def tied_rank(x):
"""
Computes the tied rank of elements in x.
This function computes the tied rank of elements in x.
Parameters
----------
x : list of numbers, numpy array
Returns
-------
score : list of numbers
The tied rank f each element in x
"""
sorted_x = sorted(zip(x,range(len(x))))
r = [0 for k in x]
cur_val = sorted_x[0][0]
last_rank = 0
for i in range(len(sorted_x)):
if cur_val != sorted_x[i][0]:
cur_val = sorted_x[i][0]
for j in range(last_rank, i):
r[sorted_x[j][1]] = float(last_rank+1+i)/2.0
last_rank = i
if i==len(sorted_x)-1:
for j in range(last_rank, i+1):
r[sorted_x[j][1]] = float(last_rank+i+2)/2.0
return r
def auc(actual, posterior):
"""
Computes the area under the receiver-operator characteristic (AUC)
This function computes the AUC error metric for binary classification.
Parameters
----------
actual : list of binary numbers, numpy array
The ground truth value
posterior : same type as actual
Defines a ranking on the binary numbers, from most likely to
be positive to least likely to be positive.
Returns
-------
score : double
The mean squared error between actual and posterior
"""
r = tied_rank(posterior)
num_positive = len([0 for x in actual if x==1])
num_negative = len(actual)-num_positive
sum_positive = sum([r[i] for i in range(len(r)) if actual[i]==1])
auc = ((sum_positive - num_positive*(num_positive+1)/2.0) /
(num_negative*num_positive))
return auc
