LASSO套索算法

LASSO

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()

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

def PolynomialRegression(degree):
    return Pipeline([
        ("poly", PolynomialFeatures(degree=degree)),
        ("std_scaler", StandardScaler()),
        ("lin_reg", LinearRegression())
    ])

from sklearn.metrics import mean_squared_error

poly_reg = PolynomialRegression(degree=20)
poly_reg.fit(X_train, y_train)

y_predict = poly_reg.predict(X_test)
mean_squared_error(y_test, y_predict)

167.94010867293571

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(poly_reg)

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)

y1_predict = lasso1_reg.predict(X_test)
mean_squared_error(y_test, y1_predict)

1.1496080843259966

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)