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import numpy as np
def apk(actual, predicted, k=10):
"""
Computes the average precision at k.
This function computes the average prescision at k between two lists of
items.
Parameters
----------
actual : list
A list of elements that are to be predicted (order doesn't matter)
predicted : list
A list of predicted elements (order does matter)
k : int, optional
The maximum number of predicted elements
Returns
-------
score : double
The average precision at k over the input lists
"""
if not actual:
return 0.0
if len(predicted)>k:
predicted = predicted[:k]
score = 0.0
num_hits = 0.0
for i,p in enumerate(predicted):
# first condition checks whether it is valid prediction
# second condition checks if prediction is not repeated
if p in actual and p not in predicted[:i]:
num_hits += 1.0
score += num_hits / (i+1.0)
return score / min(len(actual), k)
def mapk(actual: list[list], predicted: list[list], k:int=10) -> float:
"""
Computes the mean average precision at k.
This function computes the mean average prescision at k between two lists
of lists of items.
Parameters
----------
actual : list
A list of lists of elements that are to be predicted
(order doesn't matter in the lists)
predicted : list
A list of lists of predicted elements
(order matters in the lists)
k : int, optional
The maximum number of predicted elements
Returns
-------
score : double
The mean average precision at k over the input lists
"""
return np.mean([apk(a,p,k) for a,p in zip(actual, predicted)]).astype(float)
def rank_biased_overlap(l1,l2,p):
"""
Returns RBO indefinite rank similarity metric, as described in:
Webber, W., Moffat, A., & Zobel, J. (2010).
A similarity measure for indefinite rankings.
ACM Transactions on Information Systems.
doi:10.1145/1852102.1852106.
"""
sl,ll = sorted([(len(l1), l1),(len(l2),l2)])
s, S = sl
l, L = ll
# Calculate the overlaps at ranks 1 through l
# (the longer of the two lists)
ss = set([])
ls = set([])
overs = {}
for i in range(l):
ls.add(L[i])
if i<s:
ss.add(S[i])
X_d = len(ss.intersection(ls))
d = i+1
overs[d] = float(X_d)
# (1) \sum_{d=1}^l (X_d / d) * p^d
sum1 = 0
for i in range(l):
d=i+1
sum1+=overs[d]/d*pow(p,d)
X_s = overs[s]
X_l = overs[l]
# (2) \sum_{d=s+1}^l [(X_s (d - s)) / (sd)] * p^d
sum2 = 0
for i in range(s,l):
d=i+1
sum2+=(X_s*(d-s)/(s*d))*pow(p,d)
# (3) [(X_l - X_s) / l + X_s / s] * p^l
sum3 = ((X_l-X_s)/l+X_s/s)*pow(p,l)
# Equation 32.
rbo_ext = (1-p)/p*(sum1+sum2)+sum3
return rbo_ext
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