def one_predictive_var():
Y = RandomVar('Y', 2)
X1 = RandomVar('X1', 2)
X2 = RandomVar('X2', 2)
X3 = RandomVar('X3', 2)
f_X1_Y = CPD([X1, Y], [1.0, 0.0, 0.0, 1.0])
f_X2_Y = CPD([X2, Y], [0.5, 0.5, 0.5, 0.5])
f_X3_Y = CPD([X3, Y], [0.5, 0.5, 0.5, 0.5])
f_Y = CPD([Y], [0.5, 0.5])
bn = BayesianNetwork([f_Y, f_X1_Y, f_X2_Y, f_X3_Y])
# Training the model
fs = ForwardSampler(bn)
fs.sample(1000)
scope, X = fs.samples_to_matrix()
y = X[:, -1]
X = X[:, 0:-1]
nb = NaiveBayes()
nb.fit(X, y)
# Evaluating the model
fs = ForwardSampler(bn)
fs.sample(10)
_, X = fs.samples_to_matrix()
print(nb.score(X[:, 0:-1], X[:, -1]))
print(nb.predict_proba(X[:, 0:-1]))
def build_genetic_network(parents, allele_freqs, prob_trait_genotype):
prob_trait_genotype = np.array(prob_trait_genotype)
variables = {}
for person in parents.keys():
v1 = RandomVar(person + '_allele_1', len(allele_freqs))
v2 = RandomVar(person + '_allele_2', len(allele_freqs))
v3 = RandomVar(person + '_trait', 2)
variables[person] = [v1, v2, v3]
factors = []
for person in parents.keys():
v1, v2, v3 = variables[person]
if parents[person]:
p1_vars = variables[parents[person][0]]
p2_vars = variables[parents[person][1]]
f_allele1 = allele_given_parent_alleles(v1, p1_vars)
f_allele2 = allele_given_parent_alleles(v2, p2_vars)
else:
f_allele1 = CPD([v1], allele_freqs)
f_allele2 = CPD([v2], allele_freqs)
f_phenotype = phenotype_given_genotype(variables[person],
prob_trait_genotype)
factors += [f_allele1, f_allele2, f_phenotype]
return BayesianNetwork(factors)
def main():
parents = {'alice': [], 'bob': [], 'eve': ['bob', 'alice']}
allele_freqs = [0.9, 0.1]
prob_trait_genotype = [[0.0, 0.0], [0.0, 1.0]]
bn = build_genetic_network(parents, allele_freqs, prob_trait_genotype)
# Examples
alice_trait = RandomVar('alice_trait', 2)
bob_trait = RandomVar('bob_trait', 2)
eve_trait = RandomVar('eve_trait', 2)
# alice_allele_1 = RandomVar('alice_allele_1', 2)
# alice_allele_2 = RandomVar('alice_allele_2', 2)
#
# bob_allele_1 = RandomVar('bob_allele_1', 2)
# bob_allele_2 = RandomVar('bob_allele_2', 2)
#
# eve_allele_1 = RandomVar('eve_allele_1', 2)
# eve_allele_2 = RandomVar('eve_allele_2', 2)
ve = JointMarginalization(bn)
print(ve.posterior([eve_trait]))
print(ve.posterior([eve_trait], [(bob_trait, 1)]))
print(ve.posterior([alice_trait, bob_trait], [(eve_trait, 1)]))
fs = ForwardSampler(bn)
fs.sample(1000)
print(
fs.posterior([(alice_trait, 0), (bob_trait, 0),
(eve_trait, 1)]) / fs.posterior([(eve_trait, 1)]))
print(bn.graph())
def fit(self, X, y):
"""Fit a Multinomial Naive Bayes model to the data.
Parameters:
-----------
X : two-dimensional np.array or python matrix of integers
Matrix representing the observations. It is assumed that
`X[:, i]` is a sample from a discrete random variable $X_i$ that
takes values between `0` and `X[:, i].max()`
y : one-dimensional np.array or python list of integers
Array representing the classes assigned to each observation
"""
X = np.asarray(X, dtype=np.int)
if X.min() < 0:
raise Exception('Invalid samples')
self.classes_, y = np.unique(y, return_inverse=True)
C = RandomVar('Y', len(self.classes_))
scope = []
for i in range(X.shape[1]):
scope.append(RandomVar('X{0}'.format(i), X[:, i].max() + 1))
graph = {v: set() for v in scope}
graph[C] = set(scope)
scope.append(C)
Xy = np.concatenate([X, y.reshape(-1, 1)], axis=1)
self.bn_ = UniformDirichlet(scope).fit_predict(Xy, graph)
self.scope_ = scope
return self
def main():
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])
# mn = MarkovNetwork([fx1, fx2_x1, fx3_x2])
ve = VariableElimination(bn)
jm = JointMarginalization(bn)
print(ve.posterior([x1, x2], [(x3, 0)]))
print(jm.posterior([x1, x2], [(x3, 0)]))
print(ve.posterior([x1, x2, x3]))
print(jm.posterior([x1, x2, x3]))
print(ve.maximum_a_posteriori(evidence=[(x3, 0)]))
print(jm.maximum_a_posteriori([x1, x2], [(x3, 0)]))
fs = ForwardSampler(bn)
fs.sample(10000)
for c in itertools.product(range(2), repeat=3):
print('{0}: {1}'.format(c, fs.posterior(zip([x1, x2, x3], c))))
px3_0 = fs.posterior([(x3, 0)])
for c in itertools.product(range(2), repeat=2):
assg = list(zip([x1, x2], c)) + [(x3, 0)]
print('{0}: {1}'.format(c, fs.posterior(assg) / px3_0))
gs = GibbsSampler(bn)
gs.sample(burn_in=1000, n=2000)
for c in itertools.product(range(2), repeat=3):
print('{0}: {1}'.format(c, gs.posterior(zip([x1, x2, x3], c))))
gs.reset()
gs.sample(burn_in=1000, n=1000, evidence=[(x3, 0)])
for c in itertools.product(range(2), repeat=2):
print('{0}: {1}'.format(c, gs.posterior(zip([x1, x2], c))))
def simple_sampling():
V1 = RandomVar('V1', 3)
V2 = RandomVar('V2', 3)
V3 = RandomVar('V3', 5)
scope = [V1, V2, V3]
graph = {V1: {V3}, V2: {V3}, V3: set()}
X = np.zeros((1000, 3), dtype=np.int)
X[:, 0:2] = np.random.choice(range(3),
size=(X.shape[0], 2),
p=[0.2, 0.5, 0.3])
X[:, 2] = X[:, 0] + X[:, 1]
mle = MaximumLikelihood(scope)
print(mle.fit_predict(X, graph))
ud = UniformDirichlet(scope, alpha=1.0)
print(ud.fit_predict(X, graph))
def three_variables():
M = RandomVar('Market', 3)
F = RandomVar('Found', 2)
uMF = Factor([M, F], [0, -7, 0, 5, 0, 20])
cM = CPD([M], [0.5, 0.3, 0.2])
# Alternative decision rules for F
dF_1 = CPD([F], [1.0, 0])
dF_2 = CPD([F], [0, 1.0]) # Optimal
id = InfluenceDiagram([cM], [uMF])
eu = ExpectedUtility(id)
print(eu.expected_utility([dF_1]))
print(eu.expected_utility([dF_2]))
print(eu.optimal_decision_rule([F]))
def six_variables():
M = RandomVar('Market', 3)
S = RandomVar('Survey', 4) # S = 3 means no survey
T = RandomVar('Test', 2)
F = RandomVar('Found', 2)
uMF = Factor([M, F], [0, -7, 0, 5, 0, 20])
uT = Factor([T], [0, -1])
cM = CPD([M], [0.5, 0.3, 0.2])
cST = CPD([S, M, T], [
0.0, 0.6, 0.0, 0.3, 0.0, 0.1, 0.0, 0.3, 0.0, 0.4, 0.0, 0.4, 0.0, 0.1,
0.0, 0.3, 0.0, 0.5, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0
])
# Alternative decision rules for F given S
dFS_1 = CPD([F, S], [0, 0, 0, 1, 1, 1, 1, 0])
dFS_2 = CPD([F, S], [1, 0, 0, 0, 0, 1, 1, 1]) # Optimal
# Alternative decision rules for T
dT_1 = CPD([T], [1.0, 0.0])
dT_2 = CPD([T], [0.0, 1.0]) # Optimal
id = InfluenceDiagram([cM, cST], [uMF, uT])
eu = ExpectedUtility(id)
print(eu.expected_utility([dFS_1, dT_1]))
print(eu.expected_utility([dFS_1, dT_2]))
print(eu.expected_utility([dFS_2, dT_1]))
print(eu.expected_utility([dFS_2, dT_2]))
# New influence diagram with a single decision rule
dT = dT_2
id2 = InfluenceDiagram([cM, cST, dT], [uMF, uT])
eu2 = ExpectedUtility(id2)
dFS_optimal = eu2.optimal_decision_rule([F, S])
print(eu.expected_utility([dFS_optimal, dT]))
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 main():
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])
ve = VariableElimination(bn)
jm = JointMarginalization(bn)
print(ve.posterior([B, E, A, R]) == jm.posterior([B, E, A, R]))
fs = ForwardSampler(bn)
fs.sample(1000)
def occurrence_counter():
x1 = RandomVar('X1', 2)
x2 = RandomVar('X2', 2)
x3 = RandomVar('X3', 2)
graph = {x1: {x2}, x2: {x3}, x3: set()}
scope = [x1, x2, x3]
X = np.array([[0, 1, 1], [0, 1, 0], [1, 0, 0]])
oc = OccurrenceCounter(scope, maxlen=4)
oc.fit(X, graph)
oc.refit(graph).stats
print(oc.stats)
print(oc.last_scopes)
graph = {x1: set(), x2: set(), x3: set()}
oc.refit(graph)
print(oc.stats)
print(oc.last_scopes)
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(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(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 main():
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])
ve = VariableElimination(bn)
jm = JointMarginalization(bn)
print(jm.maximum_a_posteriori([A], [(T, 1)]))
print(ve.posterior([A], [(T, 1)]))
print(jm.posterior([A], [(T, 1)]))
print(ve.posterior([A, T, P]))
print(jm.posterior([A, T, P]))
def simple_sampling():
V1 = RandomVar('V1', 3)
V2 = RandomVar('V2', 3)
V3 = RandomVar('V3', 5)
scope = [V1, V2, V3]
graph = {V1: {V3}, V2: {V3}, V3: set()}
X = np.zeros((1000, 3), dtype=np.int)
X[:, 0:2] = np.random.choice(range(3),
size=(X.shape[0], 2),
p=[0.2, 0.5, 0.3])
X[:, 2] = X[:, 0] + X[:, 1]
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)
print(BayesianScore(scope).fit(X, best_graph).score)
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()))