岭回归

LASSO Regression

Least Absolute Shrinkage and Selection Operator Regression

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(42)
x = np.random.uniform(-3.0,3.0,size=100)
X = x.reshape(-1,1)
y = 0.5 * x + 3 + np.random.normal(0,1,size=100)

plt.scatter(x, y)
plt.show()

# 使用多项式回归

from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LinearRegression

def PolynomiaRegression(degree):
    return Pipeline([
        ("poly",PolynomialFeatures(degree=degree)),
        ("std_scaler",StandardScaler()),
        ("line_reg",LinearRegression())
    ])
from sklearn.model_selection import train_test_split
np.random.seed(666)
X_train,X_test,y_train,y_test = train_test_split(X,y)

from sklearn.metrics import mean_squared_error
poly_reg = PolynomiaRegression(degree=20)
poly_reg.fit(X_train,y_train) 
y_poly_predict = poly_reg.predict(X_test)
mean_squared_error(y_test,y_poly_predict)

167.9401086729357

X_plot = np.linspace(-3,3,100).reshape(100,1)
y_plot = poly_reg.predict(X_plot)
plt.scatter(x,y)
plt.plot(X_plot[:,0],y_plot,color='r')
plt.axis([-3,3,0,6])
plt.show()

LASSO

from sklearn.linear_model import Lasso

def LassoRegression(degree,alpha):
    return Pipeline([
        ("poly",PolynomialFeatures(degree=degree)),
        ("std_scaler",StandardScaler()),
        ("lasso_reg",Lasso(alpha=alpha))
    ])

lasso1_reg = LassoRegression(20,0.01)

lasso1_reg.fit(X_train,y_train)

Pipeline(memory=None,
     steps=[('poly', PolynomialFeatures(degree=20, include_bias=True, interaction_only=False)), ('std_scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('lasso_reg', Lasso(alpha=0.01, copy_X=True, fit_intercept=True, max_iter=1000,
   normalize=False, positive=False, precompute=False, random_state=None,
   selection='cyclic', tol=0.0001, warm_start=False))])

y1_predict = lasso1_reg.predict(X_test)

mean_squared_error(y_test,y1_predict)

1.1496080843259966

def plot_model(model):
    X_plot = np.linspace(-3,3,100).reshape(100,1)
    y_plot = model.predict(X_plot)
    
    plt.scatter(x,y)
    plt.plot(X_plot[:,0],y_plot,color='r')
    plt.axis([-3,3,0,6])
    plt.show()

plot_model(lasso1_reg)

lasso2_reg = LassoRegression(20,0.1)
lasso2_reg.fit(X_train,y_train)
y2_predict = lasso2_reg.predict(X_test)
mean_squared_error(y_test,y2_predict)

1.1213911351818648

plot_model(lasso2_reg)

lasso3_reg = LassoRegression(20,1)
lasso3_reg.fit(X_train,y_train)
y3_predict = lasso3_reg.predict(X_test)
mean_squared_error(y_test,y3_predict)

1.8408939659515595

plot_model(lasso3_reg)