content: """
  ===========================================
  Comparison of F-test and mutual information
  ===========================================
  
  This example illustrates the differences between univariate F-test statistics
  and mutual information.
  
  We consider 3 features x_1, x_2, x_3 distributed uniformly over [0, 1], the
  target depends on them as follows:
  
  y = x_1 + sin(6 * pi * x_2) + 0.1 * N(0, 1), that is the third features is completely irrelevant.
  
  The code below plots the dependency of y against individual x_i and normalized
  values of univariate F-tests statistics and mutual information.
  
  As F-test captures only linear dependency, it rates x_1 as the most
  discriminative feature. On the other hand, mutual information can capture any
  kind of dependency between variables and it rates x_2 as the most
  discriminative feature, which probably agrees better with our intuitive
  perception for this example. Both methods correctly marks x_3 as irrelevant.
  """
  print(__doc__)
  
  import numpy as np
  import matplotlib.pyplot as plt
  from sklearn.feature_selection import f_regression, mutual_info_regression
  
  np.random.seed(0)
  X = np.random.rand(1000, 3)
  y = X[:, 0] + np.sin(6 * np.pi * X[:, 1]) + 0.1 * np.random.randn(1000)
  
  f_test, _ = f_regression(X, y)
  f_test /= np.max(f_test)
  
  mi = mutual_info_regression(X, y)
  mi /= np.max(mi)
  
  plt.figure(figsize=(15, 5))
  for i in range(3):
      plt.subplot(1, 3, i + 1)
      plt.scatter(X[:, i], y)
      plt.xlabel("$x_{}$".format(i + 1), fontsize=14)
      if i == 0:
          plt.ylabel("$y$", fontsize=14)
      plt.title("F-test={:.2f}, MI={:.2f}".format(f_test[i], mi[i]),
                fontsize=16)
  plt.show()
  
  