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# Based on code from https://github.com/zjelveh/learning-fair-representations
import numpy as np
from scipy.spatial.distance import cdist
from scipy.special import softmax
def LFR_optim_objective(parameters, x_unprivileged, x_privileged, y_unprivileged,
y_privileged, k=10, A_x=0.01, A_y=0.1, A_z=0.5, print_interval=250, verbose=1):
num_unprivileged, features_dim = x_unprivileged.shape
num_privileged, _ = x_privileged.shape
w = parameters[:k]
prototypes = parameters[k:].reshape((k, features_dim))
M_unprivileged, x_hat_unprivileged, y_hat_unprivileged = get_xhat_y_hat(prototypes, w, x_unprivileged)
M_privileged, x_hat_privileged, y_hat_privileged = get_xhat_y_hat(prototypes, w, x_privileged)
y_hat = np.concatenate([y_hat_unprivileged, y_hat_privileged], axis=0)
y = np.concatenate([y_unprivileged.reshape((-1, 1)), y_privileged.reshape((-1, 1))], axis=0)
L_x = np.mean((x_hat_unprivileged - x_unprivileged) ** 2) + np.mean((x_hat_privileged - x_privileged) ** 2)
L_z = np.mean(abs(np.mean(M_unprivileged, axis=0) - np.mean(M_privileged, axis=0)))
L_y = - np.mean(y * np.log(y_hat) + (1. - y) * np.log(1. - y_hat))
total_loss = A_x * L_x + A_y * L_y + A_z * L_z
if verbose and LFR_optim_objective.steps % print_interval == 0:
print("step: {}, loss: {}, L_x: {}, L_y: {}, L_z: {}".format(
LFR_optim_objective.steps, total_loss, L_x, L_y, L_z))
LFR_optim_objective.steps += 1
return total_loss
def get_xhat_y_hat(prototypes, w, x):
M = softmax(-cdist(x, prototypes), axis=1)
x_hat = np.matmul(M, prototypes)
y_hat = np.clip(
np.matmul(M, w.reshape((-1, 1))),
np.finfo(float).eps,
1.0 - np.finfo(float).eps
)
return M, x_hat, y_hat
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