16、Theil-Sen回归

import time

import numpy as np

import matplotlib.pyplot as plt

from sklearn.linear_model import LinearRegression, TheilSenRegressor

from sklearn.linear_model import RANSACRegressor

estimators = [('OLS', LinearRegression()),

              ('Theil-Sen', TheilSenRegressor(random_state=42)),

              ('RANSAC', RANSACRegressor(random_state=42)), ]

colors = {'OLS': 'turquoise', 'Theil-Sen': 'gold', 'RANSAC': 'lightgreen'}

lw = 2

# 只在y方向上的异常值

np.random.seed(0)

n_samples = 200

# 线性模型 y = 3*x + N(2, 0.1**2)

x = np.random.randn(n_samples)

w = 3.

c = 2.

noise = 0.1 * np.random.randn(n_samples)

y = w * x + c + noise

# 10% 离群值

y[-20:] += -20 * x[-20:]

X = x[:, np.newaxis]

plt.scatter(x, y, color='indigo', marker='x', s=40)

line_x = np.array([-3, 3])

for name, estimator in estimators:

    t0 = time.time()

    estimator.fit(X, y)

    elapsed_time = time.time() - t0

    y_pred = estimator.predict(line_x.reshape(2, 1))

    plt.plot(line_x, y_pred, color=colors[name], linewidth=lw,

            label='%s (fit time: %.2fs)' % (name, elapsed_time))

plt.axis('tight')

plt.legend(loc='upper left')

plt.title("Corrupt y")

# X方向异常值

np.random.seed(0)

# 线性模型 y = 3*x + N(2, 0.1**2)

x = np.random.randn(n_samples)

noise = 0.1 * np.random.randn(n_samples)

y = 3 * x + 2 + noise

# 10% outliers

x[-20:] = 9.9

y[-20:] += 22

X = x[:, np.newaxis]

plt.figure()

plt.scatter(x, y, color='indigo', marker='x', s=40)

line_x = np.array([-3, 10])

for name, estimator in estimators:

    t0 = time.time()

    estimator.fit(X, y)

    elapsed_time = time.time() - t0

    y_pred = estimator.predict(line_x.reshape(2, 1))

    plt.plot(line_x, y_pred, color=colors[name], linewidth=lw,

            label='%s (fit time: %.2fs)' % (name, elapsed_time))

plt.axis('tight')

plt.legend(loc='upper left')

plt.title("Corrupt x")

plt.show()