           "Outlet_Establishment_Year",
                                           "Item_Type")]))
 
combi = cbind(combi[, "Item_Identifier"], ohe_df)
 
# Remove skewness
skewness(combiItem_Visibility)
skewness(combiprice_per_unit_wt)
 
# log + 1 to avoid division by zero
combi[, Item_Visibility := log(Item_Visibility + 1)]
 
# Scaling and Centering data
num_vars = which(sapply(combi, is.numeric)) # index of numeric features
num_vars_names = names(num_vars)
 
combi_numeric = combi[, setdiff(num_vars_names,
                              "Item_Outlet_Sales"),
                               with = F]
 
prep_num = preProcess(combi_numeric,
                      method=c("center", "scale"))
combi_numeric_norm = predict(prep_num, combi_numeric)
 
# removing numeric independent variables
combi[, setdiff(num_vars_names,
                "Item_Outlet_Sales") := NULL]
combi = cbind(combi, combi_numeric_norm)
 
# splitting data back to train and test
train = combi[1:nrow(train)]
test = combi[(nrow(train) + 1):nrow(combi)]
 
# Removing Item_Outlet_Sales
test[, Item_Outlet_Sales := NULL]
 
# Model Building :Lasso Regression
set.seed(123)
control = trainControl(method ="cv", number = 5)
Grid_la_reg = expand.grid(alpha = 1,
              lambda = seq(0.001, 0.1, by = 0.0002))
 
# Training lasso regression model
lasso_model = train(x = train[, -c("Item_Identifier",
                               "Item_Outlet_Sales")],
                    y = trainItem_Outlet_Sales,
                    method = "glmnet",
                    trControl = control,
                    tuneGrid = Grid_reg
                    )
lasso_model
 
# mean validation score
mean(lasso_modelresample$RMSE)
 
# Plot
plot(lasso_model, main = "Lasso Regression")