def detect_classifier(ce_matrix):
cbn = load_xml_to_cbn (os.path.join (src_path, '../data/adult/adult.xml'))
A1 = cbn.v['age']
A2 = cbn.v['education']
S = cbn.v['sex']
M1 = cbn.v['workclass']
M2 = cbn.v['marital-status']
N = cbn.v['hours']
Y = cbn.v['income']
for i in [0, 1, 2, 3]: # two datasets generated by two methods
test = DataSet (pd.read_csv ('temp/adult_binary_test_prediction%d.csv' % i))
for j, label in enumerate (['LR', 'SVM']): # two classifiers
# modify cpt of label before detect
for a1, a2, n, m1, m2, s, y in product (A1.domains.get_all (), A2.domains.get_all (), N.domains.get_all (), M1.domains.get_all (), M2.domains.get_all (),
S.domains.get_all (), Y.domains.get_all ()):
cbn.set_conditional_prob (Event ({Y: y}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s}),
test.get_conditional_prob (Event ({label: y}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s})))
cbn.build_joint_table ()
for k, (a1prime, a2prime, m1prime, m2prime) in enumerate (product ([0, 1], [0, 1], [0, 1], [0, 1])):
p_u, p_l = detect_after_remove (cbn=cbn, s=spos, sprime=sneg, y=1, a1prime=a1prime, a2prime=a2prime, m1prime=m1prime, m2prime=m2prime)
p = detect_after_remove (cbn=cbn, s=sneg, sprime=sneg, y=1, a1prime=a1prime, a2prime=a2prime, m1prime=m1prime, m2prime=m2prime)
ce_matrix.iloc[j * 32 + k, 2 * i:2 * i + 2] = [p_u - p, p_l - p]
for k, (a1prime, a2prime, m1prime, m2prime) in enumerate (product ([0, 1], [0, 1], [0, 1], [0, 1])):
p_u, p_l = detect_after_remove (cbn=cbn, s=sneg, sprime=spos, y=1, a1prime=a1prime, a2prime=a2prime, m1prime=m1prime, m2prime=m2prime)
p = detect_after_remove (cbn=cbn, s=spos, sprime=spos, y=1, a1prime=a1prime, a2prime=a2prime, m1prime=m1prime, m2prime=m2prime)
ce_matrix.iloc[j * 32 + k + 16, 2 * i:2 * i + 2] = [p_u - p, p_l - p]
def infer_with_complete_graph(y_val, s1_val, s0_val, ow, oa):
complete_cbn = load_xml_to_cbn(complete_model)
U = complete_cbn.v['USWAY']
S = complete_cbn.v['S']
W = complete_cbn.v['W']
A = complete_cbn.v['A']
Y_hat = complete_cbn.v['Y']
p1, p2 = 0.0, 0.0
complete_cbn.build_joint_table()
for u in U.domains.get_all():
# compute p(u|z, s)
ps = complete_cbn.get_prob(Event({U: u.index}), Event({S: s0_val, W: ow, A: oa}))
if ps == 0.00000:
continue
for w1, w0, a1 in product(W.domains.get_all(), W.domains.get_all(), A.domains.get_all()):
p1 += complete_cbn.get_prob(Event({W: w1}), Event({U: u, S: s1_val})) * \
complete_cbn.get_prob(Event({A: a1}), Event({U: u, W: w1})) * \
complete_cbn.get_prob(Event({W: w0}), Event({U: u, S: s0_val})) * \
complete_cbn.get_prob(Event({Y_hat: y_val}), Event({U: u, S: s1_val, W: w0, A: a1})) * \
ps
for w0, a0 in product(W.domains.get_all(), A.domains.get_all()):
p2 += complete_cbn.get_prob(Event({W: w0}), Event({U: u, S: s0_val})) * \
complete_cbn.get_prob(Event({A: a0}), Event({U: u, W: w0})) * \
complete_cbn.get_prob(Event({Y_hat: y_val}), Event({U: u, S: s0_val, W: w0, A: a0})) * \
ps
return p1, p2
def get_probabilistic_mode():
# # delete all hidden nodes from the deterministic graph
# fin = open (cwd + '/../data/synthetic/DeterministicGraph.xml', 'r')
# fout = open (cwd + '/../data/synthetic/ProbabilisticGraph.xml', 'w')
# for line in fin.readlines ():
# if line.find ('>U') == -1:
# fout.write (line)
# fin.close()
# fout.close()
# read the deterministic model and transfer it to a probabilistic model without all the hidden variable
deterministic_cbn = load_xml_to_cbn(
cwd + '/../data/synthetic/DeterministicBayesianModel.xml')
bayesian_net = XMLParser.parse(
cwd + '/../data/synthetic/DeterministicBayesianModel.xml')
root = bayesian_net.getroot()
# vars
for v in list(root[0])[::-1]:
if v.attrib['name'].startswith('U'):
root[0].remove(v)
# causal graph
for pf in list(root[1])[::-1]:
if pf.attrib['name'].startswith('U'):
root[1].remove(pf)
else:
for p in list(pf)[::-1]:
if p.attrib['name'].startswith('U'):
pf.remove(p)
# cpts
for c in root[2][::-1]:
name = c.attrib['variable']
if name.startswith('U'):
root[2].remove(c)
else:
index = deterministic_cbn.v[name].index
u_index = list(
deterministic_cbn.index_graph.pred[index].keys())[-1]
m, n = deterministic_cbn.cpts[index].shape
u_num = deterministic_cbn.v[u_index].domain_size
del c[m // u_num:]
c.attrib['numRows'] = str(m // u_num)
cpt = pd.DataFrame(data=np.zeros((m // u_num, n)),
columns=deterministic_cbn.cpts[index].columns)
for i in range(m // u_num):
cpt.iloc[i] = np.dot(
deterministic_cbn.cpts[u_index],
deterministic_cbn.cpts[index].iloc[i * u_num:(i + 1) *
u_num, :])
c[i].text = ' '.join(map("{:.3f}".format, cpt.iloc[i]))
bayesian_net.write(cwd +
'/../data/synthetic/ProbabilisticBayesianModel.xml')
def loosely_infer_with_partial_graph(y_val, s1_val, s0_val, ow, oa):
partial_cbn = load_xml_to_cbn(partial_model)
partial_cbn.build_joint_table()
S = partial_cbn.v['S']
W = partial_cbn.v['W']
A = partial_cbn.v['A']
Y_hat = partial_cbn.v['Y']
def max_w_a():
p_max = 0.0
p_min = 1.0
for w, a in product(W.domains.get_all(), A.domains.get_all()):
p = partial_cbn.get_prob(Event({Y_hat: y_val}),
Event({
S: s1_val,
W: w,
A: a
}))
if p < p_min:
p_min = p
if p > p_max:
p_max = p
return p_max, p_min
p1_upper, p1_lower = max_w_a()
p2 = partial_cbn.get_prob(Event({Y_hat: y_val}),
Event({
S: s0_val,
W: ow,
A: oa
}))
return p1_upper - p2, p1_lower - p2
def method2(acc_matrix):
train_df = pd.read_csv (os.path.join (src_path, '../data/adult/adult_binary_train.csv'))
test_df = pd.read_csv (os.path.join (src_path, '../data/adult/adult_binary_test.csv'))
cbn = load_xml_to_cbn (os.path.join (src_path, '../data/adult/adult.xml'))
# estimate residual error for the descendants
for att in ['marital-status', 'workclass', 'hours']:
att_index = cbn.v.name_dict[att].index
parents_index = cbn.index_graph.pred[att_index].keys ()
parents = [cbn.v[i].name for i in parents_index]
regression = LinearRegression ()
regression.fit (train_df[parents], train_df[att])
train_df[att + '-error'] = train_df[att] - regression.predict (train_df[parents])
test_df[att + '-error'] = test_df[att] - regression.predict (test_df[parents])
x = train_df[['age', 'education'] + [att + '-error' for att in ['marital-status', 'workclass', 'hours']]].values
y = train_df['income'].values
acc = []
# build classifiers using residual errors
for name, clf in zip (['LR', 'SVM'], [LogisticRegression (penalty='l2', solver='liblinear'), SVC (kernel='poly', gamma='auto')]):
clf.fit (x, y)
train_df[name] = clf.predict (train_df[['age', 'education'] + [att + '-error' for att in ['marital-status', 'workclass', 'hours']]].values)
test_df[name] = clf.predict (test_df[['age', 'education'] + [att + '-error' for att in ['marital-status', 'workclass', 'hours']]].values)
acc.append (accuracy_score (train_df['income'], train_df[name]))
acc.append (accuracy_score (test_df['income'], test_df[name]))
acc_matrix.iloc[:, 2] = acc
test_df.drop ([att + '-error' for att in ['marital-status', 'workclass', 'hours']], axis=1)
test_df.to_csv ('temp/adult_binary_test_prediction2.csv', index=False)
def build_partial_model(tetrad_model, complete_model, partial_model):
# read the SCM model and transfer it to a probabilistic model without all the hidden variable
complete_model = load_xml_to_cbn(complete_model)
# we load the original graph for modification
observed_model = XMLParser.parse(tetrad_model)
root = observed_model.getroot()
# vars
for v in list(root[0])[::-1]:
# remove exogenous variables from node list
if v.attrib['name'].startswith('U'):
root[0].remove(v)
# causal graph
for pf in list(root[1])[::-1]:
# remove exogenous variables
if pf.attrib['name'].startswith('U'):
root[1].remove(pf)
else:
# remove exogenous variables from parents
for p in list(pf)[::-1]:
if p.attrib['name'].startswith('U'):
pf.remove(p)
# cpts
for c in root[2][::-1]:
name = c.attrib['variable']
# remove cpts of exogenous variables
if name.startswith('U'):
root[2].remove(c)
else:
# todo: double check
# marginalize out the exogenous variables
index = complete_model.v[name].index
# we assume the endogenous variable only have an exogenous parent and its index is the smallest
u_index = list(complete_model.index_graph.pred[index].keys())[-1]
m, n = complete_model.cpts[index].shape
assert n == complete_model.v[name].domain_size
u_size = complete_model.v[u_index].domain_size
# delete the extra rows
del c[m // u_size:]
c.attrib['numRows'] = str(m // u_size)
cpt = pd.DataFrame(data=np.zeros((m // u_size, n)),
columns=complete_model.cpts[index].columns)
for i in range(m // u_size):
# each new row is the weighted cpts
u_cpt = complete_model.cpts[u_index]
joint_cpt = complete_model.cpts[index].iloc[i *
u_size:(i + 1) *
u_size, :]
cpt.iloc[i, :] = cpt.iloc[i, :] + np.dot(u_cpt,
joint_cpt).reshape(n)
c[i].text = ' '.join(map("{:.6f}".format, cpt.iloc[i]))
observed_model.write(partial_model)
def compute_from_observed(s, sprime, y, aprime, mprime):
probabilistic_cbn = load_xml_to_cbn(
cwd + '/../data/synthetic/ProbabilisticBayesianModel.xml')
probabilistic_cbn.build_joint_table()
A = probabilistic_cbn.v['A']
S = probabilistic_cbn.v['S']
N = probabilistic_cbn.v['N']
M = probabilistic_cbn.v['M']
Y = probabilistic_cbn.v['Y']
# Let's compute a counterfactual statement that is identifiable
# print ('-' * 20)
if s == sprime:
probabilistic_cbn.build_joint_table()
# print ('Identifiable:')
# print ('Compute according the Bayesian network: '),
# print (probabilistic_cbn.get_conditional_prob (Event ({Y: y}), Event ({A: aprime, M: mprime, S: sprime})))
return probabilistic_cbn.get_conditional_prob(
Event({Y: y}), Event({
A: aprime,
M: mprime,
S: sprime
}))
else:
# print ('Unidentifiable:')
p_u = 0.0
p_l = 0.0
for n in N.domains.get_all():
p_max = -1
p_min = 2
for m in M.domains.get_all():
p_m = probabilistic_cbn.find_prob(
Event({Y: y}), Event({
A: aprime,
N: n,
M: m,
S: s
}))
p_max = max(p_m, p_max)
p_min = min(p_m, p_min)
# print(p_max, p_min)
p_n = probabilistic_cbn.find_prob(Event({N: n}),
Event({
A: aprime,
S: s
}))
p_u += p_max * p_n
p_l += p_min * p_n
logging.info('Upper bound of counterfactual: %f' % p_u)
logging.info('Lower bound of counterfactual: %f' % p_l)
return p_u, p_l
def infer_with_complete_graph(y_val, s1_val, s0_val, ow, oa):
complete_cbn = load_xml_to_cbn(complete_model)
US = complete_cbn.v['US']
UW = complete_cbn.v['UW']
UA = complete_cbn.v['UA']
UY = complete_cbn.v['UY']
S = complete_cbn.v['S']
W = complete_cbn.v['W']
A = complete_cbn.v['A']
Y_hat = complete_cbn.v['Y']
complete_cbn.build_joint_table()
p1, p2 = 0.0, 0.0
for us, uw, ua, uy in product(US.domains.get_all(), UW.domains.get_all(),
UA.domains.get_all(), UY.domains.get_all()):
# compute p(u|z, s)
ps = complete_cbn.get_prob(Event({
US: us,
UW: uw,
UA: ua
}), Event({
S: s0_val,
W: ow,
A: oa
}))
# print(ps)
if ps == 0.00000:
continue
for w1, a1 in product(W.domains.get_all(), A.domains.get_all()):
p1 += complete_cbn.get_prob(Event({W: w1}), Event({UW: uw, S: s1_val})) * \
complete_cbn.get_prob(Event({A: a1}), Event({UA: ua, W: w1})) * \
complete_cbn.get_prob(Event({Y_hat: y_val}), Event({UY: uy, S: s1_val, W: w1, A: a1})) * \
complete_cbn.get_prob(Event({UY: uy}), Event({})) * ps
for w0, a0 in product(W.domains.get_all(), A.domains.get_all()):
p2 += complete_cbn.get_prob(Event({W: w0}), Event({UW: uw, S: s0_val})) * \
complete_cbn.get_prob(Event({A: a0}), Event({UA: ua, W: w0})) * \
complete_cbn.get_prob(Event({Y_hat: y_val}), Event({S: s0_val, W: w0, A: a0})) * \
complete_cbn.get_prob(Event({UY: uy}), Event({})) * ps
assert abs(p2 - complete_cbn.get_prob(Event({Y_hat: y_val}),
Event({
S: s0_val,
W: ow,
A: oa
}))) < 0.001
# print(p1, p2)
return p1, p2
def infer_with_complete_graph(y_val, s1_val, s0_val):
complete_cbn = load_xml_to_cbn(complete_model)
US = complete_cbn.v['US']
UW = complete_cbn.v['UW']
UA = complete_cbn.v['UA']
UY = complete_cbn.v['UY']
S = complete_cbn.v['S']
W = complete_cbn.v['W']
A = complete_cbn.v['A']
Y_hat = complete_cbn.v['Y']
p1, p2 = 0.0, 0.0
for uw, ua, uy in product(UW.domains.get_all(), UA.domains.get_all(),
UY.domains.get_all()):
for w1, w0, a1 in product(W.domains.get_all(), W.domains.get_all(),
A.domains.get_all()):
p1 += complete_cbn.get_prob(Event({W: w1}), Event({UW: uw, S: s1_val})) * \
complete_cbn.get_prob(Event({A: a1}), Event({UA: ua, W: w1})) * \
complete_cbn.get_prob(Event({W: w0}), Event({UW: uw, S: s0_val})) * \
complete_cbn.get_prob(Event({Y_hat: y_val}), Event({UY: uy, S: s1_val, W: w0, A: a1})) * \
complete_cbn.get_prob(Event({UW: uw}), Event({})) * \
complete_cbn.get_prob(Event({UA: ua}), Event({})) * \
complete_cbn.get_prob(Event({UY: uy}), Event({}))
for w0, a0 in product(W.domains.get_all(), A.domains.get_all()):
p2 += complete_cbn.get_prob(Event({W: w0}), Event({UW: uw, S: s0_val})) * \
complete_cbn.get_prob(Event({A: a0}), Event({UA: ua, W: w0})) * \
complete_cbn.get_prob(Event({Y_hat: y_val}), Event({UY: uy, S: s0_val, W: w0, A: a0})) * \
complete_cbn.get_prob(Event({UW: uw}), Event({})) * \
complete_cbn.get_prob(Event({UA: ua}), Event({})) * \
complete_cbn.get_prob(Event({UY: uy}), Event({}))
# complete_cbn.build_joint_table()
# assert abs(p2 - complete_cbn.get_prob(Event({Y_hat: y_val}), Event({S: s0_val}))) <= 0.0001
# print(p1, p2)
return p1, p2
def compute_from_observed(s, sprime, y, a1prime, m1prime, m2prime, a2prime):
probabilistic_cbn = load_xml_to_cbn (cwd + '/../data/adult/adult.xml')
probabilistic_cbn.build_joint_table ()
A1 = probabilistic_cbn.v['age']
A2 = probabilistic_cbn.v['education']
S = probabilistic_cbn.v['sex']
M1 = probabilistic_cbn.v['workclass']
M2 = probabilistic_cbn.v['marital-status']
N = probabilistic_cbn.v['hours']
Y = probabilistic_cbn.v['income']
# Let's compute a counterfactual statement that is identifiable
# print ('-' * 20)
if s == sprime:
probabilistic_cbn.build_joint_table ()
# print ('Identifiable:')
# print ('Compute according the Bayesian network: ', end=''),
p = probabilistic_cbn.get_conditional_prob (Event ({Y: y}), Event ({A1: a1prime, A2: a2prime, M1: m1prime, M2: m2prime, S: sprime}))
return p
else:
# print ('Unidentifiable:')
p_u = 0.0
p_l = 0.0
for n in N.domains.get_all ():
p_max = -1
p_min = 2
for m1, m2 in product (M1.domains.get_all (), M2.domains.get_all ()):
p_m = probabilistic_cbn.find_prob (Event ({Y: y}), Event ({A1: a1prime, A2: a2prime, N: n, M1: m1, M2: m2, S: s}))
p_max = max (p_m, p_max)
p_min = min (p_m, p_min)
# print(p_max, p_min)
p_n = probabilistic_cbn.find_prob (Event ({N: n}), Event ({A1: a1prime, A2: a2prime, M1: m1prime, M2: m2prime, S: s}))
p_u += p_max * p_n
p_l += p_min * p_n
return p_u, p_l
def loosely_infer_with_partial_graph(y_val, s1_val, s0_val, oa, oe, om):
partial_cbn = load_xml_to_cbn(partial_model)
partial_cbn.build_joint_table()
Age = partial_cbn.v['age']
Edu = partial_cbn.v['education']
Sex = partial_cbn.v['sex']
Workclass = partial_cbn.v['workclass']
Marital = partial_cbn.v['marital-status']
Hours = partial_cbn.v['hours']
Income = partial_cbn.v['income']
def max_w_h():
p_max = 0.0
p_min = 1.0
for m in Marital.domains.get_all():
p_m = partial_cbn.get_prob(
Event({Income: y_val}),
Event({
Sex: s1_val,
Age: oa,
Edu: oe,
Marital: m
}))
p_max = max(p_m, p_max)
p_min = min(p_m, p_min)
return p_max, p_min
p1_upper, p1_lower = max_w_h()
p2 = partial_cbn.get_prob(
Event({Income: y_val}),
Event({
Sex: s0_val,
Age: oa,
Edu: oe,
Marital: om
}))
return p1_upper - p2, p1_lower - p2
def test():
###############
complete_cbn = load_xml_to_cbn(complete_model)
US = complete_cbn.v['US']
UW = complete_cbn.v['UW']
UA = complete_cbn.v['UA']
UY = complete_cbn.v['UY']
S = complete_cbn.v['S']
W = complete_cbn.v['W']
A = complete_cbn.v['A']
Y_hat = complete_cbn.v['Y']
print('Generate using conditional cpts')
for s in S.domains.get_all():
p = 0.0
for us in US.domains.get_all():
p = p + complete_cbn.get_prob(Event({S: s}), Event(
{US: us})) * complete_cbn.get_prob(Event({US: us}), Event({}))
print(p)
print()
for s, w in product(S.domains.get_all(), W.domains.get_all()):
p = 0.0
for uw in UW.domains.get_all():
p = p + complete_cbn.get_prob(Event({W: w}), Event({
UW: uw,
S: s
})) * complete_cbn.get_prob(Event({UW: uw}), Event({}))
print(p)
print()
for w, a in product(W.domains.get_all(), A.domains.get_all()):
p = 0.0
for ua in UA.domains.get_all():
p = p + complete_cbn.get_prob(Event({A: a}), Event({
UA: ua,
W: w
})) * complete_cbn.get_prob(Event({UA: ua}), Event({}))
print(p)
print()
for s, w, a, y in product(S.domains.get_all(), W.domains.get_all(),
A.domains.get_all(), Y_hat.domains.get_all()):
p = 0.0
for uy in UY.domains.get_all():
p = p + complete_cbn.get_prob(Event(
{Y_hat: y}), Event({
UY: uy,
S: s,
W: w,
A: a
})) * complete_cbn.get_prob(Event({UY: uy}), Event({}))
print(p)
print()
print()
print('Generate using joint cpt')
complete_cbn.build_joint_table()
for s in S.domains.get_all():
print(complete_cbn.get_prob(Event({S: s})))
print()
for s, w in product(S.domains.get_all(), W.domains.get_all()):
print(complete_cbn.get_prob(Event({W: w}), Event({S: s})))
print()
for w, a in product(W.domains.get_all(), A.domains.get_all()):
print(complete_cbn.get_prob(Event({A: a}), Event({W: w})))
print()
for s, w, a, y in product(S.domains.get_all(), W.domains.get_all(),
A.domains.get_all(), Y_hat.domains.get_all()):
print(
complete_cbn.get_prob(Event({Y_hat: y}), Event({
S: s,
W: w,
A: a
})))
print()
print()
partial_cbn = load_xml_to_cbn(partial_model)
partial_cbn.build_joint_table()
S = partial_cbn.v['S']
W = partial_cbn.v['W']
A = partial_cbn.v['A']
Y_hat = partial_cbn.v['Y']
print('Generate using partial SCM')
for s in S.domains.get_all():
print(partial_cbn.get_prob(Event({S: s}), Event({})))
print()
for s, w in product(S.domains.get_all(), W.domains.get_all()):
print(partial_cbn.get_prob(Event({W: w}), Event({S: s})))
print()
for w, a in product(W.domains.get_all(), A.domains.get_all()):
print(partial_cbn.get_prob(Event({A: a}), Event({W: w})))
print()
for s, w, a, y in product(S.domains.get_all(), W.domains.get_all(),
A.domains.get_all(), Y_hat.domains.get_all()):
print(
partial_cbn.get_prob(Event({Y_hat: y}), Event({
S: s,
W: w,
A: a
})))
print()
print()
def pearl_three_step(s, sprime, y, aprime, mprime):
deterministic_cbn = load_xml_to_cbn(
cwd + '/../data/synthetic/DeterministicBayesianModel.xml')
UA = deterministic_cbn.v['UA']
UN = deterministic_cbn.v['UN']
UM = deterministic_cbn.v['UM']
US = deterministic_cbn.v['US']
UY = deterministic_cbn.v['UY']
A = deterministic_cbn.v['A']
S = deterministic_cbn.v['S']
N = deterministic_cbn.v['N']
M = deterministic_cbn.v['M']
Y = deterministic_cbn.v['Y']
"""
if s == sprime:
print ('Identifiable:')
print ("Let's validate pearl's three step by data")
data = DataSet (pd.read_csv ('../data/synthetic/DeterministicData.txt', sep='\t'))
print ('Read from data: ', end='')
print (data.get_conditional_prob (Event ({'Y': y}), Event ({'A': aprime, 'M': mprime, 'S': sprime})))
p = 0.0
for ua, un, um, us, uy in product (UA.domains.get_all (), UN.domains.get_all (), UM.domains.get_all (), US.domains.get_all (), UY.domains.get_all ()):
ps = data.get_conditional_prob (
Event ({'UA': ua.index, 'UN': un.index, 'UM': um.index, 'US': us.index, 'UY': uy.index}),
Event ({'A': aprime, 'M': mprime, 'S': sprime}))
for a, n, m in product (A.domains.get_all (), N.domains.get_all (), M.domains.get_all ()):
p += deterministic_cbn.find_prob (Event ({A: a}), Event ({UA: ua})) * \
deterministic_cbn.find_prob (Event ({M: m}), Event ({S: s, A: a, UM: um})) * \
deterministic_cbn.find_prob (Event ({N: n}), Event ({S: s, A: a, UN: un})) * \
deterministic_cbn.find_prob (Event ({Y: y}), Event ({S: s, A: a, N: n, M: m, UY: uy})) * \
ps
print ("Pearl's three steps: (U is obtarined from data) %f" % p)
"""
p = 0.0
deterministic_cbn.build_joint_table()
for ua, un, um, us, uy in product(UA.domains.get_all(),
UN.domains.get_all(),
UM.domains.get_all(),
US.domains.get_all(),
UY.domains.get_all()):
# compute p(u|z, s)
ps = deterministic_cbn.get_conditional_prob(
Event({
UA: ua.index,
UN: un.index,
UM: um.index,
US: us.index,
UY: uy.index
}), Event({
A: aprime,
M: mprime,
S: sprime
}))
for a, n, m in product(A.domains.get_all(), N.domains.get_all(),
M.domains.get_all()):
p += deterministic_cbn.find_prob (Event ({A: a}), Event ({UA: ua})) * \
deterministic_cbn.find_prob (Event ({M: m}), Event ({S: s, A: a, UM: um})) * \
deterministic_cbn.find_prob (Event ({N: n}), Event ({S: s, A: a, UN: un})) * \
deterministic_cbn.find_prob (Event ({Y: y}), Event ({S: s, A: a, N: n, M: m, UY: uy})) * \
ps
logging.info("Pearl's three steps: %f" % p)
return p
def pearl_detect_classifier(ce_matrix):
cbn = load_xml_to_cbn(
os.path.join(src_path,
'../data/synthetic/DeterministicBayesianModel.xml'))
UA = cbn.v['UA']
UN = cbn.v['UN']
UM = cbn.v['UM']
US = cbn.v['US']
UY = cbn.v['UY']
A = cbn.v['A']
S = cbn.v['S']
N = cbn.v['N']
M = cbn.v['M']
Y = cbn.v['Y']
cbn.build_joint_table()
event = cbn.jpt.groupby(
Event({
UA: 1,
UN: 1,
UM: 1,
US: 1,
A: 1,
M: 1,
S: 1
}).keys())
condition = cbn.jpt.groupby(Event({A: 1, M: 1, S: 1}).keys())
def pearl_after_remove_(s, sprime, y, aprime, mprime):
p = 0.0
for ua, un, um, us in product(UA.domains.get_all(),
UN.domains.get_all(),
UM.domains.get_all(),
US.domains.get_all()):
e = Event({
UA: ua,
UN: un,
UM: um,
US: us,
A: aprime,
M: mprime,
S: sprime
})
c = Event({A: aprime, M: mprime, S: sprime})
ps = event.get_group(tuple(
e.values()))['prob'].sum() / condition.get_group(
tuple(c.values()))['prob'].sum()
for a, n, m in product(A.domains.get_all(), N.domains.get_all(),
M.domains.get_all()):
p += cbn.find_prob (Event ({A: a}), Event ({UA: ua})) * \
cbn.find_prob (Event ({M: m}), Event ({S: s, A: a, UM: um})) * \
cbn.find_prob (Event ({N: n}), Event ({S: s, A: a, UN: un})) * \
cbn.find_prob (Event ({Y: y}), Event ({S: s, A: a, N: n, M: m, UY: 1})) * \
ps
return p
for i in [0, 1, 2, 3]: # two datasets generated by two methods
test = DataSet(pd.read_csv('temp/synthetic_test_prediction%d.csv' % i))
for j, label in enumerate(['LR', 'SVM']): # two classifiers
# modify cpt of label before detect
for a, n, m, s, y in product(A.domains.get_all(),
N.domains.get_all(),
M.domains.get_all(),
S.domains.get_all(),
Y.domains.get_all()):
cbn.set_conditional_prob(
Event({Y: y}), Event({
A: a,
M: m,
N: n,
S: s,
UY: 1
}),
test.get_conditional_prob(
Event({label: y}),
Event({
'A': a,
'M': m,
'N': n,
'S': s
})))
for k, (aprime, mprime) in enumerate(product([0, 1], [0, 1])):
ce = pearl_after_remove_ (s=spos, sprime=sneg, y=1, aprime=aprime, mprime=mprime) - \
pearl_after_remove_ (s=sneg, sprime=sneg, y=1, aprime=aprime, mprime=mprime)
ce_matrix.iloc[j * 8 + k, 3 * i + 2] = ce
for k, (aprime, mprime) in enumerate(product([0, 1], [0, 1])):
ce = pearl_after_remove_ (s=sneg, sprime=spos, y=1, aprime=aprime, mprime=mprime) - \
pearl_after_remove_ (s=spos, sprime=spos, y=1, aprime=aprime, mprime=mprime)
ce_matrix.iloc[j * 8 + k + 4, 3 * i + 2] = ce
def tight_infer_with_partial_graph(y_val, s1_val, s0_val, oa, oe, om):
partial_cbn = load_xml_to_cbn(partial_model)
partial_cbn.build_joint_table()
Age = partial_cbn.v['age']
Edu = partial_cbn.v['education']
Sex = partial_cbn.v['sex']
Workclass = partial_cbn.v['workclass']
Marital = partial_cbn.v['marital-status']
Hours = partial_cbn.v['hours']
Income = partial_cbn.v['income']
if s1_val == s0_val:
# there is no difference when active value = reference value
return 0.00, 0.00
else:
# define variable for P(r)
PR = cvx.Variable(Marital.domain_size**8)
# define ell functions
g = {}
for v in {Marital}:
v_index = v.index
v_domain_size = v.domain_size
parents_index = partial_cbn.index_graph.pred[v_index].keys()
parents_domain_size = np.prod(
[partial_cbn.v[i].domain_size for i in parents_index])
g[v_index] = list(
product(range(v_domain_size), repeat=int(parents_domain_size)))
# format
# [(), (), ()]
# r corresponds to the tuple
# parents corresponds to the location of the tuple
# assert the response function. (t function of Pearl, I function in our paper)
def Indicator(obs, parents, response):
# sort the parents by id
par_key = parents.keys()
# map the value to index
par_index = 0
for k in par_key:
par_index = par_index * partial_cbn.v[
k].domain_size + parents.dict[k]
return 1 if obs.first_value() == g[
obs.first_key()][response][par_index] else 0
# build the object function
weights = np.zeros(shape=[Marital.domain_size**8])
for rm in range(Marital.domain_size**8):
# assert r -> o to obtain the conditional individuals
product_i = 1
for (obs, parents, response) in [(Event({Marital: om}),
Event({
Sex: s0_val,
Age: oa,
Edu: oe
}), rm)]:
product_i *= Indicator(obs, parents, response)
if product_i == 1:
# if ALL I()= 1, then continue the counterfactual inference
# the first term for pse
sum_identity = 0.0
for m1, w, h in product(Marital.domains.get_all(),
Workclass.domains.get_all(),
Hours.domains.get_all()):
product_i = partial_cbn.get_prob(Event({Sex: s0_val}), Event({})) * \
partial_cbn.get_prob(Event({Age: oa}), Event({})) * \
partial_cbn.get_prob(Event({Edu: oe}), Event({Age: oa})) * \
Indicator(Event({Marital: m1}), Event({Sex: s1_val, Age: oa, Edu: oe}), rm) * \
partial_cbn.get_prob(Event({Workclass: w}), Event({Age: oa, Edu: oe, Marital: m1})) * \
partial_cbn.get_prob(Event({Hours: h}), Event({Workclass: w, Edu: oe, Marital: m1, Age: oa, Sex: s1_val})) * \
partial_cbn.get_prob(Event({Income: y_val}), Event({Sex: s1_val, Edu: oe, Workclass: w, Marital: m1, Hours: h, Age: oa}))
sum_identity += product_i
weights[rm] += sum_identity
# the second term for pse
sum_identity = 0.0
for m0, w, h in product(Marital.domains.get_all(),
Workclass.domains.get_all(),
Hours.domains.get_all()):
product_i = partial_cbn.get_prob(Event({Sex: s0_val}), Event({})) * \
partial_cbn.get_prob(Event({Age: oa}), Event({})) * \
partial_cbn.get_prob(Event({Edu: oe}), Event({Age: oa})) * \
Indicator(Event({Marital: m0}), Event({Sex: s0_val, Age: oa, Edu: oe}), rm) * \
partial_cbn.get_prob(Event({Workclass: w}), Event({Age: oa, Edu: oe, Marital: m0})) * \
partial_cbn.get_prob(Event({Hours: h}), Event({Workclass: w, Edu: oe, Marital: m0, Age: oa, Sex: s0_val})) * \
partial_cbn.get_prob(Event({Income: y_val}), Event({Sex: s0_val, Edu: oe, Workclass: w, Marital: m0, Hours: h, Age: oa}))
sum_identity += product_i
weights[rm] -= sum_identity
# build the objective function
objective = weights.reshape(1, -1) @ PR / partial_cbn.get_prob(
Event({
Sex: s0_val,
Age: oa,
Edu: oe,
Marital: om
}))
############################
### to build the constraints
############################
### the inferred model is consistent with the observational distribution
A_mat = np.zeros(
(Age.domain_size, Edu.domain_size, Marital.domain_size,
Sex.domain_size, Marital.domain_size**8))
b_vex = np.zeros((Age.domain_size, Edu.domain_size,
Marital.domain_size, Sex.domain_size))
# assert r -> v
for a, e, m, s in product(Age.domains.get_all(), Edu.domains.get_all(),
Marital.domains.get_all(),
Sex.domains.get_all()):
# calculate the probability of observation
b_vex[a.index, e.index, m.index, s.index] = partial_cbn.get_prob(
Event({
Age: a,
Edu: e,
Marital: m,
Sex: s
}))
# sum of P(r)
for rm in range(Marital.domain_size**8):
product_i = partial_cbn.get_prob(Event({Sex: s}), Event({})) * \
partial_cbn.get_prob(Event({Age: a}), Event({})) * \
partial_cbn.get_prob(Event({Edu: e}), Event({Age: a})) * \
Indicator(Event({Marital: m}), Event({Sex: s, Age: a, Edu: e}), rm)
A_mat[a.index, e.index, m.index, s.index, rm] = product_i
# flatten the matrix and vector
A_mat = A_mat.reshape(-1, Marital.domain_size**8)
b_vex = b_vex.reshape(-1, 1)
### the probability <= 1
C_mat = np.identity(Marital.domain_size**8)
d_vec = np.ones(Marital.domain_size**8)
### the probability is positive
E_mat = np.identity(Marital.domain_size**8)
f_vec = np.zeros(Marital.domain_size**8)
constraints = [
A_mat @ PR == b_vex, C_mat @ PR <= d_vec, E_mat @ PR >= f_vec
]
# minimize the causal effect
problem = cvx.Problem(cvx.Minimize(objective), constraints)
problem.solve()
# print('tight lower effect: %f' % (problem.value))
lower = problem.value
# maximize the causal effect
problem = cvx.Problem(cvx.Maximize(objective), constraints)
problem.solve()
# print('tight upper effect: %f' % (problem.value))
upper = problem.value
return upper, lower
def detect_classifier(ce_matrix):
cbn = load_xml_to_cbn(
os.path.join(src_path,
'../data/synthetic/ProbabilisticBayesianModel.xml'))
A = cbn.v['A']
S = cbn.v['S']
N = cbn.v['N']
M = cbn.v['M']
Y = cbn.v['Y']
for i in [0, 1, 2, 3]: # two datasets generated by two methods
test = DataSet(pd.read_csv('temp/synthetic_test_prediction%d.csv' % i))
for j, label in enumerate(['LR', 'SVM']): # two classifiers
# modify cpt of label before detect
for a, n, m, s, y in product(A.domains.get_all(),
N.domains.get_all(),
M.domains.get_all(),
S.domains.get_all(),
Y.domains.get_all()):
cbn.set_conditional_prob(
Event({Y: y}), Event({
A: a,
M: m,
N: n,
S: s
}),
test.get_conditional_prob(
Event({label: y}),
Event({
'A': a,
'M': m,
'N': n,
'S': s
})))
cbn.build_joint_table()
for k, (aprime, mprime) in enumerate(product([0, 1], [0, 1])):
p_u, p_l = detect_after_remove(cbn=cbn,
s=spos,
sprime=sneg,
y=1,
aprime=aprime,
mprime=mprime)
p = detect_after_remove(cbn=cbn,
s=sneg,
sprime=sneg,
y=1,
aprime=aprime,
mprime=mprime)
ce_matrix.iloc[j * 8 + k, 3 * i:3 * i + 2] = [p_u - p, p_l - p]
for k, (aprime, mprime) in enumerate(product([0, 1], [0, 1])):
p_u, p_l = detect_after_remove(cbn=cbn,
s=sneg,
sprime=spos,
y=1,
aprime=aprime,
mprime=mprime)
p = detect_after_remove(cbn=cbn,
s=spos,
sprime=spos,
y=1,
aprime=aprime,
mprime=mprime)
ce_matrix.iloc[j * 8 + k + 4,
3 * i:3 * i + 2] = [p_u - p, p_l - p]
def method3(acc_matrix):
df_train = pd.read_csv ('temp/adult_binary_train_prediction0.csv')
# df_train = pd.concat ([df_train] * 10, ignore_index=True)
train = DataSet (df_train)
df_test = pd.read_csv ('temp/adult_binary_test_prediction0.csv')
df_test = pd.concat ([df_test] * 3, ignore_index=True)
test = DataSet (df_test)
acc = []
for name in ['LR', 'SVM']:
probabilistic_cbn = load_xml_to_cbn (os.path.join (src_path, '../data/adult/adult.xml'))
def find_condition_prob(e, t):
return probabilistic_cbn.find_prob (e, t)
def get_loc(e):
return probabilistic_cbn.get_loc (e)
A1 = probabilistic_cbn.v['age']
A2 = probabilistic_cbn.v['education']
S = probabilistic_cbn.v['sex']
M1 = probabilistic_cbn.v['workclass']
M2 = probabilistic_cbn.v['marital-status']
N = probabilistic_cbn.v['hours']
Y = probabilistic_cbn.v['income']
YH = Variable (name=name, index=Y.index + 1, domains=Y.domains)
probabilistic_cbn.v[(YH.index, YH.name)] = YH
YT = Variable (name=name + "M", index=Y.index + 2, domains=Y.domains)
probabilistic_cbn.v[(YT.index, YT.name)] = YT
# build linear loss function
C_vector = np.zeros ((2 ** 8 + 2 ** 8 // 4, 1))
for a1, a2, n, m1, m2, s in product (A1.domains.get_all (), A2.domains.get_all (), N.domains.get_all (), M1.domains.get_all (), M2.domains.get_all (),
S.domains.get_all ()):
p_x_s = train.get_marginal_prob (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s}))
p_yh_1_y = p_x_s * train.count (Event ({Y: 0, YH: 0}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s}), 'notequal')
loc = get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s, YH: 0, YT: 0}))
C_vector[loc] = p_yh_1_y * train.get_conditional_prob (Event ({YH: 0}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s}))
loc = get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s, YH: 1, YT: 1}))
C_vector[loc] = p_yh_1_y * train.get_conditional_prob (Event ({YH: 1}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s}))
p_yh__y = p_x_s * train.count (Event ({Y: 0, YH: 0}), Event ({A1: a1, A2: a2, M1: m1, M2: m2, N: n, S: s}), 'equal')
loc = get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s, YH: 0, YT: 1}))
C_vector[loc] = p_yh__y * train.get_conditional_prob (Event ({YH: 0}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s}))
loc = get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s, YH: 1, YT: 0}))
C_vector[loc] = p_yh__y * train.get_conditional_prob (Event ({YH: 1}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s}))
# the inequality of max and min
G_matrix_1 = np.zeros ((2 ** 8, 2 ** 8 + 2 ** 8 // 4))
h_1 = np.zeros (2 ** 8)
# max
i = 0
for a1, a2, n, s, yt in product (A1.domains.get_all (), A2.domains.get_all (), N.domains.get_all (), S.domains.get_all (), YT.domains.get_all ()):
for m1, m2 in product (M1.domains.get_all (), M2.domains.get_all ()):
for yh in YH.domains.get_all ():
loc = get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s, YH: yh, YT: yt}))
G_matrix_1[i, loc] = train.get_conditional_prob (Event ({YH: yh}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s}))
loc = get_loc (Event ({A1: a1, A2: a2, N: n, S: s, YT: yt}))
G_matrix_1[i, 2 ** 8 + loc] = -1
i += 1
# min
assert i == 2 ** 8 // 2
for a1, a2, n, s, yt in product (A1.domains.get_all (), A2.domains.get_all (), N.domains.get_all (), S.domains.get_all (), YT.domains.get_all ()):
for m1, m2 in product (M1.domains.get_all (), M2.domains.get_all ()):
for yh in YH.domains.get_all ():
loc = get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s, YH: yh, YT: yt}))
G_matrix_1[i, loc] = -train.get_conditional_prob (Event ({YH: yh}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s}))
loc = get_loc (Event ({A1: a1, A2: a2, N: n, S: s, YT: yt}))
G_matrix_1[i, 2 ** 8 + 2 ** 8 // 8 + loc] = 1
i += 1
# build counterfactual fairness constraints
G_matrix_2 = np.zeros ((2 ** 4 * 2, 2 ** 8 + 2 ** 8 // 4))
h_2 = np.ones (2 ** 4 * 2) * tau
i = 0
for a1, a2, m1, m2 in product (A1.domains.get_all (), A2.domains.get_all (), M1.domains.get_all (), M2.domains.get_all ()):
for n in N.domains.get_all ():
loc = get_loc (Event ({A1: a1, A2: a2, N: n, S: spos, YT: yt_pos}))
G_matrix_2[i, 2 ** 8 + loc] = find_condition_prob (Event ({N: n}), Event ({A1: a1, A2: a2, M1: m1, M2: m2, S: spos}))
for yh in YH.domains.get_all ():
loc = get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: sneg, YH: yh, YT: yt_pos}))
G_matrix_2[i, loc] = -find_condition_prob (Event ({N: n}), Event ({A1: a1, A2: a2, M1: m1, M2: m2, S: sneg})) \
* train.get_conditional_prob (Event ({YH: yh}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: sneg}))
i += 1
assert i == 2 ** 4
for a1, a2, m1, m2 in product (A1.domains.get_all (), A2.domains.get_all (), M1.domains.get_all (), M2.domains.get_all ()):
for n in N.domains.get_all ():
loc = get_loc (Event ({A1: a1, A2: a2, N: n, S: spos, YT: yt_pos}))
G_matrix_2[i, 2 ** 8 + 2 ** 8 // 8 + loc] = -find_condition_prob (Event ({N: n}), Event ({A1: a1, A2: a2, M1: m1, M2: m2, S: spos}))
for yh in YH.domains.get_all ():
loc = get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: sneg, YH: yh, YT: yt_pos}))
G_matrix_2[i, loc] = find_condition_prob (Event ({N: n}), Event ({A1: a1, A2: a2, M1: m1, M2: m2, S: sneg})) \
* train.get_conditional_prob (Event ({YH: yh}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: sneg}))
i += 1
###########
# mapping in [0, 1]
G_matrix_3 = np.zeros ((2 * (2 ** 8 + 2 ** 8 // 4), 2 ** 8 + 2 ** 8 // 4))
h_3 = np.zeros (2 * (2 ** 8 + 2 ** 8 // 4))
for i in range (2 ** 8 + 2 ** 8 // 4):
G_matrix_3[i, i] = 1
h_3[i] = 1
G_matrix_3[2 ** 8 + 2 ** 8 // 4 + i, i] = -1
h_3[2 ** 8 + 2 ** 8 // 4 + i] = 0
# sum = 1
A_matrix = np.zeros ((2 ** 8 // 2, 2 ** 8 + 2 ** 8 // 4))
b = np.ones (2 ** 8 // 2)
i = 0
for a1, a2, n, m1, m2, s, yh in product (A1.domains.get_all (), A2.domains.get_all (), N.domains.get_all (), M1.domains.get_all (), M2.domains.get_all (),
S.domains.get_all (),
YH.domains.get_all ()):
for yt in YT.domains.get_all ():
A_matrix[i, get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s, YH: yh, YT: yt}))] = 1
i += 1
assert i == 2 ** 8 // 2
# combine the inequality constraints
G_matrix = np.vstack ([G_matrix_1, G_matrix_2, G_matrix_3])
h = np.hstack ([h_1, h_2, h_3])
# Test
# print (np.linalg.matrix_rank (A_matrix), A_matrix.shape[0])
# print (np.linalg.matrix_rank (np.vstack ([A_matrix, G_matrix])), A_matrix.shape[1])
# def check():
# sol = np.zeros (2 ** 8 + 2 ** 8 // 4)
# for a1, a2, n, m1, m2, s, yh, yt in product (A1.domains.get_all (), A2.domains.get_all (), N.domains.get_all (), M1.domains.get_all (), M2.domains.get_all (),
# S.domains.get_all (), YH.domains.get_all (), YT.domains.get_all ()):
# if yh.name == yt.name:
# sol[get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s, YH: yh, YT: yt}))] = 1.0
# else:
# sol[get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s, YH: yh, YT: yt}))] = 0.0
#
# for a1, a2, n, s, yt in product (A1.domains.get_all (), A2.domains.get_all (), N.domains.get_all (), S.domains.get_all (), YT.domains.get_all ()):
# p_min = 1
# p_max = 0
# for m1, m2 in product (M1.domains.get_all (), M2.domains.get_all ()):
# p = 0.0
# for yh in YH.domains.get_all ():
# p = train.get_conditional_prob (Event ({YH: yh}), Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s})) \
# * sol[get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s, YH: yh, YT: yt}))]
# if p < p_min:
# p_min = p
# if p > p_max:
# p_max = p
# loc = get_loc (Event ({A1: a1, A2: a2, N: n, S: s, YT: yt}))
# sol[2 ** 8 + loc] = p_max
# sol[2 ** 8 + 2 ** 8 // 8 + loc] = p_min
#
# np.dot (G_matrix_2, sol)
# check ()
# solver
solvers.options['show_progress'] = False
sol = solvers.lp (c=matrix (C_vector),
G=matrix (G_matrix),
h=matrix (h),
A=matrix (A_matrix),
b=matrix (b),
solver=solvers
)
mapping = np.array (sol['x'])
# build the post-processing result in training and testing
train.df.loc[:, name + 'M'] = train.df[name]
test.df[name + 'M'] = test.df[name]
for a1, a2, n, m1, m2, s, yh, yt in product (A1.domains.get_all (), A2.domains.get_all (), N.domains.get_all (), M1.domains.get_all (), M2.domains.get_all (),
S.domains.get_all (), YH.domains.get_all (), YT.domains.get_all ()):
if yh.name != yt.name:
p = mapping[get_loc (Event ({A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s, YH: yh, YT: yt})), 0]
train.random_assign (Event ({YH: yh, A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s}), Event ({YT: yt}), p)
test.random_assign (Event ({YH: yh, A1: a1, A2: a2, N: n, M1: m1, M2: m2, S: s}), Event ({YT: yt}), p)
train.df[name] = train.df[name + 'M']
train.df.drop ([name + 'M'], axis=1)
test.df[name] = test.df[name + 'M']
test.df.drop ([name + 'M'], axis=1)
acc.append (accuracy_score (train.df[name], train.df[Y.name]))
acc.append (accuracy_score (test.df[name], test.df[Y.name]))
acc_matrix.iloc[:, 3] = acc
train.df.to_csv ('temp/adult_binary_train_prediction3.csv', index=False)
test.df.to_csv ('temp/adult_binary_test_prediction3.csv', index=False)
def tight_infer_with_partial_graph(y_val, s1_val, s0_val, ow, oa):
partial_cbn = load_xml_to_cbn(partial_model)
partial_cbn.build_joint_table()
S = partial_cbn.v['S']
W = partial_cbn.v['W']
A = partial_cbn.v['A']
Y_hat = partial_cbn.v['Y']
if s1_val == s0_val:
# there is no difference when active value = reference value
return 0.00, 0.00
else:
# define variable for P(r)
PR = cvx.Variable(S.domain_size * \
W.domain_size ** S.domain_size * \
A.domain_size ** W.domain_size * \
Y_hat.domain_size ** (S.domain_size * W.domain_size * A.domain_size))
# define ell functions
g = {}
for v in {S, Y_hat, W, A}:
v_index = v.index
v_domain_size = v.domain_size
parents_index = partial_cbn.index_graph.pred[v_index].keys()
parents_domain_size = np.prod([partial_cbn.v[i].domain_size for i in parents_index])
g[v_index] = list(product(range(v_domain_size), repeat=int(parents_domain_size)))
# format
# [(), (), ()]
# r corresponds to the tuple
# parents corresponds to the location of the tuple
# assert the response function. (t function of Pearl, I function in our paper)
def Indicator(obs, parents, response):
# sort the parents by id
par_key = parents.keys()
# map the value to index
par_index = 0
for k in par_key:
par_index = par_index * partial_cbn.v[k].domain_size + parents.dict[k]
return 1 if obs.first_value() == g[obs.first_key()][response][par_index] else 0
# build the object function
weights = np.zeros(shape=[S.domain_size,
W.domain_size ** S.domain_size,
A.domain_size ** W.domain_size,
Y_hat.domain_size ** (S.domain_size * W.domain_size * A.domain_size)])
for rs, rw, ra, ry in product(range(S.domain_size),
range(W.domain_size ** S.domain_size),
range(A.domain_size ** W.domain_size),
range(Y_hat.domain_size ** (S.domain_size * W.domain_size * A.domain_size))):
# assert r -> o to obtain the conditional individuals
product_i = 1
for (obs, parents, response) in [(Event({S: s0_val}), Event({}), rs),
(Event({W: ow}), Event({S: s0_val}), rw),
(Event({A: oa}), Event({W: ow}), ra)]:
product_i *= Indicator(obs, parents, response)
if product_i == 1:
# if ALL I()= 1, then continue the counterfactual inference
# the first term for pse
sum_identity = 0.0
for w1, w0, a1 in product(W.domains.get_all(), W.domains.get_all(), A.domains.get_all()):
product_i = 1
for (v, parents, response) in [(Event({W: w1}), Event({S: s1_val}), rw),
(Event({A: a1}), Event({W: w1}), ra),
(Event({W: w0}), Event({S: s0_val}), rw),
(Event({Y_hat: y_val}), Event({S: s1_val, W: w0, A: a1}), ry)]:
product_i *= Indicator(v, parents, response)
sum_identity += product_i
weights[rs, rw, ra, ry] = weights[rs, rw, ra, ry] + sum_identity
# the second term for pse
sum_identity = 0.0
for w0, a0 in product(W.domains.get_all(), A.domains.get_all()):
product_i = 1
for (v, parents, response) in [(Event({W: w0}), Event({S: s0_val}), rw),
(Event({A: a0}), Event({W: w0}), ra),
(Event({Y_hat: y_val}), Event({S: s0_val, W: w0, A: a0}), ry)]:
product_i = product_i * Indicator(v, parents, response)
sum_identity += product_i
weights[rs, rw, ra, ry] -= sum_identity
# build the objective function
objective = weights.reshape(1, -1) @ PR / partial_cbn.get_prob(Event({S: s0_val, W: ow, A: oa}))
############################
### to build the constraints
############################
### the inferred model is consistent with the observational distribution
A_mat = np.zeros((S.domain_size, W.domain_size, A.domain_size, Y_hat.domain_size,
S.domain_size, W.domain_size ** S.domain_size, A.domain_size ** W.domain_size,
Y_hat.domain_size ** (S.domain_size * W.domain_size * A.domain_size)))
b_vex = np.zeros((S.domain_size, W.domain_size, A.domain_size, Y_hat.domain_size))
# assert r -> v
for s, w, a, y in product(S.domains.get_all(),
W.domains.get_all(),
A.domains.get_all(),
Y_hat.domains.get_all()):
# calculate the probability of observation
b_vex[s.index, w.index, a.index, y.index] = partial_cbn.get_prob(Event({S: s, W: w, A: a, Y_hat: y}))
# sum of P(r)
for rs, rw, ra, ry in product(range(S.domain_size),
range(W.domain_size ** S.domain_size),
range(A.domain_size ** W.domain_size),
range(Y_hat.domain_size ** (S.domain_size * W.domain_size * A.domain_size))):
product_i = 1
for (v, parents, response) in [(Event({S: s}), Event({}), rs),
(Event({W: w}), Event({S: s}), rw),
(Event({A: a}), Event({W: w}), ra),
(Event({Y_hat: y}), Event({S: s, W: w, A: a}), ry)]:
product_i = product_i * Indicator(v, parents, response)
A_mat[s.index, w.index, a.index, y.index, rs, rw, ra, ry] = product_i
# flatten the matrix and vector
A_mat = A_mat.reshape(
S.domain_size * W.domain_size * A.domain_size * Y_hat.domain_size,
S.domain_size * W.domain_size ** S.domain_size * A.domain_size ** W.domain_size * Y_hat.domain_size ** (S.domain_size * W.domain_size * A.domain_size))
b_vex = b_vex.reshape(-1, 1)
### the probability <= 1
C_mat = np.identity(S.domain_size * W.domain_size ** S.domain_size * A.domain_size ** W.domain_size * Y_hat.domain_size ** (S.domain_size * W.domain_size * A.domain_size))
d_vec = np.ones(S.domain_size * W.domain_size ** S.domain_size * A.domain_size ** W.domain_size * Y_hat.domain_size ** (S.domain_size * W.domain_size * A.domain_size))
### the probability is positive
E_mat = np.identity(S.domain_size * W.domain_size ** S.domain_size * A.domain_size ** W.domain_size * Y_hat.domain_size ** (S.domain_size * W.domain_size * A.domain_size))
f_vec = np.zeros(S.domain_size * W.domain_size ** S.domain_size * A.domain_size ** W.domain_size * Y_hat.domain_size ** (S.domain_size * W.domain_size * A.domain_size))
constraints = [
A_mat @ PR == b_vex,
# C_mat @ PR == d_vec,
C_mat @ PR <= d_vec,
E_mat @ PR >= f_vec
]
# minimize the causal effect
problem = cvx.Problem(cvx.Minimize(objective), constraints)
problem.solve()
# print('tight lower effect: %f' % (problem.value))
lower = problem.value
# maximize the causal effect
problem = cvx.Problem(cvx.Maximize(objective), constraints)
problem.solve()
# print('tight upper effect: %f' % (problem.value))
upper = problem.value
return upper, lower
def method3(acc_matrix):
df_train = pd.read_csv('temp/synthetic_train_prediction0.csv')
train = DataSet(df_train)
df_test = pd.read_csv('temp/synthetic_test_prediction0.csv')
test = DataSet(df_test)
acc = []
for name in ['LR', 'SVM']:
probabilistic_cbn = load_xml_to_cbn(
os.path.join(src_path,
'../data/synthetic/ProbabilisticBayesianModel.xml'))
def find_condition_prob(e, t):
return probabilistic_cbn.find_prob(e, t)
def get_loc(e):
return probabilistic_cbn.get_loc(e)
A = probabilistic_cbn.v['A']
S = probabilistic_cbn.v['S']
N = probabilistic_cbn.v['N']
M = probabilistic_cbn.v['M']
Y = probabilistic_cbn.v['Y']
YH = Variable(name='YH', index=Y.index + 1, domains=Y.domains)
probabilistic_cbn.v[(YH.index, YH.name)] = YH
YT = Variable(name='YT', index=Y.index + 2, domains=Y.domains)
probabilistic_cbn.v[(YT.index, YT.name)] = YT
# build linear loss function
C_vector = np.zeros((2**6 + 2**6 // 2, 1))
for a, n, m, s in product(A.domains.get_all(), N.domains.get_all(),
M.domains.get_all(), S.domains.get_all()):
p_x_s = train.get_marginal_prob(
Event({
'A': a,
'M': m,
'N': n,
'S': s
}))
p_yh_1_y = p_x_s * train.count(
Event({
'Y': 0,
name: 0
}), Event({
'A': a,
'M': m,
'N': n,
'S': s
}), 'notequal')
loc = get_loc(Event({A: a, M: m, N: n, S: s, YH: 0, YT: 0}))
C_vector[loc] = p_yh_1_y * train.get_conditional_prob(
Event({name: 0}), Event({
'A': a,
'M': m,
'N': n,
'S': s
}))
loc = get_loc(Event({A: a, M: m, N: n, S: s, YH: 1, YT: 1}))
C_vector[loc] = p_yh_1_y * train.get_conditional_prob(
Event({name: 1}), Event({
'A': a,
'M': m,
'N': n,
'S': s
}))
p_yh__y = p_x_s * train.count(
Event({
'Y': 0,
name: 0
}), Event({
'A': a,
'M': m,
'N': n,
'S': s
}), 'equal')
loc = get_loc(Event({A: a, M: m, N: n, S: s, YH: 0, YT: 1}))
C_vector[loc] = p_yh__y * train.get_conditional_prob(
Event({name: 0}), Event({
'A': a,
'M': m,
'N': n,
'S': s
}))
loc = get_loc(Event({A: a, M: m, N: n, S: s, YH: 1, YT: 0}))
C_vector[loc] = p_yh__y * train.get_conditional_prob(
Event({name: 1}), Event({
'A': a,
'M': m,
'N': n,
'S': s
}))
# the inequality of max and min
G_matrix_1 = np.zeros((2**6, 2**6 + 2**6 // 2))
h_1 = np.zeros(2**6)
# max
i = 0
for a, n, s, yt in product(A.domains.get_all(), N.domains.get_all(),
S.domains.get_all(), YT.domains.get_all()):
for m in M.domains.get_all():
for yh in YH.domains.get_all():
loc = get_loc(
Event({
A: a,
M: m,
N: n,
S: s,
YH: yh,
YT: yt
}))
G_matrix_1[i, loc] = train.get_conditional_prob(
Event({name: yh}),
Event({
'A': a,
'M': m,
'N': n,
'S': s
}))
loc = get_loc(Event({A: a, N: n, S: s, YT: yt}))
G_matrix_1[i, 2**6 + loc] = -1
i += 1
# min
assert i == 2**6 // 2
for a, n, s, yt in product(A.domains.get_all(), N.domains.get_all(),
S.domains.get_all(), YT.domains.get_all()):
for m in M.domains.get_all():
for yh in YH.domains.get_all():
loc = get_loc(
Event({
A: a,
M: m,
N: n,
S: s,
YH: yh,
YT: yt
}))
G_matrix_1[i, loc] = -train.get_conditional_prob(
Event({name: yh}),
Event({
'A': a,
'M': m,
'N': n,
'S': s
}))
loc = get_loc(Event({A: a, N: n, S: s, YT: yt}))
G_matrix_1[i, 2**6 + 2**6 // 4 + loc] = 1
i += 1
# build counterfactual fairness constraints
G_matrix_2 = np.zeros((2**2 * 2, 2**6 + 2**6 // 2))
h_2 = np.ones(2**2 * 2) * tau
i = 0
for a, m in product(A.domains.get_all(), M.domains.get_all()):
for n in N.domains.get_all():
loc = get_loc(Event({A: a, N: n, S: spos, YT: yt_pos}))
G_matrix_2[i, 2**6 + loc] = find_condition_prob(
Event({N: n}), Event({
A: a,
S: spos
}))
for yh in YH.domains.get_all():
loc = get_loc(
Event({
A: a,
M: m,
N: n,
S: sneg,
YH: yh,
YT: yt_pos
}))
G_matrix_2[i, loc] = -find_condition_prob (Event ({N: n}), Event ({A: a, S: sneg})) \
* train.get_conditional_prob (Event ({name: yh}), Event ({'A': a, 'M': m, 'N': n, 'S': sneg}))
i += 1
assert i == 2**2
for a, m in product(A.domains.get_all(), M.domains.get_all()):
for n in N.domains.get_all():
loc = get_loc(Event({A: a, N: n, S: spos, YT: yt_pos}))
G_matrix_2[i, 2**6 + 2**6 // 4 + loc] = -find_condition_prob(
Event({N: n}), Event({
A: a,
S: spos
}))
for yh in YH.domains.get_all():
loc = get_loc(
Event({
A: a,
M: m,
N: n,
S: sneg,
YH: yh,
YT: yt_pos
}))
G_matrix_2[i, loc] = find_condition_prob (Event ({N: n}), Event ({A: a, S: sneg})) \
* train.get_conditional_prob (Event ({name: yh}), Event ({'A': a, 'M': m, 'N': n, 'S': sneg}))
i += 1
###########
# mapping in [0, 1]
G_matrix_3 = np.zeros(((2**6 + 2**6 // 2) * 2, 2**6 + 2**6 // 2))
h_3 = np.zeros((2**6 + 2**6 // 2) * 2)
for i in range(2**6 + 2**6 // 2):
G_matrix_3[i, i] = 1
h_3[i] = 1
G_matrix_3[2**6 + 2**6 // 2 + i, i] = -1
h_3[2**6 + 2**6 // 2 + i] = 0
# sum = 1
A_matrix = np.zeros((2**6 // 2, 2**6 + 2**6 // 2))
b = np.ones(2**6 // 2)
i = 0
for a, n, m, s, yh in product(A.domains.get_all(), N.domains.get_all(),
M.domains.get_all(), S.domains.get_all(),
YH.domains.get_all()):
for yt in YT.domains.get_all():
A_matrix[
i,
get_loc(Event({
A: a,
M: m,
N: n,
S: s,
YH: yh,
YT: yt
}))] = 1
i += 1
assert i == 2**6 // 2
# combine the inequality constraints
G_matrix = np.vstack([G_matrix_1, G_matrix_2, G_matrix_3])
h = np.hstack([h_1, h_2, h_3])
# solver
solvers.options['show_progress'] = False
sol = solvers.lp(c=matrix(C_vector),
G=matrix(G_matrix),
h=matrix(h),
A=matrix(A_matrix),
b=matrix(b),
solver=solvers)
mapping = np.array(sol['x'])
# build the post-processing result in training and testing
train.df[name + '1'] = train.df[name]
test.df[name + '1'] = test.df[name]
for a, n, m, s, yh, yt in product(A.domains.get_all(),
N.domains.get_all(),
M.domains.get_all(),
S.domains.get_all(),
YH.domains.get_all(),
YT.domains.get_all()):
if yh.name != yt.name:
p = mapping[
get_loc(Event({
A: a,
M: m,
N: n,
S: s,
YH: yh,
YT: yt
})), 0]
train.random_assign(
Event({
name: yh,
'A': a,
'M': m,
'N': n,
'S': s
}), Event({name + '1': yt}), p)
test.random_assign(
Event({
name: yh,
'A': a,
'M': m,
'N': n,
'S': s
}), Event({name + '1': yt}), p)
train.df[name] = train.df[name + '1']
train.df.drop([name + '1'], axis=1)
test.df[name] = test.df[name + '1']
test.df.drop([name + '1'], axis=1)
acc.append(accuracy_score(train.df['Y'], train.df[name]))
acc.append(accuracy_score(test.df['Y'], test.df[name]))
acc_matrix.iloc[:, 3] = acc
train.df.to_csv('temp/synthetic_train_prediction3.csv', index=False)
test.df.to_csv('temp/synthetic_test_prediction3.csv', index=False)
