def test_leaf_bernoulli_bootstrap(self):
np.random.seed(17)
x = np.concatenate(
(
np.random.multivariate_normal([10, 10], np.eye(2), 100),
np.random.multivariate_normal([1, 1], np.eye(2), 100),
),
axis=0,
)
y = np.array([1] * 100 + [0] * 100).reshape(-1, 1)
data = concatenate_yx(y, x)
ds_context = Context(parametric_types=[Bernoulli])
ds_context.feature_size = 2
leaf = create_conditional_leaf(data, ds_context, [0])
l = likelihood(leaf, data)
neg_data = np.concatenate([1 - y, x], axis=1)
lneg = likelihood(leaf, neg_data)
np.testing.assert_array_almost_equal(l + lneg, 1.0)
self.assertTrue(np.all(l >= 0.5))
self.assertTrue(np.all(lneg < 0.5))
def meu(node, input_data, node_top_down_meu=_node_top_down_meu, node_bottom_up_meu=_node_bottom_up_meu, in_place=False):
valid, err = is_valid(node)
assert valid, err
if in_place:
data = input_data
else:
data = np.array(input_data)
nodes = get_nodes_by_type(node)
lls_per_node = np.zeros((data.shape[0], len(nodes)))
# one pass bottom up evaluating the likelihoods
# log_likelihood(node, data, dtype=data.dtype, node_log_likelihood=node_bottom_up_meu, lls_matrix=lls_per_node)
likelihood(node, data, dtype=data.dtype, node_likelihood=node_bottom_up_meu, lls_matrix=lls_per_node)
meu_val = lls_per_node[:, 0]
instance_ids = np.arange(data.shape[0])
# one pass top down to decide on the max branch until it reaches a leaf; returns all_result, decisions at each max node for each instance.
all_result, all_decisions = eval_spn_top_down_meu(node, node_top_down_meu, parent_result=instance_ids, data=data,
lls_per_node=lls_per_node)
decisions = merge_rows_for_decisions(all_decisions)
return meu_val, decisions
def test_leaf_no_variance_gaussian(self):
np.random.seed(17)
x = np.concatenate(
(
np.random.multivariate_normal([10, 10], np.eye(2), 500),
np.random.multivariate_normal([1, 1], np.eye(2), 500),
),
axis=0,
)
y = np.array([1] * 1000).reshape(-1, 1)
data = concatenate_yx(y, x)
ds_context = Context(parametric_types=[Gaussian])
ds_context.feature_size = 2
leaf = create_conditional_leaf(data, ds_context, [0])
l = likelihood(leaf, data)
self.assertEqual(np.var(l[:, 0]), 0)
self.assertAlmostEqual(l[0, 0], 0.398942280401432)
data[:, 0] = 2
leaf = create_conditional_leaf(data, ds_context, [0])
l = likelihood(leaf, data)
self.assertEqual(np.var(l[:, 0]), 0)
self.assertAlmostEqual(l[0, 0], 0.398942280401432)
data3 = np.array(data)
data3[:, 0] = 3
leaf = create_conditional_leaf(data3, ds_context, [0])
l = likelihood(leaf, data)
self.assertAlmostEqual(np.var(l[:, 0]), 0)
self.assertAlmostEqual(l[0, 0], 0.241970724519143)
def test_leaf_categorical(self):
np.random.seed(17)
x = np.concatenate(
(
np.random.multivariate_normal([20, 20], np.eye(2), 500),
np.random.multivariate_normal([10, 10], np.eye(2), 500),
np.random.multivariate_normal([1, 1], np.eye(2), 500),
),
axis=0,
)
y = np.array([2] * 500 + [1] * 500 + [0] * 500).reshape(-1, 1)
data = concatenate_yx(y, x)
ds_context = Context(parametric_types=[Categorical])
ds_context.feature_size = 2
leaf = create_conditional_leaf(data, ds_context, [0])
l0 = likelihood(leaf, concatenate_yx(np.ones_like(y) * 0, x))
l1 = likelihood(leaf, concatenate_yx(np.ones_like(y) * 1, x))
l2 = likelihood(leaf, concatenate_yx(np.ones_like(y) * 2, x))
np.testing.assert_array_almost_equal(l0 + l1 + l2, 1.0)
self.assertTrue(np.all(l0[1000:1500] > 0.85))
self.assertTrue(np.all(l0[0:1000] < 0.15))
self.assertTrue(np.all(l1[500:1000] > 0.85))
self.assertTrue(np.all(l1[0:500] < 0.15))
self.assertTrue(np.all(l1[1000:1500] < 0.15))
self.assertTrue(np.all(l2[0:500] > 0.85))
self.assertTrue(np.all(l2[500:15000] < 0.15))
def meu(root,
input_data,
node_bottom_up_meu=_node_bottom_up_meu,
in_place=False):
# valid, err = is_valid(node)
# assert valid, err
if in_place:
data = input_data
else:
data = np.copy(input_data)
nodes = get_nodes_by_type(root)
utility_scope = set()
for node in nodes:
if type(node) is Utility:
utility_scope.add(node.scope[0])
assert np.all(np.isnan(data[:, list(utility_scope)])
), "Please specify all utility values as np.nan"
likelihood_per_node = np.zeros((data.shape[0], len(nodes)))
meu_per_node = np.zeros((data.shape[0], len(nodes)))
meu_per_node.fill(np.nan)
# one pass bottom up evaluating the likelihoods
likelihood(root, data, dtype=data.dtype, lls_matrix=likelihood_per_node)
eval_spmn_bottom_up_meu(root,
_node_bottom_up_meu,
meu_per_node=meu_per_node,
data=data,
lls_per_node=likelihood_per_node)
result = meu_per_node[:, root.id]
return result
def Expectation(spn, feature_id, ranges, node_expectation, node_likelihood):
def leaf_expectation(node, data, dtype=np.float64, **kwargs):
if node.scope[0] == feature_id:
t_node = type(node)
if t_node in node_expectation:
exps = np.zeros((data.shape[0], 1), dtype=dtype)
exps[:] = node_expectation[t_node](node)
return exps
else:
raise Exception("Node type unknown for expectation: " +
str(t_node))
else:
t_node = type(node)
if t_node in node_likelihood:
return node_likelihood[t_node](node,
ranges,
node_likelihood=node_likelihood)
node_expectations = {
type(leaf): leaf_expectation
for leaf in get_nodes_by_type(spn, Leaf)
}
node_expectations.update({Sum: sum_likelihood, Product: prod_likelihood})
expectation = likelihood(spn, ranges, node_likelihood=node_expectations)
expectation = expectation / likelihood(
spn, ranges, node_likelihood=node_likelihood)
return expectation
def test_ll_matrix(self):
add_node_likelihood(Leaf, sum_and_multiplier_ll)
node_1_1_1_1 = leaf(2, 1)
node_1_1_1_2 = leaf(2, 2)
node_1_1_1 = 0.7 * node_1_1_1_1 + 0.3 * node_1_1_1_2
node_1_1_2 = leaf([0, 1], 3)
node_1_1 = node_1_1_1 * node_1_1_2
node_1_2_1_1_1 = leaf(0, 5)
node_1_2_1_1_2 = leaf(1, 4)
node_1_2_1_1 = node_1_2_1_1_1 * node_1_2_1_1_2
node_1_2_1_2 = leaf([0, 1], 6)
node_1_2_1 = 0.1 * node_1_2_1_1 + 0.9 * node_1_2_1_2
node_1_2_2 = leaf(2, 3)
node_1_2 = node_1_2_1 * node_1_2_2
spn = 0.4 * node_1_1 + 0.6 * node_1_2
assign_ids(spn)
max_id = max([n.id for n in get_nodes_by_type(spn)])
data = np.random.rand(10, 10)
node_1_1_1_1_r = data[:, 2] * 1
node_1_1_1_2_r = data[:, 2] * 2
node_1_1_1_r = 0.7 * node_1_1_1_1_r + 0.3 * node_1_1_1_2_r
node_1_1_2_r = 3 * (data[:, 0] + data[:, 1])
node_1_1_r = node_1_1_1_r * node_1_1_2_r
node_1_2_1_1_1_r = data[:, 0] * 5
node_1_2_1_1_2_r = data[:, 1] * 4
node_1_2_1_1_r = node_1_2_1_1_1_r * node_1_2_1_1_2_r
node_1_2_1_2_r = 6 * (data[:, 0] + data[:, 1])
node_1_2_1_r = 0.1 * node_1_2_1_1_r + 0.9 * node_1_2_1_2_r
node_1_2_2_r = data[:, 2] * 3
node_1_2_r = node_1_2_1_r * node_1_2_2_r
spn_r = 0.4 * node_1_1_r + 0.6 * node_1_2_r
self.assert_correct(spn, data, spn_r)
lls = np.zeros((data.shape[0], max_id + 1))
likelihood(spn, data, lls_matrix=lls)
llls = np.zeros((data.shape[0], max_id + 1))
log_likelihood(spn, data, lls_matrix=llls)
self.assertTrue(np.alltrue(np.isclose(lls, np.exp(llls))))
self.assertTrue(np.alltrue(np.isclose(spn_r, lls[:, spn.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_2_r, lls[:, node_1_2.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_2_2_r, lls[:, node_1_2_2.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_2_1_r, lls[:, node_1_2_1.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_2_1_2_r, lls[:, node_1_2_1_2.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_2_1_1_r, lls[:, node_1_2_1_1.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_2_1_1_2_r, lls[:, node_1_2_1_1_2.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_2_1_1_1_r, lls[:, node_1_2_1_1_1.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_1_r, lls[:, node_1_1.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_1_2_r, lls[:, node_1_1_2.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_1_1_r, lls[:, node_1_1_1.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_1_1_2_r, lls[:, node_1_1_1_2.id])))
self.assertTrue(np.alltrue(np.isclose(node_1_1_1_1_r, lls[:, node_1_1_1_1.id])))
def Expectation(spn,
feature_scope,
evidence_scope,
evidence,
node_expectation=_node_expectation):
"""Compute the Expectation:
E[X_feature_scope | X_evidence_scope] given the spn and the evidence data
Keyword arguments:
spn -- the spn to compute the probabilities from
feature_scope -- set() of integers, the scope of the features to get the expectation from
evidence_scope -- set() of integers, the scope of the evidence features
evidence -- numpy 2d array of the evidence data
"""
if evidence_scope is None:
evidence_scope = set()
assert not (len(evidence_scope) > 0 and evidence is None)
assert len(feature_scope.intersection(evidence_scope)) == 0
marg_spn = marginalize(spn, keep=feature_scope | evidence_scope)
def leaf_expectation(node, data, dtype=np.float64, **kwargs):
if node.scope[0] in feature_scope:
t_node = type(node)
if t_node in node_expectation:
exps = np.zeros((data.shape[0], 1), dtype=dtype)
exps[:] = node_expectation[t_node](node)
return exps
else:
raise Exception('Node type unknown: ' + str(t_node))
return likelihood(node, evidence)
node_expectations = {
type(leaf): leaf_expectation
for leaf in get_nodes_by_type(marg_spn, Leaf)
}
node_expectations.update({Sum: sum_likelihood, Product: prod_likelihood})
if evidence is None:
#fake_evidence is not used
fake_evidence = np.zeros((1, len(spn.scope))).reshape(1, -1)
expectation = likelihood(marg_spn,
fake_evidence,
node_likelihood=node_expectations)
return expectation
#if we have evidence, we want to compute the conditional expectation
expectation = likelihood(marg_spn,
evidence,
node_likelihood=node_expectations)
expectation = expectation / likelihood(
marginalize(marg_spn, keep=evidence_scope), evidence)
return expectation
def get_mutual_information_correlation(spn, context):
categoricals = get_categoricals(spn, context)
num_features = len(spn.scope)
correlation_matrix = []
for x in range(num_features):
if x not in categoricals:
correlation_matrix.append(np.full((num_features), np.nan))
else:
x_correlation = [np.nan] * num_features
x_range = context.get_domains_by_scope([x])[0]
spn_x = marginalize(spn, [x])
query_x = np.array([[np.nan] * num_features] * len(x_range))
query_x[:, x] = x_range
for y in categoricals:
if x == y:
x_correlation[x] = 1
continue
spn_y = marginalize(spn, [y])
spn_xy = marginalize(spn, [x, y])
y_range = context.get_domains_by_scope([y])[0]
query_y = np.array([[np.nan] * num_features] * len(y_range))
query_y[:, y] = y_range
query_xy = np.array([[np.nan] * num_features] *
(len(x_range + 1) * (len(y_range + 1))))
xy = np.mgrid[x_range[0]:x_range[-1]:len(x_range) * 1j,
y_range[0]:y_range[-1]:len(y_range) * 1j]
xy = xy.reshape(2, -1)
query_xy[:, x] = xy[0, :]
query_xy[:, y] = xy[1, :]
results_xy = likelihood(spn_xy, query_xy)
results_xy = results_xy.reshape(len(x_range), len(y_range))
results_x = likelihood(spn_x, query_x)
results_y = likelihood(spn_y, query_y)
xx, yy = np.mgrid[0:len(x_range) - 1:len(x_range) * 1j,
0:len(y_range) - 1:len(y_range) * 1j]
xx = xx.astype(int)
yy = yy.astype(int)
grid_results_x = results_x[xx]
grid_results_y = results_y[yy]
grid_results_xy = results_xy
log = np.log(
grid_results_xy /
(np.multiply(grid_results_x, grid_results_y).squeeze()))
prod = np.prod(np.array([log, grid_results_xy]), axis=0)
log_x = np.log(results_x)
log_y = np.log(results_y)
entropy_x = -1 * np.sum(np.multiply(log_x, results_x))
entropy_y = -1 * np.sum(np.multiply(log_y, results_y))
x_correlation[y] = (np.sum(prod) /
np.sqrt(entropy_x * entropy_y))
correlation_matrix.append(np.array(x_correlation))
return np.array(correlation_matrix)
def assert_correct(self, spn, data, result):
l = likelihood(spn, data)
self.assertEqual(l.shape[0], data.shape[0])
self.assertEqual(l.shape[1], 1)
self.assertTrue(np.alltrue(np.isclose(result.reshape(-1, 1), l)))
self.assertTrue(np.alltrue(np.isclose(np.log(l), log_likelihood(spn, data))))
self.assertTrue(np.alltrue(np.isclose(np.log(l), log_likelihood(spn, data, debug=True))))
self.assertTrue(np.alltrue(np.isclose(l, likelihood(spn, data, debug=True))))
def test_type(self):
add_node_likelihood(Leaf, identity_ll)
# test that we get basic computations right
spn = 0.5 * Leaf(scope=[0, 1]) + 0.5 * (Leaf(scope=0) * Leaf(scope=1))
data = np.random.rand(10, 4)
l = likelihood(spn, data, dtype=np.float32)
self.assertEqual(l.dtype, np.float32)
l = likelihood(spn, data, dtype=np.float128)
self.assertEqual(l.dtype, np.float128)
def conditional_probability(spn, y_index, x_instance):
"""
calculation of conditional probability P(Y|X)
:param spn:
:param y_index: index of y in vector x_instance
:param x_instance: vector, with value of requested RVs(and y) and NaN of non-requested RVs
:return:
vector x_instance includes the value at y th index
"""
x_without_y = np.copy(x_instance)
x_without_y[0][y_index] = np.nan
# P(Y|X)
p_y_given_x = likelihood(spn, x_instance) / likelihood(spn, x_without_y)
return p_y_given_x
def test_piecewise_linear_multiplied(self):
piecewise_spn = (
0.5 * PiecewiseLinear([0, 1, 2], [0, 1, 0], [], scope=[0]) +
0.5 * PiecewiseLinear([-2, -1, 0], [0, 1, 0], [], scope=[0])) * (
0.5 * PiecewiseLinear([0, 1, 2], [0, 1, 0], [], scope=[1]) +
0.5 * PiecewiseLinear([-2, -1, 0], [0, 1, 0], [], scope=[1]))
evidence = np.array([
[-2, -2],
[-1.5, -1.5],
[-1, -1],
[-0.5, -0.5],
[0, 0],
[0.5, 0.5],
[1, 1],
[1.5, 1.5],
[2, 2],
[3, 3],
[-3, -3],
[0, 100],
])
results = likelihood(piecewise_spn, evidence)
expected_results = np.array([[0], [0.25], [0.5], [0.25], [0], [0.25],
[0.5], [0.25], [0], [0], [0], [0]])**2
self.assertTrue(np.all(np.equal(results, expected_results)))
def _density(self, x):
# map all inputs from categorical to numeric values
for i in range(len(x)):
if self.names[i] in self._categorical_variables:
inverse_mapping = self._categorical_variables[self.names[i]]['name_to_int']
x[i] = inverse_mapping[x[i]]
# if variable has integer representation round
elif self.data.dtypes[i] == int:
x[i] = round(x[i])
# Copy the current state of the network
input = self._density_mask.copy()
counter = 0
for i in range(input.shape[1]):
# if variable on index i is not conditioned or marginalized
# set input i to the value in the input array indicated by counter
if input[0, i] == 2:
input[0, i] = x[counter]
counter += 1
# if the variable i is conditioned set the input value to the condition
elif input[0, i] == 1:
input[0, i] = self._condition[0, i]
# else the value of input at index i is np.nan by initialization and indicates a marginalized variable
res = likelihood(self._spn, input)
return res[0][0]
def assert_correct_node_sampling_continuous(self, node, samples, plot):
node.scope = [0]
rand_gen = np.random.RandomState(1234)
samples_gen = sample_parametric_node(node, 1000000, rand_gen)
if plot:
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
x = np.linspace(np.min(samples), np.max(samples), 1000)
ax.plot(x, likelihood(node, x.reshape(-1, 1)), 'r-', lw=2, alpha=0.6,
label=node.__class__.__name__ + ' pdf')
ax.hist(samples, normed=True, histtype='stepfilled', alpha=0.7, bins=1000)
ax.legend(loc='best', frameon=False)
plt.show()
scipy_obj, params = get_scipy_obj_params(node)
# H_0 dist are identical
test_outside_samples = kstest(samples, lambda x: scipy_obj.cdf(x, **params))
# reject H_0 (dist are identical) if p < 0.05
# we pass the test if they are identical, pass if p >= 0.05
self.assertGreaterEqual(test_outside_samples.pvalue, 0.05)
test_generated_samples = kstest(samples_gen, lambda x: scipy_obj.cdf(x, **params))
# reject H_0 (dist are identical) if p < 0.05
# we pass the test if they are identical, pass if p >= 0.05
self.assertGreaterEqual(test_generated_samples.pvalue, 0.05)
def execute_python():
start = time.perf_counter()
py_ll = likelihood(spn, test_data)
end = time.perf_counter()
elapsed = (end - start)
return py_ll, elapsed * 1000000000
def plot_density(spn, data):
import matplotlib.pyplot as plt
import numpy as np
x_max = data[:, 0].max()
x_min = data[:, 0].min()
y_max = data[:, 1].max()
y_min = data[:, 1].min()
nbinsx = int(x_max - x_min) / 1
nbinsy = int(y_max - y_min) / 1
xi, yi = np.mgrid[x_min:x_max:nbinsx * 1j, y_min:y_max:nbinsy * 1j]
spn_input = np.vstack([xi.flatten(), yi.flatten()]).T
marg_spn = marginalize(spn, set([0, 1]))
zill = likelihood(marg_spn, spn_input)
z = zill.reshape(xi.shape)
# Make the plot
# plt.pcolormesh(xi, yi, z)
plt.imshow(z + 1,
extent=(x_min, x_max, y_min, y_max),
cmap=cm.hot,
norm=PowerNorm(gamma=1. / 5.))
# plt.pcolormesh(xi, yi, z)
plt.colorbar()
plt.show()
def test_leaf_gaussian(self):
np.random.seed(17)
x = np.concatenate(
(
np.random.multivariate_normal([10, 10], np.eye(2), 5000),
np.random.multivariate_normal([1, 1], np.eye(2), 5000),
),
axis=0,
)
y = np.array(
np.random.normal(20, 2, 5000).tolist() +
np.random.normal(60, 2, 5000).tolist()).reshape(-1, 1)
# associates y=20 with X=[10,10]
# associates y=60 with X=[1,1]
data = concatenate_yx(y, x)
ds_context = Context(parametric_types=[Gaussian])
ds_context.feature_size = 2
leaf = create_conditional_leaf(data, ds_context, [0])
self.assertFalse(np.any(np.isnan(likelihood(leaf, data))))
self.assertGreater(get_ll(leaf, [20, 10, 10]),
get_ll(leaf, [20, 1, 1]))
self.assertGreater(get_ll(leaf, [60, 1, 1]),
get_ll(leaf, [60, 10, 10]))
self.assertAlmostEqual(get_ll(leaf, [60, 1, 1]), 0.3476232862652)
self.assertAlmostEqual(get_ll(leaf, [20, 10, 10]), 0.3628922322773634)
def test_sum_one_dimension(self):
add_node_likelihood(Leaf, identity_ll)
# test that we get basic computations right
spn = 0.5 * Leaf(scope=0) + 0.5 * Leaf(scope=0)
data = np.random.rand(10, 1)
self.assert_correct(spn, data, data)
spn = 0.1 * Leaf(scope=0) + 0.9 * Leaf(scope=0)
data = np.random.rand(10, 1)
self.assert_correct(spn, data, data)
# test that we can pass whatever dataset, and the scopes are being respected
# this is important for inner nodes
spn = 0.1 * Leaf(scope=0) + 0.9 * Leaf(scope=0)
data = np.random.rand(10, 3)
r = 0.1 * data[:, 0] + 0.9 * data[:, 0]
r = r.reshape(-1, 1)
self.assert_correct(spn, data, r)
# test that it fails if the weights are not normalized
spn = 0.1 * Leaf(scope=0) + 0.9 * Leaf(scope=0)
spn.weights[1] = 0.2
data = np.random.rand(10, 3)
with self.assertRaises(AssertionError):
l = likelihood(spn, data)
with self.assertRaises(AssertionError):
log_likelihood(spn, data)
# test the log space
spn = 0.1 * Leaf(scope=0) + 0.9 * Leaf(scope=0)
data = np.random.rand(10, 3)
r = 0.1 * data[:, 0] + 0.9 * data[:, 0]
r = r.reshape(-1, 1)
self.assert_correct(spn, data, r)
def test_piecewise_linear_constant(self):
piecewise_spn = ((0.5 * PiecewiseLinear([1, 2], [1, 1], [], scope=[0]) +
0.5 * PiecewiseLinear([-2, -1], [1, 1], [], scope=[0])))
evidence = np.array([[-3000]])
results = likelihood(piecewise_spn, evidence)
expected_results = np.array([[1]])
self.assertTrue(np.all(np.equal(results, expected_results)))
def test_piecewise_linear_simple(self):
piecewise_spn = 0.5 * PiecewiseLinear([0, 1, 2], [0, 1, 0], [], scope=[0]) + \
0.5 * PiecewiseLinear([-2, -1, 0], [0, 1, 0], [], scope=[0])
evidence = np.array([[-2], [-1.5], [-1], [-0.5], [0], [0.5], [1], [1.5], [2], [3], [-3]])
results = likelihood(piecewise_spn, evidence)
expected_results = np.array([[0], [0.25], [0.5], [0.25], [0], [0.25], [0.5], [0.25], [0], [0], [0]])
self.assertTrue(np.all(np.equal(results, expected_results)))
def test_sum_multiple_dimension(self):
add_node_likelihood(Leaf, identity_ll)
# test basic computations in multiple dimensions
spn = 0.5 * Leaf(scope=[0, 1]) + 0.5 * Leaf(scope=[0, 1])
data = np.random.rand(10, 2)
l = likelihood(spn, data)
self.assert_correct(spn, data, data[:, 0] * data[:, 1])
def plot_likelihoods(spn, classes, plot_pdf, res=100, test_sample=None):
"""Generates for each class a 2D heightmap of likelihoods."""
if len(classes) > 10:
raise Exception(
"Not more than 10 distinct classes allowed for likelihood "
"plot, but given %d." % len(classes))
# Samples
lin = np.linspace(0.5, 127.5, res)
xgrid, ygrid = np.meshgrid(lin, lin)
samples = np.asarray(list(itertools.product(lin, lin)), dtype=np.float32)
# Compute likelihood values for each sample regarding each class
n = res**2
likelihoods = np.empty((0, n))
for c in classes:
data = np.column_stack((samples, c * np.ones(n)))
likelihoods_of_c = likelihood(spn, data).reshape((1, n)) * 100000
likelihoods = np.append(likelihoods, likelihoods_of_c, axis=0)
# Determine colormap levels
l_max = np.max(likelihoods)
l_min = np.min(likelihoods)
levels = np.linspace(l_min, l_max, 15, endpoint=True)
# Get default colormap for default colors
def_cmap = plt.get_cmap("tab10")
# Plot the likelihoods
for i, c in enumerate(classes):
fig, ax = plt.subplots(figsize=(4, 3.5))
zgrid = griddata(samples, likelihoods[i], (xgrid, ygrid))
cmap = matplotlib.colors.LinearSegmentedColormap.from_list(
"", [(1, 1, 1, 0), def_cmap(i)])
cont = plt.contourf(xgrid, ygrid, zgrid, levels, cmap=cmap)
if test_sample is not None:
ax.scatter(test_sample[0],
test_sample[1],
c='gold',
s=200,
edgecolors='w',
linewidth='3',
label=r'$z_{\mathrm{test}}$')
plt.legend()
# plt.title('Learned Probability Distribution\nfor Class %d' % c)
plt.xlabel('x')
plt.ylabel('y')
plt.axis('equal')
ax.set_xlim([0, 128])
ax.set_ylim([0, 128])
ax.get_xaxis().set_ticks([])
ax.get_yaxis().set_ticks([])
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size=0.3, pad=0.1)
fig.colorbar(cont, cax=cax, ticks=[])
plot_pdf.savefig(fig)
plt.show()
def assert_correct(self, node, x, result):
self.tested.add(type(node))
data = np.array([x], dtype=np.float).reshape(-1, 1)
node.scope = [0]
l = likelihood(node, data)
self.assertAlmostEqual(result, l[0, 0], 5)
self.assertTrue(np.alltrue(np.isclose(np.log(l), log_likelihood(node, data))))
data = np.random.rand(10, 10)
data[:, 5] = x
node.scope = [5]
l = likelihood(node, data)
self.assertEqual(l.shape[0], data.shape[0])
self.assertEqual(l.shape[1], 1)
self.assertTrue(np.isclose(np.var(l), 0))
self.assertTrue(np.alltrue(np.isclose(result, l[0, 0])))
self.assertTrue(np.alltrue(np.isclose(np.log(l), log_likelihood(node, data))))
def assert_correct_node_sampling_discrete(self, node, samples, plot):
node.scope = [0]
rand_gen = np.random.RandomState(1234)
samples_gen = sample_parametric_node(node, 1000000, rand_gen)
fvals, fobs = np.unique(samples, return_counts=True)
# H_0 data comes from same dist
test_outside_samples = chisquare(fobs, (likelihood(node, fvals.reshape(-1, 1)) * samples.shape[0])[:, 0])
# reject H_0 (data comes from dist) if p < 0.05
# we pass the test if they come from the dist, pass if p >= 0.05
self.assertGreaterEqual(test_outside_samples.pvalue, 0.05)
fvals, fobs = np.unique(samples_gen, return_counts=True)
test_generated_samples = chisquare(fobs, (likelihood(node, fvals.reshape(-1, 1)) * samples.shape[0])[:, 0])
# reject H_0 (data comes from dist) if p < 0.05
# we pass the test if they come from the dist, pass if p >= 0.05
self.assertGreaterEqual(test_generated_samples.pvalue, 0.05)
def approximate_density(dist_node, X, bins=100):
if dist_node.type.meta_type == MetaType.DISCRETE:
x = np.array(
[i for i in range(int(np.nanmin(X)),
int(np.nanmax(X)) + 1)])
else:
x = np.linspace(np.nanmin(X), np.nanmax(X), bins)
x = x.reshape(-1, 1)
y = likelihood(dist_node, x)
return x[:, 0], y[:, 0]
def leaf_expectation(node, data, dtype=np.float64, **kwargs):
if node.scope[0] in feature_scope:
t_node = type(node)
if t_node in node_expectation:
exps = np.zeros((data.shape[0], 1), dtype=dtype)
exps[:] = node_expectation[t_node](node)
return exps
else:
raise Exception('Node type unknown: ' + str(t_node))
return likelihood(node, evidence)
def expectation_recursive_batch(node, feature_scope, inverted_features,
relevant_scope, evidence, node_expectation,
node_likelihoods):
if isinstance(node, Product):
llchildren = np.concatenate([
expectation_recursive_batch(
child, feature_scope, inverted_features, relevant_scope,
evidence, node_expectation, node_likelihoods)
for child in node.children
if len(relevant_scope.intersection(child.scope)) > 0
],
axis=1)
return np.nanprod(llchildren, axis=1).reshape(-1, 1)
elif isinstance(node, Sum):
if len(relevant_scope.intersection(node.scope)) == 0:
return np.full((evidence.shape[0], 1), np.nan)
llchildren = np.concatenate([
expectation_recursive_batch(
child, feature_scope, inverted_features, relevant_scope,
evidence, node_expectation, node_likelihoods)
for child in node.children
],
axis=1)
relevant_children_idx = np.where(np.isnan(llchildren[0]) == False)[0]
if len(relevant_children_idx) == 0:
return np.array([np.nan])
weights_normalizer = sum(node.weights[j]
for j in relevant_children_idx)
b = np.array(node.weights)[relevant_children_idx] / weights_normalizer
return np.dot(llchildren[:, relevant_children_idx], b).reshape(-1, 1)
else:
if node.scope[0] in feature_scope:
t_node = type(node)
if t_node in node_expectation:
exps = np.zeros((evidence.shape[0], 1))
feature_idx = feature_scope.index(node.scope[0])
inverted = inverted_features[feature_idx]
exps[:] = node_expectation[t_node](node,
evidence,
inverted=inverted)
return exps
else:
raise Exception('Node type unknown: ' + str(t_node))
return likelihood(node, evidence, node_likelihood=node_likelihoods)
def leaf_expectation(node, data, dtype=np.float64, **kwargs):
if node.scope[0] in feature_scope:
t_node = type(node)
if t_node in node_distinct_vals:
vals = node_distinct_vals[t_node](node, evidence)
return vals
else:
raise Exception('Node type unknown: ' + str(t_node))
return likelihood(node, evidence, node_likelihood=node_likelihoods)
def assert_correct(self, node, x, result):
self.tested.add(type(node))
data = np.array([x], dtype=np.float).reshape(1, -1)
node.scope = list(range(data.shape[1]))
l = likelihood(node, data)
self.assertAlmostEqual(result, l[0, 0], 5)
self.assertTrue(
np.alltrue(np.isclose(np.log(l), log_likelihood(node, data))))
new_scope = (np.array(node.scope) + 5).tolist()
data = np.random.rand(10, max(new_scope) + 2)
data[:, new_scope] = x
node.scope = new_scope
l = likelihood(node, data)
self.assertEqual(l.shape[0], data.shape[0])
self.assertEqual(l.shape[1], 1)
self.assertTrue(np.isclose(np.var(l), 0))
self.assertTrue(np.alltrue(np.isclose(result, l[0, 0])))
self.assertTrue(
np.alltrue(np.isclose(np.log(l), log_likelihood(node, data))))