回歸算法比較【線性回歸，Ridge回歸，Lasso回歸】

代碼實現：

# -*- coding: utf-8 -*-
"""
Created on Mon Jul 16 09:08:09 2018

@author: zhen
"""

from sklearn.linear_model import LinearRegression, Ridge, Lasso
import mglearn
from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt
import numpy as np
# 線性回歸
x, y = mglearn.datasets.load_extended_boston()
x_train, x_test, y_train, y_test = train_test_split(x, y, random_state=0)

linear_reg = LinearRegression()
lr = linear_reg.fit(x_train, y_train)

print("lr.coef_:{}".format(lr.coef_))  # 斜率
print("lr.intercept_:{}".format(lr.intercept_))  # 截距

print("="*25+"線性回歸"+"="*25)
print("Training set score:{:.2f}".format(lr.score(x_train, y_train)))
print("Rest set score:{:.2f}".format(lr.score(x_test, y_test)))

"""
    總結：
        訓練集和測試集上的分數非常接近，這說明可能存在欠耦合。
        訓練集和測試集之間的顯著性能差異是過擬合的明顯標志。解決方式是使用嶺回歸！
"""
print("="*25+"嶺回歸（默認值1.0）"+"="*25)
# 嶺回歸
ridge = Ridge().fit(x_train, y_train)

print("Training set score:{:.2f}".format(ridge.score(x_train, y_train)))
print("Test set score:{:.2f}".format(ridge.score(x_test, y_test)))

print("="*25+"嶺回歸（alpha=10）"+"="*25)
# 嶺回歸
ridge_10 = Ridge(alpha=10).fit(x_train, y_train)

print("Training set score:{:.2f}".format(ridge_10.score(x_train, y_train)))
print("Test set score:{:.2f}".format(ridge_10.score(x_test, y_test)))

print("="*25+"嶺回歸（alpha=0.1）"+"="*25)
# 嶺回歸
ridge_01 = Ridge(alpha=0.1).fit(x_train, y_train)

print("Training set score:{:.2f}".format(ridge_01.score(x_train, y_train)))
print("Test set score:{:.2f}".format(ridge_01.score(x_test, y_test)))


# 可視化
fig = plt.figure(10)
plt.subplots_adjust(wspace =0, hspace =0.6)#調整子圖間距
ax1 = plt.subplot(2, 1, 1)

ax2 = plt.subplot(2, 1, 2)

ax1.plot(ridge_01.coef_, 'v', label="Ridge alpha=0.1")
ax1.plot(ridge.coef_, 's', label="Ridge alpha=1")
ax1.plot(ridge_10.coef_, '^', label="Ridge alpha=10")

ax1.plot(lr.coef_, 'o', label="LinearRegression")


ax1.set_ylabel("Cofficient magnitude")
ax1.set_ylim(-25,25)
ax1.hlines(0, 0, len(lr.coef_))
ax1.legend(ncol=2, loc=(0.1, 1.05))

print("="*25+"Lasso回歸（默認配置）"+"="*25)
lasso = Lasso().fit(x_train, y_train)

print("Training set score:{:.2f}".format(lasso.score(x_train, y_train)))
print("Test set score:{:.2f}".format(lasso.score(x_test, y_test)))
print("Number of features used:{}".format(np.sum(lasso.coef_ != 0)))

print("="*25+"Lasso回歸（aplpha=0.01）"+"="*25)
lasso_001 = Lasso(alpha=0.01, max_iter=1000).fit(x_train, y_train)

print("Training set score:{:.2f}".format(lasso_001.score(x_train, y_train)))
print("Test set score:{:.2f}".format(lasso_001.score(x_test, y_test)))
print("Number of features used:{}".format(np.sum(lasso_001.coef_ != 0)))


print("="*15+"Lasso回歸（aplpha=0.0001）太小可能會過擬合"+"="*15)
lasso_00001 = Lasso(alpha=0.0001, max_iter=1000).fit(x_train, y_train)

print("Training set score:{:.2f}".format(lasso_00001.score(x_train, y_train)))
print("Test set score:{:.2f}".format(lasso_00001.score(x_test, y_test)))
print("Number of features used:{}".format(np.sum(lasso_00001.coef_ != 0)))


# 可視化
ax2.plot(ridge_01.coef_, 'o', label="Ridge alpha=0.1")
ax2.plot(lasso.coef_, 's', label="lasso alpha=1")
ax2.plot(lasso_001.coef_, '^', label="lasso alpha=0.001")
ax2.plot(lasso_00001.coef_, 'v', label="lasso alpha=0.00001")

ax2.set_ylabel("Cofficient magnitude")
ax2.set_xlabel("Coefficient index")
ax2.set_ylim(-25,25)
ax2.legend(ncol=2, loc=(0.1, 1))

結果：

總結：各回歸算法在相同的測試數據中表現差距很多，且算法內的配置參數調整對自身算法的效果影響也是巨大的，

　　因此合理挑選合適的算法和配置合適的配置參數是使用算法的關鍵！