/
fairness_loss.py
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/
fairness_loss.py
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import numpy as np
from scipy.optimize import minimize
def relevant_indices_to_onehot(rel, num_docs):
onehot = np.zeros(num_docs)
for relevant_doc in rel:
onehot[relevant_doc] = 1
return onehot
def get_exposures(ranking, position_bias_vector):
num_docs = len(ranking)
exposure = np.zeros(num_docs)
exposure[ranking] = position_bias_vector[:num_docs]
return exposure
def get_expected_exposure(rankings, position_bias_vector):
exp_exposure = np.zeros(len(rankings[0]))
for ranking in rankings:
exp_exposure += get_exposures(ranking, position_bias_vector)
exp_exposure = exp_exposure / len(rankings)
return exp_exposure
def minimize_for_k(rel, exposure, skip_zero=False):
if skip_zero:
inds = rel != 0
rel, exposure = rel[inds], exposure[inds]
res = minimize(
lambda k: np.sum(np.square((exposure - k * rel))),
1.0,
method='Nelder-Mead')
return res.x # res.x is the value of k for which the minimum occurs
class IndividualFairnessLoss(object):
@staticmethod
def compute_disparities(rankings,
one_hot_rel,
position_biases,
k,
skip_zero=False):
"""
returns a (num_rankings, num_docs) matrix of
disparities, disparity = relevance - z * positionbias
"""
disparitiy_matrix = np.zeros((len(rankings), len(rankings[0])))
for i, ranking in enumerate(rankings):
disparitiy_matrix[i, ranking] = (
position_biases[:len(ranking)] * k - one_hot_rel[ranking])**2
if skip_zero:
disparitiy_matrix[i, one_hot_rel == 0] = 0.0
return disparitiy_matrix
@staticmethod
def get_scale_invariant_mse_coeffs(rankings,
rels,
position_biases,
skip_zero=True):
"""
given the rankings, gives a vector of coeffients that is then multiplied with
the log \pi(r) to compute gradient over. See derivation in paper/appendix
skip_zero always has to be True
"""
n = len(rankings)
coeffs = np.zeros(n)
num_docs = len(rankings[0])
exposures = np.zeros((n, num_docs))
for i in range(n):
ranking = rankings[i]
exposures[i, ranking] = position_biases[:num_docs]
mean_exposures = np.mean(exposures, axis=0)
diffs = np.log(mean_exposures) - np.log(rels)
if skip_zero:
zero_inds = rels == 0
diffs[zero_inds] = 0
mean_diff = np.mean(diffs)
for i in range(n):
weighted_diffs = (diffs - mean_diff) * (
exposures[i, :] / mean_exposures)
if skip_zero:
weighted_diffs[zero_inds] = 0.0
coeffs[i] = 2 * np.mean(weighted_diffs)
return coeffs
@staticmethod
def compute_marginal_disparity(disparitiy_matrix):
"""
disparity matrix is of size (num_rankings, num_docs)
rankings (num_rankings, num_docs)
returns the marginal_disparity i.e averaged over the columns
"""
return np.mean(disparitiy_matrix, axis=0)
@staticmethod
def compute_sq_individual_fairness_loss_coeff(ranking, disparity_vector,
marginal_disparity, k):
inner_sum = np.sum(
2 * k * marginal_disparity[ranking] * disparity_vector[ranking])
return float(inner_sum)
@staticmethod
def compute_cross_entropy_fairness_loss(
ranking, one_hot_rel, expected_exposures, position_biases):
# print(ranking, position_biases[:len(ranking)])
exposures = np.zeros(len(ranking))
exposures[ranking] = position_biases[:len(ranking)]
numerators = expected_exposures - one_hot_rel
denominators = expected_exposures * (1 - expected_exposures)
inner_sum = np.sum(exposures * (numerators / denominators))
return float(inner_sum)
@staticmethod
def compute_pairwise_disparity_matrix(rankings, relevance_vector,
position_bias_vector):
num_rankings = len(rankings)
N = len(rankings[0])
matrix = np.zeros((num_rankings, N, N))
for k, ranking in enumerate(rankings):
for i in range(N): # index in ranking 1
for j in range(N): # index in ranking 2
if relevance_vector[ranking[i]] == 0 or relevance_vector[ranking[j]] == 0:
matrix[k, ranking[i], ranking[j]] = 0.0
else:
matrix[k, ranking[i], ranking[
j]] = (position_bias_vector[i] /
relevance_vector[ranking[i]]) - (
position_bias_vector[j] /
relevance_vector[ranking[j]])
return matrix
def get_H_matrix(relevance_vector):
N = len(relevance_vector)
H_mat = np.zeros((N, N))
for i in range(N):
for j in range(N):
if (relevance_vector[i] >= relevance_vector[j]):
H_mat[i, j] = 1
return H_mat
class GroupFairnessLoss:
@staticmethod
def compute_group_fairness_coeffs_generic(
rankings, rel_labels, group_identities, position_bias_vector,
group_fairness_version, skip_zero_relevance):
if group_fairness_version == "sq_disparity":
group_fairness_coeffs = GroupFairnessLoss.compute_group_disparity_coeffs(
rankings, rel_labels, group_identities, position_bias_vector,
skip_zero_relevance)
elif group_fairness_version == "asym_disparity":
group_fairness_coeffs = GroupFairnessLoss.compute_asym_group_disparity_coeffs(
rankings, rel_labels, group_identities, position_bias_vector,
skip_zero_relevance)
return group_fairness_coeffs
@staticmethod
def compute_group_disparity(ranking,
rel,
group_identities,
position_biases,
skip_zero=False):
exposures = get_exposures(ranking, position_biases)
inds_g0 = group_identities == 0
inds_g1 = group_identities == 1
if skip_zero:
inds_g0 = np.logical_and(inds_g0, rel != 0)
inds_g1 = np.logical_and(inds_g1, rel != 0)
return np.sum(exposures[inds_g0]) / np.sum(rel[inds_g0]) - np.sum(
exposures[inds_g1]) / np.sum(rel[inds_g1])
@staticmethod
def compute_group_disparity_coeffs(rankings,
rels,
group_identities,
position_biases,
skip_zero=False):
group_disparities = []
for j, ranking in enumerate(rankings):
group_disparities.append(
GroupFairnessLoss.compute_group_disparity(
ranking, rels, group_identities, position_biases,
skip_zero))
return 2 * np.mean(group_disparities) * np.array(group_disparities)
@staticmethod
def compute_asym_group_disparity_coeffs(rankings,
rels,
group_identities,
position_biases,
skip_zero=False):
"""
compute disparity and then compute the gradient coefficients for
asymmetric group disaprity loss
"""
# compute average v_i/r_i for each group, then the group which has higher relevance
group_disparities = []
sign = +1 if np.mean(rels[group_identities == 0]) >= np.mean(
rels[group_identities == 1]) else -1
for j, ranking in enumerate(rankings):
group_disparities.append(
GroupFairnessLoss.compute_group_disparity(
ranking, rels, group_identities, position_biases,
skip_zero))
indicator = (sign * np.mean(group_disparities)) > 0
return sign * indicator * np.array(group_disparities)