鲍鱼数据案例岭回归 、LASSO回归

数据集探索性分析

import pandas as pd
import warnings
warnings.filterwarnings('ignore')
data=pd.read_csv(r"E:\大二下\机器学习实践\abalone_dataset.csv")
data.head()

#查看数据集中样本数量和特征数量
data.shape

(4177, 9)

#查看数据信息，检查是否有缺失值
data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 4177 entries, 0 to 4176
Data columns (total 9 columns):
sex               4177 non-null object
length            4177 non-null float64
diameter          4177 non-null float64
height            4177 non-null float64
whole weight      4177 non-null float64
shucked weight    4177 non-null float64
viscera weight    4177 non-null float64
shell weight      4177 non-null float64
rings             4177 non-null int64
dtypes: float64(7), int64(1), object(1)
memory usage: 293.8  KB

data.describe()

#观察sex列的取值的分布情况
import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline

sns.countplot(x = "sex",data=data)

<matplotlib.axes._subplots.AxesSubplot at 0x27f16455080>

data['sex'].value_counts()

M    1528
I    1342
F    1307
Name: sex, dtype: int64

i=1 #子图计数
plt.figure(figsize=(16,8))
for col in data.columns[1:]:
    plt.subplot(4,2,i)
    i = i   1
    sns.distplot(data[col])
plt.tight_layout()

sns.pairplot(data,hue="sex")

<seaborn.axisgrid.PairGrid at 0x27f16d16eb8>

corr_df = data.corr()
corr_df

fig ,ax =plt.subplots(figsize=(12,12))
##绘制热力图
ax = sns.heatmap(corr_df,linewidths=.5,
                cmap="Greens",
                annot=True,
                xticklabels=corr_df.columns,
                yticklabels=corr_df.index)
ax.xaxis.set_label_position('top')
ax.xaxis.tick_top()

鲍鱼数据预处理

对sex特征进行OneHot编码，便于后续模型纳入哑变量

#只用pandas的get_dummies函数对sex特征做OneHot编码处理
sex_onehot = pd.get_dummies(data["sex"],prefix="sex")
data[sex_onehot.columns] = sex_onehot
data.head()

data["ones"]=1
data.head()

data["age"]=data["rings"]   1.5
data.head()

筛选特征

data.columns

Index(['sex', 'length', 'diameter', 'height', 'whole weight', 'shucked weight',
       'viscera weight', 'shell weight', 'rings', 'sex_F', 'sex_I', 'sex_M',
       'ones', 'age'],
      dtype='object')

y = data["age"] #因变量
features_with_ones = ["length", "diameter", "height", "whole weight", "shucked weight",
       "viscera weight", "shell weight", "sex_F", "sex_M","ones"]
features_without_ones = ["length", "diameter", "height", "whole weight", "shucked weight",
       "viscera weight", "shell weight", "sex_F", "sex_M"]
X=data[features_with_ones]

将鲍鱼数据集划分为训练集和测试集

#拆分训练集和测试集
from sklearn.model_selection import train_test_split

X_train,X_test,y_train,y_test = train_test_split(X,y,test_size=0.2,random_state=111)

X

4177 rows × 10 columns

实现线性回归和岭回归

使用numpy实现线性回归

import numpy as np

def linear_regression(X,y):
    w = np.zeros_like(X.shape[1])
    if np.linalg.det(X.T.dot(X)) != 0:
        w = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)
    return w

#使用上述实现的线性回归模型在鲍鱼训练集上训练模型
w1 = linear_regression(X_train,y_train)

w1 = pd.DataFrame(data = w1,index=X.columns,columns =["numpy_w"])
w1.round(decimals=2)

使用sklearn实现线性回归

from sklearn.linear_model import LinearRegression 
lr = LinearRegression()
lr.fit(X_train[features_without_ones],y_train)
print(lr.coef_)

[ -1.118146    10.00094599  20.73712616   9.61484657 -20.05079291
 -12.06849193   6.54529076   0.87855188   0.87283083]

w1

w_lr=[]
w_lr.extend(lr.coef_)
w_lr.append(lr.intercept_)
w1["lr_sklearn_w"]=w_lr
w1.round(decimals=2)

#做正则化时不包含b lambda I不是真正的系数

使用Numpy实现岭回归

def ridge_regression(X,y,ridge_lambda):
    penalty_matrix = np.eye(X.shape[1])
    penalty_matrix[X.shape[1]-1][X.shape[1]-1] = 0
    w = np.linalg.inv(X.T.dot(X)   ridge_lambda * penalty_matrix).dot(X.T).dot(y)
    return w

在鲍鱼训练集上使用ridge_regression函数训练岭回归模型，正则化系数设置为1

w2 = ridge_regression(X_train,y_train,1.0)
print(w2)

[  2.30976528   6.72038628  10.23298909   7.05879189 -17.16249532
  -7.2343118    9.3936994    0.96869974   0.9422174    4.80583032]

w1["numpy_ridge_w"] = w2
w1.round(decimals=2)

利用sklearn实现岭回归

与sklearn中岭回归对比，同样正则化叙述设置为1

from sklearn.linear_model import Ridge
ridge = Ridge(alpha=1.0)
ridge.fit(X_train[features_without_ones],y_train)
w_ridge = []
w_ridge.extend(ridge.coef_)
w_ridge.append(ridge.intercept_)
w1["ridge_sklearn_w"] = w_ridge
w1.round(decimals=2)

岭迹分析

alphas = np.logspace(-10,10,20)
coef = pd.DataFrame()
for alpha in alphas:
    ridge_clf = Ridge(alpha=alpha)
    ridge_clf.fit(X_train[features_without_ones],y_train)
    df = pd.DataFrame([ridge_clf.coef_],columns=X_train[features_without_ones].columns)
    df['alpha']=alpha
    coef =coef.append(df,ignore_index=True)
coef.round(decimals=2)

plt.rcParams['figure.dpi'] = 300#分辨率
plt.figure(figsize=(9,6))
coef['alpha']=coef['alpha']

for feature in X_train.columns[:-1]:
    plt.plot('alpha',feature,data=coef)
ax = plt.gca()
ax.set_xscale('log')
plt.legend(loc='upper right')
plt.xlabel(r'$\alpha$',fontsize=15)
plt.ylabel('系数',fontsize=15)

Text(0, 0.5, '系数')



Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.
Font 'default' does not have a glyph for '-' [U 2212], substituting with a dummy symbol.

使用LASSO构建鲍鱼年龄预测模型

from sklearn.linear_model import Lasso
lasso = Lasso(alpha=0.01)
lasso.fit(X_train[features_without_ones],y_train)
print(lasso.coef_)
print(lasso.intercept_)

[  0.           6.37435514   0.           4.46703234 -13.44947667
  -0.          11.85934842   0.98908791   0.93313403]
6.500338023591298

LASSO的正则化路径

coef = pd.DataFrame()
for alpha in np.linspace(0.0001,0.2,20):
    lasso_clf = Lasso(alpha=alpha)
    lasso_clf.fit(X_train[features_without_ones],y_train)
    df = pd.DataFrame([lasso_clf.coef_],columns=X_train[features_without_ones].columns)
    df['alpha']=alpha
    coef = coef.append(df,ignore_index=True)
coef.head()
#绘图
plt.figure(figsize=(9,6),dpi=600)
for feature in X_train.columns[:-1]:
    plt.plot('alpha',feature,data=coef)
plt.legend(loc='upper right')
plt.xlabel(r'$\alpha$',fontsize=15)
plt.ylabel('系数',fontsize=15)
plt.show()

coef

from sklearn.metrics import mean_squared_error
from sklearn.metrics import mean_absolute_error
from sklearn.metrics import r2_score

#MAE
y_test_pred_lr = lr.predict(X_test.iloc[:,:-1])
print(round(mean_absolute_error(y_test,y_test_pred_lr),4))

1.6016

y_test_pred_ridge = ridge.predict(X_test[features_without_ones])
print(round(mean_absolute_error(y_test,y_test_pred_ridge),4))

1.5984

y_test_pred_lasso = lasso.predict(X_test[features_without_ones])
print(round(mean_absolute_error(y_test,y_test_pred_lasso),4))

1.6402

#MSE
y_test_pred_lr = lr.predict(X_test.iloc[:,:-1])
print(round(mean_squared_error(y_test,y_test_pred_lr),4))

5.3009

y_test_pred_ridge = ridge.predict(X_test[features_without_ones])
print(round(mean_squared_error(y_test,y_test_pred_ridge),4))

4.959

y_test_pred_lasso = lasso.predict(X_test[features_without_ones])
print(round(mean_squared_error(y_test,y_test_pred_lasso),4))

5.1

#R2系数
print(round(r2_score(y_test,y_test_pred_lr),4))
print(round(r2_score(y_test,y_test_pred_ridge),4))
print(round(r2_score(y_test,y_test_pred_lasso),4))

0.5257
0.5563
0.5437

残差图

plt.figure(figsize=(9,6),dpi=600)
y_train_pred_ridge = ridge.predict(X_train[features_without_ones])
plt.scatter(y_train_pred_ridge,y_train_pred_ridge - y_train,c="g",alpha=0.6)
plt.scatter(y_test_pred_ridge,y_test_pred_ridge - y_test,c="r",alpha=0.6)
plt.hlines(y=0,xmin=0,xmax=30,color="b",alpha=0.6)
plt.ylabel("Residuals")
plt.xlabel("Predict")

Text(0.5, 0, 'Predict')

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