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fico_util.py
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import pandas as pd
import numpy as np
import random
from scipy.stats import beta
from scipy.optimize import newton
from pynverse import inversefunc
def gamma(x,a0,b0,a1,b1,alpha):
return 1/((beta.pdf(x, a0, b0, loc=0, scale=1)/beta.pdf(x, a1, b1, loc=0, scale=1))*(1/alpha -1 )+1)
def gamma_1(x,a0,b0,a1,b1,alpha):
return (beta.pdf(x, a0, b0, loc=0, scale=1)/beta.pdf(x, a1, b1, loc=0, scale=1))*(1/alpha -1 )+1
def P_fair(x,a0,b0,a1,b1,alpha):
return (beta.pdf(x, a0, b0, loc=0, scale=1) * (1-alpha) + beta.pdf(x, a1, b1, loc=0, scale=1) * alpha)
# DP
# alpha_aa * beta.cdf(x, a_aa1, b_aa1)+(1-alpha_aa)*beta.cdf(x, a_aa0, b_aa0) =
# alpha_c * beta.cdf(fn(x), a_c1, b_c1)+(1-alpha_c)*beta.cdf(fn(x), a_c0, b_c0)
def P_evidence(x,alpha,a0,b0,a1,b1):
return alpha * beta.pdf(x, a1, b1)+(1-alpha)*beta.pdf(x, a0, b0)
def f_dp(x,alpha_aa,alpha_c,a_aa0,b_aa0,a_c0,b_c0,a_aa1,b_aa1,a_c1,b_c1):
f_c = (lambda x_c: alpha_c * beta.cdf(x_c, a_c1, b_c1,0,1)+(1-alpha_c)*beta.cdf(x_c, a_c0, b_c0,0,1))
inv_f_c = inversefunc(f_c, domain=[0,1], open_domain=[False,False])
return float(inv_f_c( alpha_aa * beta.cdf(x, a_aa1, b_aa1)+(1-alpha_aa)*beta.cdf(x, a_aa0, b_aa0)))
def Pdp_aa(x,alpha_aa,a_aa0,b_aa0,a_aa1,b_aa1):
return alpha_aa * beta.pdf(x, a_aa1, b_aa1)+(1-alpha_aa)*beta.pdf(x, a_aa0, b_aa0)
def Pdp_c(x,alpha_c,a_c0,b_c0,a_c1,b_c1):
return alpha_c * beta.pdf(x, a_c1, b_c1)+(1-alpha_c)*beta.pdf(x, a_c0, b_c0)
# EqOpt
# beta.cdf(x_aa, a_aa1, b_aa1) = beta.cdf(x_c, a_c1, b_c1)
def f_eqopt(x,alpha_aa,alpha_c,a_aa0,b_aa0,a_c0,b_c0,a_aa1,b_aa1,a_c1,b_c1):
return beta.ppf(beta.cdf(x, a_aa1, b_aa1),a_c1,b_c1)
def Peqopt_aa(x,alpha_aa,a_aa0,b_aa0,a_aa1,b_aa1):
return beta.pdf(x, a_aa1, b_aa1)
def Peqopt_c(x,alpha_c,a_c0,b_c0,a_c1,b_c1):
return beta.pdf(x, a_c1, b_c1)
# EO
# beta.pdf(x, a_aa0, b_aa0) = beta.pdf(fn(x), a_c0, b_c0)
def f_eo(x,alpha_aa,alpha_c,a_aa0,b_aa0,a_c0,b_c0,a_aa1,b_aa1,a_c1,b_c1):
return beta.ppf(beta.cdf(x, a_c0, b_c0), a_aa0, b_aa0)
def Peo_aa(x,alpha_aa,a_aa0,b_aa0,a_aa1,b_aa1):
return beta.pdf(x, a_aa0, b_aa0)
def Peo_c(x,alpha_c,a_c0,b_c0,a_c1,b_c1):
return beta.pdf(x, a_c0, b_c0)
def balanced_eqn_fn(x, alpha_aa,alpha_c, fn, Pf_aa, Pf_c,paa, pc,a_aa0, b_aa0,a_aa1, b_aa1,a_c0, b_c0,a_c1, b_c1):
if x < 0 or x == 0:
x = 0.001
if x > 1 or x == 1:
x = 0.999
x_aa = x
x_c = fn(x,alpha_aa,alpha_c,a_aa0,b_aa0,a_c0,b_c0,a_aa1,b_aa1,a_c1,b_c1)
return paa*(gamma(x,a_aa0,b_aa0,a_aa1,b_aa1,alpha_aa)-0.5)*P_evidence(x,alpha_aa,a_aa0,b_aa0,a_aa1,b_aa1)/Pf_aa(x,alpha_aa,a_aa0,b_aa0,a_aa1,b_aa1)+pc*(gamma(x_c,a_c0,b_c0,a_c1,b_c1,alpha_c)-0.5)*P_evidence(x_c,alpha_c,a_c0,b_c0,a_c1,b_c1)/Pf_c(x_c,alpha_c,a_c0,b_c0,a_c1,b_c1)
def balanced_eqn_un(x, a0,b0,a1,b1,alpha):
if x < 0 or x == 0:
x = 0.001
if x > 1 or x == 1:
x = 0.999
return gamma_1(x,a0,b0,a1,b1,alpha) - 2
def get_policy_fn(alpha_aa, alpha_c, fn, Pf_aa, Pf_c, paa, pc,a_aa0, b_aa0,a_aa1, b_aa1,a_c0, b_c0, a_c1, b_c1):
root=[]
for i in np.arange(0.01,0.99,0.01):
try:
root.append(newton(balanced_eqn_fn,
x0 = i,
maxiter=50,
args = (alpha_aa,alpha_c, fn, Pf_aa, Pf_c,paa, pc,
a_aa0, b_aa0,a_aa1, b_aa1,
a_c0, b_c0,a_c1, b_c1)))
except(RuntimeError):
pass
root = [float(format(round(r, 4))) for r in root]
return np.unique(root)[0],fn(np.unique(root)[0],alpha_aa,alpha_c,a_aa0,b_aa0,a_c0,b_c0,a_aa1,b_aa1,a_c1,b_c1),len(np.unique(root)),np.unique(root)[0]
def get_policy_un(alpha_aa,alpha_c, fn, Pf_aa, Pf_c,paa, pc,a_aa0, b_aa0,a_aa1, b_aa1,a_c0, b_c0, a_c1, b_c1):
root_aa=[]
root_c=[]
for i in np.arange(0.01,0.99,0.01):
try:
root_aa.append(newton(balanced_eqn_un,
x0 = i,
maxiter=50,
args = (a_aa0, b_aa0,a_aa1, b_aa1, alpha_aa)))
except(RuntimeError):
pass
try:
root_c.append(newton(balanced_eqn_un,
x0 = i,
maxiter=50,
args = (a_c0, b_c0,a_c1, b_c1, alpha_c)))
except(RuntimeError):
pass
root_aa = [float(format(round(r, 4))) for r in root_aa]
root_c = [float(format(round(r, 4))) for r in root_c]
return np.unique(root_aa)[0],np.unique(root_c)[0],len(np.unique(root_aa)),len(np.unique(root_aa))
def eva_policy(theta_aa,theta_c,a_aa0, b_aa0,a_aa1, b_aa1,a_c0, b_c0, a_c1, b_c1):
tpr = []
fpr = []
tpr.append(1-beta.cdf(theta_aa, a_aa1, b_aa1))
tpr.append(1-beta.cdf(theta_c, a_c1, b_c1))
fpr.append(1-beta.cdf(theta_aa, a_aa0, b_aa0))
fpr.append(1-beta.cdf(theta_c, a_c0, b_c0))
return tpr,fpr
def eva_classifier_fn(alpha_aa,alpha_c,policy,fn, Pf_aa, Pf_c,paa, pc,a_aa0, b_aa0,a_aa1, b_aa1,a_c0, b_c0, a_c1, b_c1):
if policy == 'UN' :
theta_aa, theta_c, _ , _ = get_policy_un(alpha_aa,alpha_c, fn, Pf_aa, Pf_c,paa, pc,a_aa0, b_aa0,a_aa1, b_aa1,a_c0, b_c0, a_c1, b_c1)
else:
theta_aa, theta_c, _ , _ = get_policy_fn(alpha_aa, alpha_c, fn, Pf_aa, Pf_c, paa, pc,a_aa0, b_aa0,a_aa1, b_aa1,a_c0, b_c0, a_c1, b_c1)
return eva_policy(theta_aa,theta_c, a_aa0, b_aa0,a_aa1, b_aa1,a_c0, b_c0, a_c1, b_c1)
def update(alpha,tpr,fpr,T, group):
g0 = T[0,0,group]*(1-fpr[group]) + T[0,1,group]*fpr[group]
g1 = T[1,0,group]*(1-tpr[group]) + T[1,1,group]*tpr[group]
return alpha*g1 + (1-alpha)*g0
def balance_diff(alpha,tpr,fpr,T, group):
g0 = T[0,0,group]*(1-fpr[group]) + T[0,1,group]*fpr[group]
g1 = T[1,0,group]*(1-tpr[group]) + T[1,1,group]*tpr[group]
return g0 + (g1-g0-1)*alpha
# def eva_classifier(alpha_aa,alpha_c,get_policy,paa, pc,a_aa0, b_aa0,a_aa1, b_aa1,a_c0, b_c0, a_c1, b_c1):
# theta_aa, theta_c, _ , _ = get_policy(alpha_aa,alpha_c, paa, pc, a_aa0, b_aa0,a_aa1, b_aa1,a_c0, b_c0, a_c1, b_c1)
# return eva_policy(theta_aa,theta_c, a_aa0, b_aa0,a_aa1, b_aa1,a_c0, b_c0, a_c1, b_c1)
# def get_policy_eqopt(alpha_aa,alpha_c,
# paa, pc,
# a_aa0, b_aa0,a_aa1, b_aa1,
# a_c0, b_c0, a_c1, b_c1):
# root=[]
# for i in np.arange(0.01,0.99,0.01):
# try:
# root.append(newton(balanced_eqn_eqopt,
# x0 = i,
# maxiter=50,
# args = (alpha_aa,alpha_c,
# paa, pc,
# a_aa0, b_aa0,a_aa1, b_aa1,
# a_c0, b_c0,a_c1, b_c1)))
# except(RuntimeError):
# pass
# root = [float(format(round(r, 4))) for r in root]
# return np.unique(root)[0],np.unique(root)[0],len(np.unique(root)),np.unique(root)[0]
#
# def balanced_eqn_eqopt(x, alpha_aa,alpha_c,
# paa, pc,
# a_aa0, b_aa0,a_aa1, b_aa1,
# a_c0, b_c0,a_c1, b_c1):
# return gamma_1(x,a_aa0, b_aa0,a_aa1, b_aa1,alpha_aa) * paa *alpha_aa- 2*(paa * alpha_aa + pc * alpha_c) + pc *alpha_c* gamma_1(x,a_c0, b_c0,a_c1, b_c1,alpha_c)