# Theil-Sen Regression¶

# Author: Florian Wilhelm -- <florian.wilhelm@gmail.com>

import time
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression, TheilSenRegressor
from sklearn.linear_model import RANSACRegressor

print(__doc__)

estimators = [('OLS', LinearRegression()),
('Theil-Sen', TheilSenRegressor(random_state=42)),
('RANSAC', RANSACRegressor(random_state=42)), ]
colors = {'OLS': 'turquoise', 'Theil-Sen': 'gold', 'RANSAC': 'lightgreen'}
lw = 2

# #############################################################################
# 只有 y 方向有离群点

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% outliers
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 方向上有离群点

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()


Total running time of the script: ( 0 minutes 1.114 seconds)

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