def traffic():
A = RandomVar('A', 2)
T = RandomVar('T', 2)
P = RandomVar('P', 2)
fP = CPD([P], [0.99, 0.01])
fA = CPD([A], [0.9, 0.1])
fT_AP = CPD([T, P, A], [0.9, 0.5, 0.4, 0.1, 0.1, 0.5, 0.6, 0.9])
bn = BayesianNetwork([fP, fA, fT_AP])
print(bn)
fs = ForwardSampler(bn)
fs.sample(1000)
scope, X = fs.samples_to_matrix()
mle = MaximumLikelihood(scope)
print(mle.fit_predict(X, bn.graph()))
ud = UniformDirichlet(scope, alpha=1.0)
print(ud.fit_predict(X, bn.graph()))
def traffic():
A = RandomVar('A', 2)
T = RandomVar('T', 2)
P = RandomVar('P', 2)
fP = CPD([P], [0.99, 0.01])
fA = CPD([A], [0.9, 0.1])
fT_AP = CPD([T, P, A], [0.9, 0.5, 0.4, 0.1, 0.1, 0.5, 0.6, 0.9])
bn = BayesianNetwork([fP, fA, fT_AP])
print(bn)
fs = ForwardSampler(bn)
fs.sample(1000)
scope, X = fs.samples_to_matrix()
mle = MaximumLikelihood(scope)
print(mle.fit_predict(X, bn.graph()))
ud = UniformDirichlet(scope, alpha=1.0)
print(ud.fit_predict(X, bn.graph()))
def earthquake():
B = RandomVar('B', 2)
E = RandomVar('E', 2)
A = RandomVar('A', 2)
R = RandomVar('R', 2)
a_be = CPD(
[A, B, E], [0.999, 0.01, 0.01, 0.0001, 0.001, 0.99, 0.99, 0.9999])
r_e = CPD([R, E], [1.0, 0.0, 0.0, 1.0])
b = CPD([B], [0.99, 0.01])
e = CPD([E], [0.999, 0.001])
bn = BayesianNetwork([a_be, r_e, b, e])
print(bn)
fs = ForwardSampler(bn)
fs.sample(1000)
scope, X = fs.samples_to_matrix()
mle = MaximumLikelihood(scope)
print(mle.fit_predict(X, bn.graph()))
ud = UniformDirichlet(scope, alpha=1.0)
print(ud.fit_predict(X, bn.graph()))
def earthquake():
B = RandomVar('B', 2)
E = RandomVar('E', 2)
A = RandomVar('A', 2)
R = RandomVar('R', 2)
a_be = CPD([A, B, E],
[0.999, 0.01, 0.01, 0.0001, 0.001, 0.99, 0.99, 0.9999])
r_e = CPD([R, E], [1.0, 0.0, 0.0, 1.0])
b = CPD([B], [0.99, 0.01])
e = CPD([E], [0.999, 0.001])
bn = BayesianNetwork([a_be, r_e, b, e])
print(bn)
fs = ForwardSampler(bn)
fs.sample(1000)
scope, X = fs.samples_to_matrix()
mle = MaximumLikelihood(scope)
print(mle.fit_predict(X, bn.graph()))
ud = UniformDirichlet(scope, alpha=1.0)
print(ud.fit_predict(X, bn.graph()))
def earthquake():
B = RandomVar('B', 2)
E = RandomVar('E', 2)
A = RandomVar('A', 2)
R = RandomVar('R', 2)
a_be = CPD([A, B, E],
[0.999, 0.01, 0.01, 0.0001, 0.001, 0.99, 0.99, 0.9999])
r_e = CPD([R, E], [1.0, 0.0, 0.0, 1.0])
b = CPD([B], [0.99, 0.01])
e = CPD([E], [0.999, 0.001])
bn = BayesianNetwork([a_be, r_e, b, e])
fs = ForwardSampler(bn)
fs.sample(1000)
scope, X = fs.samples_to_matrix()
graph = bn.graph()
# graph = {B : set(), E: set(), A: set(), R: set()}
score_l = LikelihoodScore(scope).fit(X, graph).score
print(score_l)
score_bic = BICScore(scope).fit(X, graph).score
print(score_bic)
score_b = BayesianScore(scope).fit(X, graph).score
print(score_b)
# scorer = LikelihoodScore(scope)
# scorer = BICScore(scope)
scorer = BayesianScore(scope)
best_graph, best_score = restarting_local_search(X,
scope,
scorer,
restarts=1,
iterations=100,
epsilon=0.2,
verbose=1)
print('Best:')
print(best_score)
print(best_graph)
def earthquake():
B = RandomVar('B', 2)
E = RandomVar('E', 2)
A = RandomVar('A', 2)
R = RandomVar('R', 2)
a_be = CPD(
[A, B, E], [0.999, 0.01, 0.01, 0.0001, 0.001, 0.99, 0.99, 0.9999])
r_e = CPD([R, E], [1.0, 0.0, 0.0, 1.0])
b = CPD([B], [0.99, 0.01])
e = CPD([E], [0.999, 0.001])
bn = BayesianNetwork([a_be, r_e, b, e])
fs = ForwardSampler(bn)
fs.sample(1000)
scope, X = fs.samples_to_matrix()
graph = bn.graph()
# graph = {B : set(), E: set(), A: set(), R: set()}
score_l = LikelihoodScore(scope).fit(X, graph).score
print(score_l)
score_bic = BICScore(scope).fit(X, graph).score
print(score_bic)
score_b = BayesianScore(scope).fit(X, graph).score
print(score_b)
# scorer = LikelihoodScore(scope)
# scorer = BICScore(scope)
scorer = BayesianScore(scope)
best_graph, best_score = restarting_local_search(X, scope, scorer,
restarts=1,
iterations=100,
epsilon=0.2,
verbose=1)
print('Best:')
print(best_score)
print(best_graph)
def simple_chain():
x1 = RandomVar('X1', 2)
x2 = RandomVar('X2', 2)
x3 = RandomVar('X3', 2)
fx1 = CPD([x1], [0.11, 0.89])
fx2_x1 = CPD([x2, x1], [0.59, 0.22, 0.41, 0.78])
fx3_x2 = CPD([x3, x2], [0.39, 0.06, 0.61, 0.94])
bn = BayesianNetwork([fx1, fx2_x1, fx3_x2])
graph = bn.graph()
print(bn)
fs = ForwardSampler(bn)
fs.sample(1000)
scope, X = fs.samples_to_matrix()
mle = MaximumLikelihood(scope)
print(mle.fit_predict(X, graph))
ud = UniformDirichlet(scope, alpha=1.0)
print(ud.fit_predict(X, graph))
def simple_chain():
x1 = RandomVar('X1', 2)
x2 = RandomVar('X2', 2)
x3 = RandomVar('X3', 2)
fx1 = CPD([x1], [0.11, 0.89])
fx2_x1 = CPD([x2, x1], [0.59, 0.22, 0.41, 0.78])
fx3_x2 = CPD([x3, x2], [0.39, 0.06, 0.61, 0.94])
bn = BayesianNetwork([fx1, fx2_x1, fx3_x2])
fs = ForwardSampler(bn)
fs.sample(2000)
scope, X = fs.samples_to_matrix()
graph = bn.graph()
# graph = {x1 : set(), x2: set(), x3: set()}
score_l = LikelihoodScore(scope).fit(X, graph).score
print(score_l)
score_bic = BICScore(scope).fit(X, graph).score
print(score_bic)
score_b = BayesianScore(scope).fit(X, graph).score
print(score_b)
# scorer = LikelihoodScore(scope)
scorer = BICScore(scope)
# scorer = BayesianScore(scope)
best_graph, best_score = restarting_local_search(X,
scope,
scorer,
restarts=5,
iterations=50,
epsilon=0.2,
verbose=1)
print('Best:')
print(best_score)
print(best_graph)
def traffic():
A = RandomVar('A', 2)
T = RandomVar('T', 2)
P = RandomVar('P', 2)
fP = CPD([P], [0.99, 0.01])
fA = CPD([A], [0.9, 0.1])
fT_AP = CPD([T, P, A], [0.9, 0.5, 0.4, 0.1, 0.1, 0.5, 0.6, 0.9])
bn = BayesianNetwork([fP, fA, fT_AP])
# print(bn)
fs = ForwardSampler(bn)
fs.sample(2000)
scope, X = fs.samples_to_matrix()
graph = bn.graph()
score_l = LikelihoodScore(scope).fit(X, graph).score
print(score_l)
score_bic = BICScore(scope).fit(X, graph).score
print(score_bic)
score_b = BayesianScore(scope).fit(X, graph).score
print(score_b)
# scorer = LikelihoodScore(scope)
scorer = BICScore(scope)
# scorer = BayesianScore(scope)
best_graph, best_score = restarting_local_search(X,
scope,
scorer,
restarts=5,
iterations=50,
epsilon=0.2,
verbose=1)
print('Best:')
print(best_score)
print(best_graph)
def simple_chain():
x1 = RandomVar('X1', 2)
x2 = RandomVar('X2', 2)
x3 = RandomVar('X3', 2)
fx1 = CPD([x1], [0.11, 0.89])
fx2_x1 = CPD([x2, x1], [0.59, 0.22, 0.41, 0.78])
fx3_x2 = CPD([x3, x2], [0.39, 0.06, 0.61, 0.94])
bn = BayesianNetwork([fx1, fx2_x1, fx3_x2])
graph = bn.graph()
print(bn)
fs = ForwardSampler(bn)
fs.sample(1000)
scope, X = fs.samples_to_matrix()
mle = MaximumLikelihood(scope)
print(mle.fit_predict(X, graph))
ud = UniformDirichlet(scope, alpha=1.0)
print(ud.fit_predict(X, graph))
def simple_chain():
x1 = RandomVar('X1', 2)
x2 = RandomVar('X2', 2)
x3 = RandomVar('X3', 2)
fx1 = CPD([x1], [0.11, 0.89])
fx2_x1 = CPD([x2, x1], [0.59, 0.22, 0.41, 0.78])
fx3_x2 = CPD([x3, x2], [0.39, 0.06, 0.61, 0.94])
bn = BayesianNetwork([fx1, fx2_x1, fx3_x2])
fs = ForwardSampler(bn)
fs.sample(2000)
scope, X = fs.samples_to_matrix()
graph = bn.graph()
# graph = {x1 : set(), x2: set(), x3: set()}
score_l = LikelihoodScore(scope).fit(X, graph).score
print(score_l)
score_bic = BICScore(scope).fit(X, graph).score
print(score_bic)
score_b = BayesianScore(scope).fit(X, graph).score
print(score_b)
# scorer = LikelihoodScore(scope)
scorer = BICScore(scope)
# scorer = BayesianScore(scope)
best_graph, best_score = restarting_local_search(X, scope, scorer,
restarts=5,
iterations=50,
epsilon=0.2,
verbose=1)
print('Best:')
print(best_score)
print(best_graph)
def traffic():
A = RandomVar('A', 2)
T = RandomVar('T', 2)
P = RandomVar('P', 2)
fP = CPD([P], [0.99, 0.01])
fA = CPD([A], [0.9, 0.1])
fT_AP = CPD([T, P, A], [0.9, 0.5, 0.4, 0.1, 0.1, 0.5, 0.6, 0.9])
bn = BayesianNetwork([fP, fA, fT_AP])
# print(bn)
fs = ForwardSampler(bn)
fs.sample(2000)
scope, X = fs.samples_to_matrix()
graph = bn.graph()
score_l = LikelihoodScore(scope).fit(X, graph).score
print(score_l)
score_bic = BICScore(scope).fit(X, graph).score
print(score_bic)
score_b = BayesianScore(scope).fit(X, graph).score
print(score_b)
# scorer = LikelihoodScore(scope)
scorer = BICScore(scope)
# scorer = BayesianScore(scope)
best_graph, best_score = restarting_local_search(X, scope, scorer,
restarts=5,
iterations=50,
epsilon=0.2,
verbose=1)
print('Best:')
print(best_score)
print(best_graph)
def die():
# Parameters
# d1_ = [0.2, 0.0, 0.5, 0.1, 0.1, 0.1]
# d2_ = [0.2, 0.3, 0.1, 0.05, 0.05, 0.3]
d1_ = [0.1, 0.9]
d2_ = [0.6, 0.4]
n_samples = 5000
n_iterations = 10
n_restarts = 2
verbose = 2
# Model creation
if len(d1_) != len(d2_):
raise Exception('The die should have the same cardinality')
h = RandomVar('h', 2)
o1 = RandomVar('o1', len(d1_))
o2 = RandomVar('o2', len(d2_))
f_h = CPD([h], [0.5, 0.5])
f_o1_h = Factor([o1, h])
f_o2_h = Factor([o2, h])
for i in range(len(f_o1_h.values)):
o_, h_ = f_o1_h.itoa(i)
f_o1_h.values[i] = d1_[o_] if h_ == 0 else d2_[o_]
f_o2_h.values[i] = d2_[o_] if h_ == 0 else d1_[o_]
f_o1_h = CPD(f_o1_h.scope, f_o1_h.values)
f_o2_h = CPD(f_o2_h.scope, f_o2_h.values)
bn = BayesianNetwork([f_h, f_o1_h, f_o2_h])
# Sampling from true model
fs = ForwardSampler(bn)
fs.sample(n_samples)
scope, X = fs.samples_to_matrix()
em = ExpectationMaximization(scope, known_cpds=[f_h],
n_iterations=n_iterations,
n_restarts=n_restarts, alpha=10.0,
verbose=verbose)
print('True log-likelihood (no missing variables):')
print(em.log_likelihood(X, bn))
print('Maximum log-likelihood (no missing variables):')
ls = LikelihoodScore(scope)
ls.fit(X, bn.graph())
print(ls.score)
# Hiding variable
X[:, scope.index(h)] = -1
print('True log-likelihood (missing variables):')
print(em.log_likelihood(X, bn))
bn_pred = em.fit_predict(X, bn.graph())
print('Best log-likelihood (missing variables)')
print(em.log_likelihood(X, bn_pred))
# Estimation results
print('Results:')
f_o1_h = [f for f in bn_pred.factors if f.scope[0] == o1][0]
f_o2_h = [f for f in bn_pred.factors if f.scope[0] == o2][0]
d = np.zeros(o1.k)
d1 = np.zeros(o1.k)
d2 = np.zeros(o1.k)
with printoptions(precision=3):
print('d1: {0}'.format(d1_))
for i in range(o1.k):
d[i] = f_o1_h.values[f_o1_h.atoi([i, 0])]
print('d1 according to o1: {0}'.format(d))
d1 += d
for i in range(o2.k):
d[i] = f_o2_h.values[f_o2_h.atoi([i, 1])]
print('d1 according to o2: {0}'.format(d))
d1 += d
print('d2: {0}'.format(d2_))
for i in range(o1.k):
d[i] = f_o1_h.values[f_o1_h.atoi([i, 1])]
print('d2 according to o1: {0}'.format(d))
d2 += d
for i in range(o2.k):
d[i] = f_o2_h.values[f_o2_h.atoi([i, 0])]
print('d2 according to o2: {0}'.format(d))
d2 += d
print('Average estimate:')
print('d1: {0}'.format(d1/2.))
print('d2: {0}'.format(d2/2.))