def objective_accuracy(W, X1, X2, X1_labels, X2_labels):
"""
W : weight matrix,
X1 : prediction by m1
X2 : prediction by m2
X1_label : actual label for instance1
X2_label : actual label for instance2
abs(1-ratio) ?
Objective : 1 - ratio
normalized weights here as well.
check which one is small and use that as numerator.
"""
weighted_sum_m_norm, weighted_sum_f_norm = prepare_normalized_weighted_sum(
W, X1, X2)
acc1 = accuracy(weighted_sum_m_norm, X1_labels)
acc2 = accuracy(weighted_sum_f_norm, X2_labels)
denom = acc1
numer = acc2
if acc1 < acc2:
denom = acc2
numer = acc1
ratio = numer / denom
return -(1 - ratio)
def objective_error(W, X1, X2, X1_label, X2_label):
"""
Calculates prediction error
each instance will have different prediction and different associated label
Can we combine the error ? (error1+error2)/2 ?
Error : normalized by weights
"""
weighted_sum_m_norm, weighted_sum_f_norm = prepare_normalized_weighted_sum(
W, X1, X2)
combined_weighted_sum = np.hstack(
(weighted_sum_m_norm, weighted_sum_f_norm))
combined_labels = np.hstack((X1_label, X2_label))
combined_error = error(combined_weighted_sum, combined_labels)
return -combined_error
def objective_independence(W, X1, X2, X1_label, X2_label):
"""
Fairness objective based on independence
"""
# combined effect
weighted_sum_m_norm, weighted_sum_f_norm = prepare_normalized_weighted_sum(
W, X1, X2)
predictions1 = [1 if w >= 0.5 else 0 for w in weighted_sum_m_norm]
positive_count_1 = predictions1.count(1)
predictions2 = [1 if w >= 0.5 else 0 for w in weighted_sum_f_norm]
positive_count_2 = predictions2.count(1)
positive_count_1_norm = positive_count_1 / len(predictions1)
positive_count_2_norm = positive_count_2 / len(predictions2)
ratio = get_ratio(positive_count_1_norm, positive_count_2_norm)
return -(1 - ratio)
def objective_recall(W, X1, X2, X1_label, X2_label):
"""
Fairness objective based on recall
"""
weighted_sum_m_norm, weighted_sum_f_norm = prepare_normalized_weighted_sum(
W, X1, X2)
predictions1 = [1 if w >= 0.5 else 0 for w in weighted_sum_m_norm]
conf_mat1 = cm(X1_label, predictions1)
TP1, FN1, FP1, TN1 = conf_mat1.ravel()
recall1 = TP1 / (TP1 + FN1)
predictions2 = [1 if w >= 0.5 else 0 for w in weighted_sum_f_norm]
conf_mat2 = cm(X2_label, predictions2)
TP2, FN2, FP2, TN2 = conf_mat2.ravel()
recall2 = TP2 / (TP2 + FN2)
ratio = get_ratio(recall1, recall2)
return -(1 - ratio)