regression_roc_auc_score.py

def regression_roc_auc_score(y_true, y_pred, num_rounds = 10000):
  """
  Computes Regression-ROC-AUC-score.
  
  Parameters:
  ----------
  y_true: array-like of shape (n_samples,). Binary or continuous target variable.
  y_pred: array-like of shape (n_samples,). Target scores.
  num_rounds: int or string. If integer, number of random pairs of observations. 
              If string, 'exact', all possible pairs of observations will be evaluated.
  
  Returns:
  -------
  rroc: float. Regression-ROC-AUC-score.
  """
  
  import numpy as np
    
  y_true = np.array(y_true)
  y_pred = np.array(y_pred)

  num_pairs = 0
  num_same_sign = 0
  
  for i, j in _yield_pairs(y_true, num_rounds):
    diff_true = y_true[i] - y_true[j]
    diff_score = y_pred[i] - y_pred[j]
    if diff_true * diff_score > 0:
      num_same_sign += 1
    elif diff_score == 0:
      num_same_sign += .5
    num_pairs += 1
      
  return num_same_sign / num_pairs


def _yield_pairs(y_true, num_rounds):
  """
  Returns pairs of valid indices. Indices must belong to observations having different values.
  
  Parameters:
  ----------
  y_true: array-like of shape (n_samples,). Binary or continuous target variable.
  num_rounds: int or string. If integer, number of random pairs of observations to return. 
              If string, 'exact', all possible pairs of observations will be returned.
  
  Yields:
  -------
  i, j: tuple of int of shape (2,). Indices referred to a pair of samples.
  
  """
  import numpy as np
  
  if num_rounds == 'exact':
    for i in range(len(y_true)):
      for j in np.where((y_true != y_true[i]) & (np.arange(len(y_true)) > i))[0]:
        yield i, j     
  else:
    for r in range(num_rounds):
      i = np.random.choice(range(len(y_true)))
      j = np.random.choice(np.where(y_true != y_true[i])[0])
      yield i, j