def test_get_log_likelihood_by_parameters(self):
a = DiscreteFactor(['1', '2'], parameters=np.array([['a', 'b'], ['c', 'd']]))
b = DiscreteFactor(['2', '3'], parameters=np.array([['e', 'f'], ['g', 'h']]))
model = Model([a, b])
prior_sigma2 = 2.3
learner = LearnMrfParameters(model, prior=1.0/(prior_sigma2 ** 1.0))
D = 8
parameters = np.zeros(D)
parameter_out_of_order = [1, 2, 3, 4, 3, 4, 5, 7]
parameter_names = [c for c in 'abcdefgh']
for param, param_name in zip(parameter_out_of_order, parameter_names):
parameters[learner._parameters_to_index[param_name]] = np.log(param)
evidence = {'1': 0, '3': 1}
learner._parameters = parameters
actual_log_likelihood, _ = learner.log_likelihood_and_gradient(evidence)
prior_factor = D * (-0.5 * np.log((2.0 * np.pi * prior_sigma2)))
print 'pn', prior_factor, D * -0.5 * np.log(prior_sigma2)
prior_factor += sum([-0.5 / (prior_sigma2) * param ** 2.0 for param in parameters])
print 'dim', D
print actual_log_likelihood, np.log(0.18) + prior_factor, prior_factor
self.assertAlmostEqual(actual_log_likelihood, np.log(0.18) + prior_factor)
def test_compare_gradientless_and_gradient_learning():
seq = [1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]
seqh = [1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]
factors = []
hidden_factors = []
evidence = {}
o_parameters = np.array([['a', 'b'], ['c', 'd']])
h_parameters = np.array([['e', 'f'], ['g', 'h']])
for i, (s, sh) in enumerate(zip(seq, seqh)):
obs = DiscreteFactor(['o_{}'.format(i), 'h_{}'.format(i)], parameters=o_parameters)
evidence['o_{}'.format(i)] = s
evidence['h_{}'.format(i)] = sh
factors.append(obs)
if i < len(seq):
hid = DiscreteFactor(['h_{}'.format(i), 'h_{}'.format(i + 1)], parameters=h_parameters)
factors.append(hid)
hidden_factors.append(hid)
model = Model(factors)
update_order = DistributeCollectProtocol(model)
learn = LearnMrfParameters(model, update_order=update_order)
learn.fit(evidence)
print learn._optimizer_result
#print learn.iterations
ans1 = learn._optimizer_result[:2]
print
update_order = DistributeCollectProtocol(model)
learn = LearnMrfParameters(model, update_order=update_order)
fit_without_gradient(learn, evidence)
print learn._optimizer_result
#print learn.iterations
ans2 = learn._optimizer_result[:2]
assert_array_almost_equal(ans1[1], ans2[1], decimal=4)
assert_array_almost_equal(ans1[0], ans2[0], decimal=4)
def test_get_log_likelihood(self):
a = DiscreteFactor([1, 2], parameters=np.array([[1, 2.0], [3, 4]]))
b = DiscreteFactor([2, 3], parameters=np.array([[3, 4.0], [5, 7]]))
# 1 2 3 |
# -------+----------
# 0 0 0 | 1 * 3 = 3
# 0 0 1 | 1 * 4 = 4
# 0 1 0 | 2 * 5 = 10
# 0 1 1 | 2 * 7 = 14
# 1 0 0 | 3 * 3 = 9
# 1 0 1 | 3 * 4 = 12
# 1 1 0 | 4 * 5 = 20
# 1 1 1 | 4 * 7 = 28
#
# p(1=0, 2, 3=1) = [4, 14] / 100
# => p(1=0, 3=1) = 18 / 100
model = Model([a, b])
evidence = {1: 0, 3: 1}
exact_inference = ExhaustiveEnumeration(model)
c = exact_inference.calibrate(evidence).belief
print c
print c.data
print c.get_potential(evidence.items())
learner = LearnMrfParameters(model)
actual_log_likelihood, _ = learner.log_likelihood_and_gradient(evidence)
print actual_log_likelihood, np.log(0.18)
self.assertAlmostEqual(actual_log_likelihood, np.log(0.18))
def test_learn_with_gradient_binary(self):
tc1 = 70
tc2 = 14
obs = [DiscreteFactor([(i, 2)], parameters=np.array(['m0', 'm1'])) for i in xrange(tc1 + tc2)]
model = Model(obs)
evidence = dict((i, 0 if i < tc1 else 1) for i in xrange(tc1 + tc2))
print 'evidence', evidence
print model.edges
learner = LearnMrfParameters(model, prior=1.0)
def nlog_posterior(x):
c1 = tc1
c2 = tc2
x = x.reshape((2, 1))
N = np.zeros((2, 1))
Lamb = np.array([[1.0, 0], [0, 1.0]])
lp = -0.5 * np.dot(np.dot((x - N).T, Lamb), (x - N))
lp += -0.5 * x.shape[0] * np.log(2.0 * np.pi)
lp += +0.5 * np.log(np.linalg.det((Lamb)))
lp += np.dot(x.T, np.array([c1, c2])) - (c1 + c2) * np.log(sum(np.exp(x)))
return -lp[0, 0]
x0 = np.zeros(2)
print 'zeros', x0
expected_ans = scipy.optimize.fmin_l_bfgs_b(nlog_posterior, x0, approx_grad=True, pgtol=10.0**-10)
actual_ans = learner.fit(evidence).result()
print actual_ans
print expected_ans
self.assertAlmostEqual(actual_ans[0], expected_ans[1])
assert_array_almost_equal(actual_ans[1], expected_ans[0], decimal=5)
def test_evaluate_derivative(self):
D = 8
delta = 10.0**-10
for variable_index in range(1, D):
a = DiscreteFactor(['1', '2'], parameters=np.array([['a', 'b'], ['c', 'd']]))
b = DiscreteFactor(['2', '3'], parameters=np.array([['e', 'f'], ['g', 'h']]))
c = DiscreteFactor(['3', '4'], parameters=np.array([['i', 'j'], ['k', 'l']]))
model = Model([a, b, c])
prior_sigma2 = 2.3
learner = LearnMrfParameters(model, prior=1.0/(prior_sigma2 ** 1.0))
D = 12
delta_vector = np.zeros(D)
delta_vector[variable_index] = delta
parameters = np.zeros(D)
parameters_plus_delta = np.zeros(D)
parameter_out_of_order = [1, 2, 3, 4, 3, 4, 5, 7, 8, 9, 10, 11]
parameter_names = [c for c in 'abcdefghijkl']
for param, param_name in zip(parameter_out_of_order, parameter_names):
parameters[learner._parameters_to_index[param_name]] = np.log(param)
parameters_plus_delta[learner._parameters_to_index[param_name]] = np.log(param)
parameters_plus_delta += delta_vector
evidence = {'1': 0, '3': 1}
learner._parameters = parameters
actual_log_likelihood1, actual_derivative1 = learner.log_likelihood_and_gradient(evidence)
learner._parameters = parameters_plus_delta
actual_log_likelihood2, actual_derivative2 = learner.log_likelihood_and_gradient(evidence)
expected_deriv = (actual_log_likelihood2 - actual_log_likelihood1) / delta # * delta_vector / delta / delta
prior_factor = D * (-0.5 * np.log((2.0 * np.pi * prior_sigma2)))
print 'pn', prior_factor, D * -0.5 * np.log(prior_sigma2)
prior_factor += sum([-0.5 / (prior_sigma2) * param ** 2.0 for param in parameters])
print 'dim', D
print actual_log_likelihood1, np.log(0.18) + prior_factor, prior_factor
#self.assertAlmostEqual(actual_log_likelihood1, np.log(0.18) + prior_factor)
#self.assertAlmostEqual(actual_log_likelihood2, np.log(0.18) + prior_factor, delta=10.0**-3)
print 'derivs'
print actual_derivative1
print actual_derivative2
print expected_deriv
self.assertAlmostEqual(expected_deriv, actual_derivative1[variable_index], delta=10.0**-4)