def _test_linear_regression(self, default, dtype):
def build_toy_dataset(N, w, noise_std=0.1):
D = len(w)
x = np.random.randn(N, D)
y = np.dot(x, w) + np.random.normal(0, noise_std, size=N)
return x, y
with self.test_session() as sess:
N = 40 # number of data points
D = 10 # number of features
w_true = np.random.randn(D)
X_train, y_train = build_toy_dataset(N, w_true)
X_test, y_test = build_toy_dataset(N, w_true)
X = tf.placeholder(dtype, [N, D])
w = Normal(loc=tf.zeros(D, dtype=dtype),
scale=tf.ones(D, dtype=dtype))
b = Normal(loc=tf.zeros(1, dtype=dtype),
scale=tf.ones(1, dtype=dtype))
y = Normal(loc=ed.dot(X, w) + b,
scale=0.1 * tf.ones(N, dtype=dtype))
n_samples = 2000
if not default:
qw = Empirical(
tf.Variable(tf.zeros([n_samples, D], dtype=dtype)))
qb = Empirical(
tf.Variable(tf.zeros([n_samples, 1], dtype=dtype)))
inference = ed.SGLD({
w: qw,
b: qb
},
data={
X: X_train,
y: y_train
})
else:
inference = ed.SGLD([w, b], data={X: X_train, y: y_train})
qw = inference.latent_vars[w]
qb = inference.latent_vars[b]
inference.run(step_size=0.001)
self.assertAllClose(qw.mean().eval(), w_true, rtol=5e-1, atol=5e-1)
self.assertAllClose(qb.mean().eval(), [0.0], rtol=5e-1, atol=5e-1)
old_t, old_n_accept = sess.run([inference.t, inference.n_accept])
if not default:
self.assertEqual(old_t, n_samples)
else:
self.assertEqual(old_t, 1e4)
self.assertGreater(old_n_accept, 0.1)
sess.run(inference.reset)
new_t, new_n_accept = sess.run([inference.t, inference.n_accept])
self.assertEqual(new_t, 0)
self.assertEqual(new_n_accept, 0)
def test_sgld(self):
with self.test_session():
N, D, W_1, W_2, W_3, b_1, b_2, X, y, X_train, y_train = self._test(
)
T = 1 # number of MCMC samples
qW_1 = Empirical(params=tf.Variable(tf.random_normal([T, D, 20])))
qW_2 = Empirical(params=tf.Variable(tf.random_normal([T, 20, 15])))
qW_3 = Empirical(params=tf.Variable(tf.random_normal([T, 15, 1])))
qb_1 = Empirical(params=tf.Variable(tf.random_normal([T, 20])))
qb_2 = Empirical(params=tf.Variable(tf.random_normal([T, 15])))
inference = ed.SGLD(
{
W_1: qW_1,
b_1: qb_1,
W_2: qW_2,
b_2: qb_2,
W_3: qW_3
},
data={
y: y_train,
X: X_train
})
inference.run()
def _test_normal_normal(self, default, dtype):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(loc=tf.constant(0.0, dtype=dtype),
scale=tf.constant(1.0, dtype=dtype))
x = Normal(loc=mu,
scale=tf.constant(1.0, dtype=dtype),
sample_shape=50)
n_samples = 2000
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
if not default:
qmu = Empirical(
params=tf.Variable(tf.ones(n_samples, dtype=dtype)))
inference = ed.SGLD({mu: qmu}, data={x: x_data})
else:
inference = ed.SGLD([mu], data={x: x_data})
qmu = inference.latent_vars[mu]
inference.run(step_size=0.10)
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-1, atol=1e-1)
self.assertAllClose(qmu.stddev().eval(),
np.sqrt(1 / 51),
rtol=1e-1,
atol=1e-1)
old_t, old_n_accept = sess.run([inference.t, inference.n_accept])
if not default:
self.assertEqual(old_t, n_samples)
else:
self.assertEqual(old_t, 1e4)
self.assertGreater(old_n_accept, 0.1)
sess.run(inference.reset)
new_t, new_n_accept = sess.run([inference.t, inference.n_accept])
self.assertEqual(new_t, 0)
self.assertEqual(new_n_accept, 0)
def test_normalnormal_run(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(mu=0.0, sigma=1.0)
x = Normal(mu=tf.ones(50) * mu, sigma=1.0)
qmu = Empirical(params=tf.Variable(tf.ones(5000)))
# analytic solution: N(mu=0.0, sigma=\sqrt{1/51}=0.140)
inference = ed.SGLD({mu: qmu}, data={x: x_data})
inference.run(step_size=0.2)
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-2, atol=1e-2)
self.assertAllClose(qmu.std().eval(), np.sqrt(1 / 51),
rtol=5e-2, atol=5e-2)
def main(_):
ed.set_seed(42)
# MODEL
z = MultivariateNormalTriL(loc=tf.ones(2),
scale_tril=tf.cholesky(
tf.constant([[1.0, 0.8], [0.8, 1.0]])))
# INFERENCE
qz = Empirical(params=tf.get_variable("qz/params", [2000, 2]))
inference = ed.SGLD({z: qz})
inference.run(step_size=5.0)
# CRITICISM
sess = ed.get_session()
mean, stddev = sess.run([qz.mean(), qz.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
def test_normalnormal_float64(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float64)
mu = Normal(loc=tf.constant(0.0, dtype=tf.float64),
scale=tf.constant(1.0, dtype=tf.float64))
x = Normal(loc=mu,
scale=tf.constant(1.0, dtype=tf.float64),
sample_shape=50)
qmu = Empirical(
params=tf.Variable(tf.ones(5000, dtype=tf.float64)))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.SGLD({mu: qmu}, data={x: x_data})
inference.run(step_size=0.10)
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-1, atol=1e-1)
self.assertAllClose(qmu.stddev().eval(),
np.sqrt(1 / 51),
rtol=1e-1,
atol=1e-1)
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import edward as ed
import tensorflow as tf
from edward.models import Empirical, MultivariateNormalFull
ed.set_seed(42)
# MODEL
z = MultivariateNormalFull(
mu=tf.ones(2),
sigma=tf.constant([[1.0, 0.8], [0.8, 1.0]]))
# INFERENCE
qz = Empirical(params=tf.Variable(tf.random_normal([2000, 2])))
inference = ed.SGLD({z: qz})
inference.run(step_size=5.0)
# CRITICISM
sess = ed.get_session()
mean, std = sess.run([qz.mean(), qz.std()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior std:")
print(std)
def bayes_mult_cmd(table_file, metadata_file, formula, output_file):
#metadata = _type_cast_to_float(metadata.copy())
metadata = pd.read_table(metadata_file, index_col=0)
G_data = dmatrix(formula, metadata, return_type='dataframe')
table = load_table(table_file)
# basic filtering parameters
soil_filter = lambda val, id_, md: id_ in metadata.index
read_filter = lambda val, id_, md: np.sum(val) > 10
#sparse_filter = lambda val, id_, md: np.mean(val > 0) > 0.1
sample_filter = lambda val, id_, md: np.sum(val) > 1000
table = table.filter(soil_filter, axis='sample')
table = table.filter(sample_filter, axis='sample')
table = table.filter(read_filter, axis='observation')
#table = table.filter(sparse_filter, axis='observation')
print(table.shape)
y_data = pd.DataFrame(np.array(table.matrix_data.todense()).T,
index=table.ids(axis='sample'),
columns=table.ids(axis='observation'))
y_data, G_data = y_data.align(G_data, axis=0, join='inner')
psi = _gram_schmidt_basis(y_data.shape[1])
G_data = G_data.values
y_data = y_data.values
N, D = y_data.shape
p = G_data.shape[1] # number of covariates
r = G_data.shape[1] # rank of covariance matrix
psi = tf.convert_to_tensor(psi, dtype=tf.float32)
n = tf.convert_to_tensor(y_data.sum(axis=1), dtype=tf.float32)
# hack to get multinomial working
def _sample_n(self, n=1, seed=None):
# define Python function which returns samples as a Numpy array
def np_sample(p, n):
return multinomial.rvs(p=p, n=n, random_state=seed).astype(np.float32)
# wrap python function as tensorflow op
val = tf.py_func(np_sample, [self.probs, n], [tf.float32])[0]
# set shape from unknown shape
batch_event_shape = self.batch_shape.concatenate(self.event_shape)
shape = tf.concat(
[tf.expand_dims(n, 0), tf.convert_to_tensor(batch_event_shape)], 0)
val = tf.reshape(val, shape)
return val
Multinomial._sample_n = _sample_n
# dummy variable for gradient
G = tf.placeholder(tf.float32, [N, p])
b = Exponential(rate=1.0)
B = Normal(loc=tf.zeros([p, D-1]),
scale=tf.ones([p, D-1]) )
# Factorization of covariance matrix
# http://edwardlib.org/tutorials/klqp
l = Exponential(rate=1.0)
L = Normal(loc=tf.zeros([p, D-1]),
scale=tf.ones([p, D-1]) )
z = Normal(loc=tf.zeros([N, p]),
scale=tf.ones([N, p]))
# Cholesky trick to get multivariate normal
v = tf.matmul(G, B) + tf.matmul(z, L)
# get clr transformed values
eta = tf.matmul(v, psi)
Y = Multinomial(total_count=n, logits=eta)
T = 100000 # the number of mixin samples from MCMC sampling
qb = PointMass(params=tf.Variable(tf.random_normal([])))
qB = PointMass(params=tf.Variable(tf.random_normal([p, D-1])))
qz = Empirical(params=tf.Variable(tf.random_normal([T, N, p])))
ql = PointMass(params=tf.Variable(tf.random_normal([])))
qL = PointMass(params=tf.Variable(tf.random_normal([p, D-1])))
# Imputation
inference_z = ed.SGLD(
{z: qz},
data={G: G_data, Y: y_data, B: qB, L: qL}
)
# Maximization
inference_BL = ed.MAP(
{B: qB, L: qL, b: qb, l: ql},
data={G: G_data, Y: y_data, z: qz}
)
inference_z.initialize(step_size=1e-10)
inference_BL.initialize(n_iter=1000)
sess = ed.get_session()
saver = tf.train.Saver()
tf.global_variables_initializer().run()
for i in range(inference_BL.n_iter):
inference_z.update() # e-step
# will need to compute the expectation of z
info_dict = inference_BL.update() # m-step
inference_BL.print_progress(info_dict)
save_path = saver.save(sess, output_file)
print("Model saved in file: %s" % save_path)
pickle.dump({'qB': sess.run(qB.mean()),
'qL': sess.run(qL.mean()),
'qz': sess.run(qz.mean())},
open(output_file + '.params.pickle', 'wb')
)
def test_monte_carlo(self):
tf.InteractiveSession()
ed.set_seed(42)
# DATA
X_train = np.zeros([500, 100])
y_train = np.zeros(500)
N = X_train.shape[0] # data points
D = X_train.shape[1] # feature
T = 1 # number of MCMC samples
# MODEL
W_1 = Normal(mu=tf.zeros([D, 20]), sigma=tf.ones([D, 20]) * 100)
W_2 = Normal(mu=tf.zeros([20, 15]), sigma=tf.ones([20, 15]) * 100)
W_3 = Normal(mu=tf.zeros([15, 1]), sigma=tf.ones([15, 1]) * 100)
b_1 = Normal(mu=tf.zeros(20), sigma=tf.ones(20) * 100)
b_2 = Normal(mu=tf.zeros(15), sigma=tf.ones(15) * 100)
x_ph = tf.placeholder(tf.float32, [N, D])
y = Bernoulli(logits=four_layer_nn(x_ph, W_1, W_2, W_3, b_1, b_2))
# INFERENCE
qW_1 = Empirical(params=tf.Variable(tf.random_normal([T, D, 20])))
qW_2 = Empirical(params=tf.Variable(tf.random_normal([T, 20, 15])))
qW_3 = Empirical(params=tf.Variable(tf.random_normal([T, 15, 1])))
qb_1 = Empirical(params=tf.Variable(tf.random_normal([T, 20])))
qb_2 = Empirical(params=tf.Variable(tf.random_normal([T, 15])))
# note ideally these would be separate test methods; there's an
# issue with the tensorflow graph when re-running the above
# unfortunately
inference = ed.HMC(
{
W_1: qW_1,
b_1: qb_1,
W_2: qW_2,
b_2: qb_2,
W_3: qW_3
},
data={
y: y_train,
x_ph: X_train
})
inference.run()
inference = ed.SGLD(
{
W_1: qW_1,
b_1: qb_1,
W_2: qW_2,
b_2: qb_2,
W_3: qW_3
},
data={
y: y_train,
x_ph: X_train
})
inference.run()
inference = ed.MetropolisHastings(
{
W_1: qW_1,
b_1: qb_1,
W_2: qW_2,
b_2: qb_2,
W_3: qW_3
}, {
W_1: W_1,
b_1: b_1,
W_2: W_2,
b_2: b_2,
W_3: W_3
},
data={
y: y_train,
x_ph: X_train
})
inference.run()