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 init(self, graph):
if self.known_cpds is None:
self.known_cpds = []
self.alpha = float(self.alpha)
known = {cpd.scope[0] for cpd in self.known_cpds}
self.unknown = set(self.scope) - known
known_cpds = [CPD(cpd.scope, cpd.values) for cpd in self.known_cpds]
unknown_cpds = []
self.parents = find_parents(self.scope, graph)
for v in self.unknown:
pa_v = sorted(self.parents[v])
f = Factor([v] + pa_v)
val_pa_v = product(*(range(pa.k) for pa in pa_v))
for assg in val_pa_v:
dist = np.random.dirichlet([self.alpha / len(f.values)] * v.k)
assg = list(assg)
for i in range(v.k):
f.values[f.atoi([i] + assg)] = dist[i]
unknown_cpds.append(CPD(f.scope, f.values))
self.bn = BayesianNetwork(known_cpds + unknown_cpds)
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 optimal_decision_rule(self, scope):
cf = self.id.chance_factors
uf = Factor([], [0.0])
for f in self.id.utility_factors:
uf += f
gd = GibbsDistribution(cf + [uf])
ve = VariableElimination(gd)
mu = ve.posterior(scope, normalize=False)
assg_map = [scope.index(v) for v in mu.scope]
ind = mu.scope.index(scope[0])
rule = Factor(scope, np.zeros(np.prod([v.k for v in scope])))
n = int(np.prod([v.k for v in scope[1:]]))
for i in range(n):
assg = rule.itoa(i)
assg_mu = np.array(assg)[assg_map]
assg_mu[ind] = -1
assg_max = [mu.argmax(assg_mu)] + list(assg[1:])
rule.values[rule.atoi(assg_max)] = 1.0
return CPD(rule.scope, rule.values)
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 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 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 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 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 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 phenotype_given_genotype(variables, prob_trait_genotype):
v1, v2, v3 = variables
dims = [v1.k, v2.k, v3.k]
values = np.zeros(np.prod(dims))
for i in range(len(values)):
assg = np.unravel_index(i, dims)
values[i] = prob_trait_genotype[assg[1], assg[2]]
if not assg[0]:
values[i] = 1 - values[i]
return CPD([v3, v1, v2], values)
def allele_given_parent_alleles(allele, p_alleles):
dims = [allele.k, p_alleles[0].k, p_alleles[1].k]
values = np.zeros(np.prod(dims))
for i in range(len(values)):
assg = np.unravel_index(i, dims)
if assg[0] == assg[1]:
values[i] += 0.5
if assg[0] == assg[2]:
values[i] += 0.5
return CPD([allele, p_alleles[0], p_alleles[1]], values)
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 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 fit(self, X, graph):
"""Find the parameters for a probabilistic graphical model, given a
graph and a data set that possibly contains missing data.
After fitting, the model is available as a BayesianNetwork `self.bn`.
Parameters
----------
X : two-dimensional np.array or python matrix of integers
Matrix representing the observations. The value `X[i, j]` should
correspond to the discrete random variable `self.scope[j]` in
sample element `i`. The number -1 represents a missing value.
graph: dict from RandomVariables to sets of RandomVariables
the graph for the probabilistic graphical model
"""
var_index = {v: i for (i, v) in enumerate(self.scope)}
best_ll = float('-inf')
best_bn = None
for irestart in range(self.n_restarts):
if self.verbose > 0:
print('Restart {0}.'.format(irestart + 1))
self.init(graph)
known_cpds = [
CPD(cpd.scope, cpd.values) for cpd in self.known_cpds
]
M_scopes = []
for v in self.unknown:
M_scopes.append([v] + sorted(self.parents[v]))
for iiteration in range(self.n_iterations):
ess = [Factor(M_scope) for M_scope in M_scopes]
for x in X:
evidence = []
hidden = []
for (i, xi) in enumerate(x):
if xi == -1:
hidden.append(self.scope[i])
else:
evidence.append((self.scope[i], xi))
for M in ess:
M_assg = x[[var_index[v] for v in M.scope]]
M_h = []
for (i, v) in enumerate(M.scope):
if M_assg[i] == -1:
M_h.append(v)
if M_h:
ve = VariableElimination(self.bn)
f = ve.posterior(M_h, evidence=evidence)
Mh_index = [M.scope.index(v) for v in f.scope]
for i in range(len(f.values)):
f_assg = f.itoa(i)
M_assg[Mh_index] = f_assg
M.values[M.atoi(M_assg)] += f.values[i]
else:
M.values[M.atoi(M_assg)] += 1
self.bn = BayesianNetwork([M.to_cpd()
for M in ess] + known_cpds)
if self.verbose > 1:
print('Iteration {0}. '.format(iiteration + 1))
if self.verbose > 2:
ll = self.log_likelihood(X, self.bn)
print('Current log-likelihood {0}.'.format(ll))
ll = self.log_likelihood(X, self.bn)
print('Final log-likelihood {0}.'.format(ll))
if ll > best_ll:
best_ll = ll
best_bn = self.bn
self.bn = best_bn
return self
