def log_likelihood_and_gradient(self, evidence):
"""
Run inference on the model to find the log-likelihood of the model given evidence and its gradient with respect
to the model parameters.
:param evidence: A dictionary where the key is a variable name and the value its observed value.
:returns: The log-likelihood and a vector of derivatives.
"""
self._update_order.reset()
inference = LoopyBeliefUpdateInference(self._model, update_order=self._update_order)
inference.calibrate(parameters=self.parameters)
log_z_total = inference.partition_approximation()
model_expected_counts = self._accumulate_expected_counts(inference)
self._update_order.reset()
inference = LoopyBeliefUpdateInference(self._model, update_order=self._update_order)
inference.calibrate(evidence, parameters=self.parameters)
log_z_observed = inference.partition_approximation()
empirical_expected_counts = self._accumulate_expected_counts(inference)
log_likelihood = log_z_observed - log_z_total
derivative = empirical_expected_counts - model_expected_counts
if self._dimension > 0:
derivative += -numpy.dot(self._prior_precision, (self._parameters - self._prior_location))
log_likelihood += -0.5 * numpy.dot(numpy.dot((self._parameters - self._prior_location).T,
self._prior_precision),
(self._parameters - self._prior_location))
log_likelihood += self._prior_normaliser
return log_likelihood, derivative
def test_belief_update_larger_tree(self):
a = DiscreteFactor([0, 1], data=np.array([[1, 2], [2, 2]], dtype=np.float64))
b = DiscreteFactor([1, 2], data=np.array([[3, 2], [1, 2]], dtype=np.float64))
c = DiscreteFactor([2, 3], data=np.array([[1, 2], [3, 4]], dtype=np.float64))
d = DiscreteFactor([3], data=np.array([2, 1], dtype=np.float64))
e = DiscreteFactor([0], data=np.array([4, 1], dtype=np.float64))
f = DiscreteFactor([2], data=np.array([1, 2], dtype=np.float64))
#
# a{0 1} - b{1 2} - c{2 3} - d{3}
# | |
# e{0} f{2}
#
model = Model([a, b, c, d, e, f])
print 'edges', model.edges
update_order = DistributeCollectProtocol(model)
inference = LoopyBeliefUpdateInference(model, update_order=update_order)
exact_inference = ExhaustiveEnumeration(model)
exhaustive_answer = exact_inference.calibrate().belief
print 'bp'
change = inference.calibrate()
print change
for factor in model.factors:
print factor
for variable in model.variables:
marginal_beliefs = inference.get_marginals(variable)
true_marginal = exhaustive_answer.marginalize([variable])
for marginal in marginal_beliefs:
assert_array_almost_equal(true_marginal.normalized_data, marginal.normalized_data)
expected_ln_Z = np.log(exhaustive_answer.data.sum())
self.assertAlmostEqual(expected_ln_Z, inference.partition_approximation())
def test_update_beliefs_disconnected(self):
a = DiscreteFactor([(1, 2), (2, 2)], data=np.array([[1, 2], [3, 4]], dtype=np.float64))
b = DiscreteFactor([(2, 2), (3, 2)], data=np.array([[1, 2], [3, 4]], dtype=np.float64))
c = DiscreteFactor([(4, 2), (5, 2)], data=np.array([[5, 6], [8, 9]], dtype=np.float64))
d = DiscreteFactor([(5, 2), (6, 2)], data=np.array([[1, 6], [2, 3]], dtype=np.float64))
e = DiscreteFactor([(7, 2), (8, 2)], data=np.array([[2, 1], [2, 3]], dtype=np.float64))
model = Model([a, b, c, d, e])
for factor in model.factors:
print 'before', factor, np.sum(factor.data)
update_order = DistributeCollectProtocol(model)
inference = LoopyBeliefUpdateInference(model, update_order=update_order)
exact_inference = ExhaustiveEnumeration(model)
exhaustive_answer = exact_inference.calibrate().belief
print 'Exhaust', np.sum(exhaustive_answer.data)
change = inference.calibrate()
print change
for factor in model.factors:
print factor, np.sum(factor.data)
for variable in model.variables:
marginal_beliefs = inference.get_marginals(variable)
true_marginal = exhaustive_answer.marginalize([variable])
for marginal in marginal_beliefs:
assert_array_almost_equal(true_marginal.normalized_data, marginal.normalized_data)
expected_ln_Z = np.log(exhaustive_answer.data.sum())
self.assertAlmostEqual(expected_ln_Z, inference.partition_approximation())
def test_loopy_distribute_collect(self):
a = DiscreteFactor([0, 1], data=np.array([[1, 2], [2, 2]], dtype=np.float64))
b = DiscreteFactor([1, 2], data=np.array([[3, 2], [1, 2]], dtype=np.float64))
c = DiscreteFactor([2, 0], data=np.array([[1, 2], [3, 4]], dtype=np.float64))
#
# a{0 1} - b{1 2}
# \ /
# c{2 0}
#
# a{0 1} - {0} - c{2 0}
#
#
#
#
model = Model([a, b, c])
update_order = LoopyDistributeCollectProtocol(model, max_iterations=40)
inference = LoopyBeliefUpdateInference(model, update_order=update_order)
inference.calibrate()
exact_inference = ExhaustiveEnumeration(model)
exhaustive_answer = exact_inference.calibrate().belief
for factor in model.factors:
print factor, np.sum(factor.data)
for var in model.variables_to_factors.keys():
print var, exhaustive_answer.marginalize([var]).data
print
for var in model.variables_to_factors.keys():
print var, inference.get_marginals(var)[0].data
for variable in model.variables:
for factor in inference.get_marginals(variable):
expected_table = exhaustive_answer.marginalize([variable])
actual_table = factor.marginalize([variable])
assert_array_almost_equal(expected_table.normalized_data, actual_table.normalized_data, decimal=2)
expected_ln_Z = np.log(exhaustive_answer.data.sum())
self.assertAlmostEqual(expected_ln_Z, inference.partition_approximation(), places=1)
def test_belief_update_long_tree(self):
label_template = np.array([['same', 'different'],
['different', 'same']])
observation_template = np.array([['obs_low'] * 32,
['obs_high'] * 32])
observation_template[0, 13:17] = 'obs_high'
observation_template[1, 13:17] = 'obs_low'
N = 2
pairs = [DiscreteFactor([(i, 2), (i + 1, 2)], parameters=label_template) for i in xrange(N - 1)]
obs = [DiscreteFactor([(i, 2), (i + N, 32)], parameters=observation_template) for i in xrange(N)]
repe = [16., 16., 14., 13., 15., 16., 14., 13., 15., 16., 15.,
13., 14., 16., 16., 15., 13., 13., 14., 14., 13., 14.,
14., 14., 14., 14., 14., 14., 14., 14., 14., 14., 14.,
14., 14., 14., 14., 14., 14., 14., 14., 9., 4., 4.,
4., 4., 5., 3., 2., 3., 2., 3., 3., 3., 3.,
3., 3., 3., 3., 4., 4., 5., 5., 5.]
evidence = dict((i + N, 0 if repe[i % len(repe)] >= 13 and repe[i % len(repe)] < 17 else 1) for i in xrange(N))
model = Model(pairs + obs)
parameters = {'same': 2.0, 'different': -1.0, 'obs_high': 0.0, 'obs_low': -0.0}
update_order = FloodingProtocol(model, max_iterations=4)
inference = LoopyBeliefUpdateInference(model, update_order=update_order)
inference.calibrate(evidence, parameters)
exact_inference = ExhaustiveEnumeration(model)
exhaustive_answer = exact_inference.calibrate(evidence, parameters).belief
for i in xrange(N):
expected_marginal = exhaustive_answer.marginalize([i])
for actual_marginal in inference.get_marginals(i):
print i
print expected_marginal.normalized_data
print actual_marginal.normalized_data
assert_array_almost_equal(expected_marginal.normalized_data, actual_marginal.normalized_data)
expected_ln_Z = np.log(exhaustive_answer.data.sum())
self.assertAlmostEqual(expected_ln_Z, inference.partition_approximation())
