def generate_dataset(num_rows, num_cols, num_cats=4, rate=1.0):
"""Generate a random dataset.
Returns:
A dataset dict with fields 'schema' and 'table'.
"""
set_random_seed(0)
N = num_rows
V = num_cols
K = V * (V - 1) // 2
ragged_index = np.arange(0, num_cats * (V + 1), num_cats, np.int32)
ragged_index.flags.writeable = False
data = np.zeros((N, V * num_cats), np.int8)
for v in range(V):
beg, end = ragged_index[v:v + 2]
column = data[:, beg:end]
probs = np.random.dirichlet(np.zeros(num_cats) + 0.5)
for n in range(N):
count = np.random.poisson(rate)
column[n, :] = np.random.multinomial(count, probs)
data.flags.writeable = False
feature_types = [TY_MULTINOMIAL] * V
table = Table(feature_types, ragged_index, data)
dataset = {
'schema': {
'ragged_index': ragged_index,
'tree_prior': np.zeros(K, np.float32),
},
'table': table,
}
return dataset
def test_estimate_tree(num_edges):
set_random_seed(0)
E = num_edges
V = 1 + E
grid = make_complete_graph(V)
K = grid.shape[1]
edge_logits = np.random.random([K]) - 0.5
edges = estimate_tree(grid, edge_logits)
# Check size.
assert len(edges) == E
for v in range(V):
assert any(v in edge for edge in edges)
# Check optimality.
edges = tuple(edges)
if V < len(TREE_GENERATORS):
all_trees = get_spanning_trees(V)
assert edges in all_trees
all_trees = list(all_trees)
logits = []
for tree in all_trees:
logits.append(
sum(edge_logits[find_complete_edge(u, v)] for (u, v) in tree))
expected = all_trees[np.argmax(logits)]
assert edges == expected
def split_data(ragged_index, num_rows, num_parts, partid):
"""Split a dataset into training + holdout for n-fold crossvalidation.
This splits a dataset into num_parts disjoint parts by randomly holding out
cells. Note that whereas supervised crossvalidation typically holds out
entire rows, our unsupervised crossvalidation is intended to evaluate a
model of the full joint distribution.
Args:
ragged_index: A [V+1]-shaped numpy array of indices into the ragged
data array, where V is the number of features.
num_rows: An integer, the number of rows in the dataset.
num_parts: An integer, the number of folds in n-fold crossvalidation.
partid: An integer in [0, num_parts).
Returns:
A [N,R]-shaped mask where True means held-out and False means training.
Here N = num_rows and R = ragged_index[-1].
"""
set_random_seed(0)
assert 0 <= partid < num_parts
N = num_rows
V = ragged_index.shape[0] - 1
R = ragged_index[-1]
dense_mask = (partid == np.random.randint(num_parts, size=(N, V)))
ragged_mask = make_ragged_mask(ragged_index, dense_mask.T).T
assert ragged_mask.shape == (N, R)
return ragged_mask
def test_server_conditional_gof(N, V, C, M):
set_random_seed(make_seed(N, V, C, M, 1))
model = generate_fake_model(N, V, C, M)
config = TINY_CONFIG.copy()
config['model_num_clusters'] = M
model['config'] = config
server = TreeCatServer(model)
validate_gof(N, V, C, M, server, conditional=True)
def test_ensemble_latent_perplexity(N, V, C, M):
set_random_seed(make_seed(N, V, C, M))
ensemble = generate_fake_ensemble(N, V, C, M)
server = EnsembleServer(ensemble)
perplexity = server.latent_perplexity()
print(perplexity)
assert perplexity.shape == (V, )
assert np.all(1 <= perplexity)
assert np.all(perplexity <= M)
def train(self):
"""Train a model using subsample-annealed MCMC.
Returns:
A trained model as a dictionary with keys:
config: A global config dict.
tree: A TreeStructure instance with the learned latent
structure.
edge_logits: A [K]-shaped array of all edge logits.
"""
logger.info('TreeTrainer.train')
set_random_seed(self._config['seed'])
init_epochs = self._config['learning_init_epochs']
full_epochs = self._config['learning_full_epochs']
sample_tree_rate = self._config['learning_sample_tree_rate']
num_rows = self._num_rows
# Initialize using subsample annealing.
assert len(self._added_rows) == 0
schedule = make_annealing_schedule(num_rows, init_epochs,
sample_tree_rate)
for action, row_id in schedule:
if action == 'add_row':
self.add_row(row_id)
elif action == 'remove_row':
self.remove_row(row_id)
elif action == 'sample_tree':
edges, edge_logits = self.sample_tree()
self.set_edges(edges)
else:
raise ValueError(action)
# Run full gibbs scans.
assert len(self._added_rows) == num_rows
for step in range(full_epochs):
edges, edge_logits = self.sample_tree()
self.set_edges(edges)
for row_id in range(num_rows):
self.remove_row(row_id)
self.add_row(row_id)
# Compute optimal tree.
assert len(self._added_rows) == num_rows
edges, edge_logits = self.estimate_tree()
if self._config['learning_estimate_tree']:
self.set_edges(edges)
self._tree.gc()
return {
'config': self._config,
'tree': self._tree,
'edge_logits': edge_logits,
}
def test_sample_from_probs_gof(size):
set_random_seed(size)
probs = np.exp(2 * np.random.random(size)).astype(np.float32)
counts = np.zeros(size, dtype=np.int32)
num_samples = 2000 * size
for _ in range(num_samples):
counts[sample_from_probs(probs)] += 1
probs /= probs.sum() # Normalize afterwards.
print(counts)
print(probs * num_samples)
gof = multinomial_goodness_of_fit(probs, counts, num_samples, plot=True)
assert 1e-2 < gof
def generate_fake_ensemble(num_rows, num_cols, num_cats, num_components):
dataset = generate_dataset(num_rows, num_cols, num_cats)
ensemble = []
config = make_config(model_num_clusters=num_components, seed=0)
for sub_seed in range(3):
sub_config = config.copy()
sub_config['seed'] += sub_seed
set_random_seed(sub_config['seed'])
model = generate_fake_model(num_rows, num_cols, num_cats,
num_components, dataset)
model['config'] = sub_config
ensemble.append(model)
return ensemble
def test_sample_from_probs2_gof(size):
set_random_seed(size)
probs = np.exp(2 * np.random.random(size)).astype(np.float32)
counts = np.zeros(size, dtype=np.int32)
num_samples = 2000 * size
probs2 = np.tile(probs, (num_samples, 1))
samples = sample_from_probs2(probs2)
probs /= probs.sum() # Normalize afterwards.
counts = np.bincount(samples, minlength=size)
print(counts)
print(probs * num_samples)
gof = multinomial_goodness_of_fit(probs, counts, num_samples, plot=True)
assert 1e-2 < gof
def test_ensemble_latent_correlation(N, V, C, M):
set_random_seed(make_seed(N, V, C, M))
ensemble = generate_fake_ensemble(N, V, C, M)
server = EnsembleServer(ensemble)
correlation = server.latent_correlation()
print(correlation)
assert np.all(0 <= correlation)
assert np.all(correlation <= 1)
assert np.allclose(correlation, correlation.T)
for v in range(V):
assert correlation[v, :].argmax() == v
assert correlation[:, v].argmax() == v
def test_latent_perplexity(N, V, C, M):
set_random_seed(make_seed(N, V, C, M))
model = generate_fake_model(N, V, C, M)
config = TINY_CONFIG.copy()
config['model_num_clusters'] = M
model['config'] = config
server = TreeCatServer(model)
perplexity = server.latent_perplexity()
print(perplexity)
assert perplexity.shape == (V, )
assert np.all(1 <= perplexity)
assert np.all(perplexity <= M)
def test_latent_correlation(N, V, C, M):
set_random_seed(make_seed(N, V, C, M))
model = generate_fake_model(N, V, C, M)
config = TINY_CONFIG.copy()
config['model_num_clusters'] = M
model['config'] = config
server = TreeCatServer(model)
correlation = server.latent_correlation()
print(correlation)
assert np.all(0 <= correlation)
assert np.all(correlation <= 1)
assert np.allclose(correlation, correlation.T)
for v in range(V):
assert correlation[v, :].argmax() == v
assert correlation[:, v].argmax() == v
def test_observed_perplexity(N, V, C, M):
set_random_seed(make_seed(N, V, C, M))
model = generate_fake_model(N, V, C, M)
config = TINY_CONFIG.copy()
config['model_num_clusters'] = M
model['config'] = config
server = TreeCatServer(model)
for count in [1, 2, 3]:
if count > 1 and C > 2:
continue # NotImplementedError.
counts = 1
perplexity = server.observed_perplexity(counts)
print(perplexity)
assert perplexity.shape == (V, )
assert np.all(1 <= perplexity)
assert np.all(perplexity <= count * C)
def test_recover_structure(V, C):
set_random_seed(V + C * 10)
N = 200
M = 2 * C
K = V * (V - 1) // 2
tree_prior = np.zeros(K, np.float32)
tree = generate_tree(num_cols=V)
table = generate_clean_dataset(tree, num_rows=N, num_cats=C)['table']
config = make_config(model_num_clusters=M)
model = train_model(table, tree_prior, config)
# Compute three types of edges.
expected_edges = tree.get_edges()
optimal_edges = estimate_tree(tree.complete_grid, model['edge_logits'])
actual_edges = model['tree'].get_edges()
# Print debugging information.
feature_names = [str(v) for v in range(V)]
root = '0'
readable_data = np.zeros([N, V], np.int8)
for v in range(V):
beg, end = table.ragged_index[v:v + 2]
readable_data[:, v] = table.data[:, beg:end].argmax(axis=1)
with np_printoptions(precision=2, threshold=100, edgeitems=5):
print('Expected:')
print(print_tree(expected_edges, feature_names, root))
print('Optimal:')
print(print_tree(optimal_edges, feature_names, root))
print('Actual:')
print(print_tree(actual_edges, feature_names, root))
print('Correlation:')
print(np.corrcoef(readable_data.T))
print('Edge logits:')
print(triangular_to_square(tree.complete_grid, model['edge_logits']))
print('Data:')
print(readable_data)
print('Feature Sufficient Statistics:')
print(model['suffstats']['feat_ss'])
print('Edge Sufficient Statistics:')
print(model['suffstats']['edge_ss'])
# Check agreement.
assert actual_edges == optimal_edges, 'Error in sample_tree'
assert actual_edges == expected_edges, 'Error in likelihood'
def test_make_annealing_schedule():
set_random_seed(0)
num_rows = 10
init_epochs = 10
sample_tree_rate = 3
schedule = make_annealing_schedule(num_rows, init_epochs, sample_tree_rate)
assigned_rows = 0
for step, (action, row_id) in enumerate(schedule):
assert step < 1000
assert action in ['add_row', 'remove_row', 'sample_tree']
if action == 'sample_tree':
assert row_id is None
else:
assert 0 <= row_id and row_id < num_rows
if action == 'add_row':
assigned_rows += 1
elif action == 'remove_row':
assigned_rows -= 1
assert assigned_rows == num_rows
def test_assignment_sampler_gof(N, V, C, M):
config = make_config(model_num_clusters=M)
K = V * (V - 1) // 2
dataset = generate_dataset(num_rows=N, num_cols=V, num_cats=C)
table = dataset['table']
tree_prior = np.exp(np.random.random(K), dtype=np.float32)
trainer = TreeCatTrainer(table, tree_prior, config)
print('Data:')
print(dataset['table'].data)
# Add all rows.
set_random_seed(1)
for row_id in range(N):
trainer.add_row(row_id)
# Collect samples.
num_samples = 500 * M**(N * V)
counts = {}
logprobs = {}
for _ in range(num_samples):
for row_id in range(N):
# This is a single-site Gibbs sampler.
trainer.remove_row(row_id)
trainer.add_row(row_id)
key = hash_assignments(trainer._assignments)
if key in counts:
counts[key] += 1
else:
counts[key] = 1
logprobs[key] = trainer.logprob()
assert len(counts) == M**(N * V)
# Check accuracy using Pearson's chi-squared test.
keys = sorted(counts.keys())
counts = np.array([counts[k] for k in keys], dtype=np.int32)
probs = np.exp(np.array([logprobs[k] for k in keys]))
probs /= probs.sum()
print('Actual\tExpected\tAssignment')
for count, prob, key in zip(counts, probs, keys):
print('{:}\t{:0.1f}\t{}'.format(count, prob * num_samples, key))
gof = multinomial_goodness_of_fit(probs, counts, num_samples, plot=True)
assert 1e-2 < gof
def test_quantize_from_probs2(size, resolution):
set_random_seed(make_seed(size, resolution))
probs = np.exp(np.random.random(size)).astype(np.float32)
probs2 = probs.reshape((1, size))
quantized = quantize_from_probs2(probs2, resolution)
assert quantized.shape == probs2.shape
assert quantized.dtype == np.int8
assert np.all(quantized.sum(axis=1) == resolution)
# Check that quantized result is closer to target than any other value.
quantized = quantized.reshape((size, ))
target = resolution * probs / probs.sum()
distance = np.abs(quantized - target).sum()
for combo in itertools.combinations(range(size), resolution):
other = np.zeros(size, np.int8)
for i in combo:
other[i] += 1
assert other.sum() == resolution
other_distance = np.abs(other - target).sum()
assert distance <= other_distance
def test_sample_tree_gof(num_edges):
set_random_seed(num_edges)
E = num_edges
V = 1 + E
grid = make_complete_graph(V)
K = grid.shape[1]
edge_logits = np.random.random([K])
edge_probs = np.exp(edge_logits)
edge_probs_dict = {(v1, v2): edge_probs[k] for k, v1, v2 in grid.T}
# Generate many samples via MCMC.
num_samples = 30 * NUM_SPANNING_TREES[V]
counts = defaultdict(lambda: 0)
edges = [(v, v + 1) for v in range(V - 1)]
for _ in range(num_samples):
edges = sample_tree(grid, edge_logits, edges)
counts[tuple(edges)] += 1
assert len(counts) == NUM_SPANNING_TREES[V]
# Check accuracy using Pearson's chi-squared test.
keys = counts.keys()
counts = np.array([counts[key] for key in keys])
probs = np.array(
[np.prod([edge_probs_dict[edge] for edge in key]) for key in keys])
probs /= probs.sum()
# Possibly truncate.
T = 100
truncated = False
if len(counts) > T:
counts = counts[:T]
probs = probs[:T]
truncated = True
gof = multinomial_goodness_of_fit(probs,
counts,
num_samples,
plot=True,
truncated=truncated)
assert 1e-2 < gof
