def deep_gaussian_process(X, Y):
"""Deep Gaussian Process Regression."""
lambda_ = 0.1 # Initial weight prior std. dev, this is optimised later
noise = tf.Variable(.01) # Likelihood st. dev. initialisation
lenscale = tf.Variable(1.) # learn the length scale
net = (ab.InputLayer(name="X", n_samples=n_samples_) >> ab.RandomFourier(
n_features=20, kernel=ab.RBF(ab.pos(lenscale))) >> ab.DenseVariational(
output_dim=5, std=lambda_, full=False) >> ab.RandomFourier(
n_features=10, kernel=ab.RBF(1.)) >> ab.DenseVariational(
output_dim=1, std=lambda_, full=False))
f, kl = net(X=X)
lkhood = tf.distributions.Normal(loc=f, scale=ab.pos(noise))
loss = ab.elbo(lkhood, Y, N, kl)
return f, loss
def gaussian_process(X, Y):
"""Gaussian Process Regression."""
lambda_ = 0.1 # Initial weight prior std. dev, this is optimised later
noise = tf.Variable(.5) # Likelihood st. dev. initialisation, and learning
lenscale = tf.Variable(1.) # learn the length scale
kern = ab.RBF(lenscale=ab.pos(lenscale)) # keep the length scale positive
# kern = ab.RBFVariational(lenscale=ab.pos(lenscale))
net = (ab.InputLayer(name="X", n_samples=n_samples_) >> ab.RandomFourier(
n_features=50, kernel=kern) >> ab.DenseVariational(
output_dim=1, std=lambda_, full=True))
f, kl = net(X=X)
lkhood = tf.distributions.Normal(loc=f, scale=ab.pos(noise))
# lkhood = tf.distributions.StudentT(df=1., loc=f, scale=ab.pos(noise))
loss = ab.elbo(lkhood, Y, N, kl)
return f, loss
def bayesian_linear(X, Y):
"""Bayesian Linear Regression."""
lambda_ = 100.
std = (1 / lambda_)**.5 # Weight st. dev. prior
noise = tf.Variable(1.) # Likelihood st. dev. initialisation, and learning
net = (ab.InputLayer(name="X", n_samples=n_samples_) >>
ab.DenseVariational(output_dim=1, std=std, full=True))
f, kl = net(X=X)
lkhood = tf.distributions.Normal(loc=f, scale=ab.pos(noise))
loss = ab.elbo(lkhood, Y, N, kl)
return f, loss
def bayesian_linear(X, Y):
"""Bayesian Linear Regression."""
reg = .01 # Initial weight prior std. dev, this is optimised later
noise = tf.Variable(.5) # Likelihood st. dev. initialisation, and learning
net = (
ab.InputLayer(name="X", n_samples=n_samples) >>
ab.DenseVariational(output_dim=1, std=reg, full=True)
)
phi, kl = net(X=X)
lkhood = tf.distributions.Normal(loc=phi, scale=ab.pos(noise))
loss = ab.elbo(lkhood, Y, N, kl)
return phi, loss
def nnet_bayesian(X, Y):
"""Bayesian neural net."""
lambda_ = 1e-1 # Weight prior
noise = tf.Variable(0.01) # Likelihood st. dev. initialisation
net = (ab.InputLayer(name="X", n_samples=n_samples_) >>
ab.DenseVariational(output_dim=20, std=lambda_) >> ab.Activation(
tf.nn.relu) >> ab.DenseVariational(output_dim=7, std=lambda_) >>
ab.Activation(tf.nn.relu) >> ab.DenseVariational(
output_dim=5, std=lambda_) >> ab.Activation(
tf.tanh) >> ab.DenseVariational(output_dim=1, std=lambda_))
f, kl = net(X=X)
lkhood = tf.distributions.Normal(loc=f, scale=ab.pos(noise))
loss = ab.elbo(lkhood, Y, N, kl)
return f, loss
def main():
"""Run the demo."""
data = fetch_gpml_sarcos_data()
Xr = data.train.data.astype(np.float32)
Yr = data.train.targets.astype(np.float32)[:, np.newaxis]
Xs = data.test.data.astype(np.float32)
Ys = data.test.targets.astype(np.float32)[:, np.newaxis]
N, D = Xr.shape
print("Iterations: {}".format(int(round(N * NEPOCHS / BATCH_SIZE))))
# Scale and centre the data, as per the original experiment
ss = StandardScaler()
Xr = ss.fit_transform(Xr)
Xs = ss.transform(Xs)
ym = Yr.mean()
Yr -= ym
Ys -= ym
# Training batches
data_tr = Dataset.from_tensor_slices({'X': Xr, 'Y': Yr}) \
.shuffle(buffer_size=1000) \
.batch(BATCH_SIZE)
# Testing iterators
data_ts = Dataset.from_tensors({'X': Xs, 'Y': Ys}).repeat()
with tf.name_scope("DataIterators"):
iterator = Iterator.from_structure(data_tr.output_types,
data_tr.output_shapes)
data = iterator.get_next()
training_init = iterator.make_initializer(data_tr)
testing_init = iterator.make_initializer(data_ts)
with tf.name_scope("Deepnet"):
phi, kl = net(X=data['X'])
std = tf.Variable(NOISE, name="noise")
lkhood = tf.distributions.Normal(phi, scale=ab.pos(std))
loss = ab.elbo(lkhood, data['Y'], N, kl)
tf.summary.scalar('loss', loss)
with tf.name_scope("Train"):
optimizer = tf.train.AdamOptimizer()
global_step = tf.train.create_global_step()
train = optimizer.minimize(loss, global_step=global_step)
with tf.name_scope("Test"):
r2 = rsquare(data['Y'], phi)
# Logging
log = tf.train.LoggingTensorHook(
{'step': global_step, 'loss': loss},
every_n_iter=1000
)
with tf.train.MonitoredTrainingSession(
config=CONFIG,
scaffold=tf.train.Scaffold(local_init_op=training_init),
checkpoint_dir="./sarcos/",
save_summaries_steps=None,
save_checkpoint_secs=20,
save_summaries_secs=20,
hooks=[log]
) as sess:
summary_writer = sess._hooks[1]._summary_writer
for i in range(NEPOCHS):
# Train for one epoch
try:
while not sess.should_stop():
sess.run(train)
except tf.errors.OutOfRangeError:
pass
# Init testing and assess and log R-square score on test set
sess.run(testing_init)
r2_score = sess.run(r2)
score_sum = tf.Summary(value=[
tf.Summary.Value(tag='r-square', simple_value=r2_score)
])
summary_writer.add_summary(score_sum, sess.run(global_step))
# Re-init training
sess.run(training_init)
# Prediction
sess.run(testing_init)
Ey = ab.predict_samples(phi, feed_dict=None, n_groups=NPREDICTSAMPLES,
session=sess)
sigma = sess.run(std)
r2_score = sess.run(r2)
# Score mean standardised log likelihood
Eymean = Ey.mean(axis=0)
Eyvar = Ey.var(axis=0) + sigma**2 # add sigma2 for obervation noise
snlp = msll(Ys.flatten(), Eymean, Eyvar, Yr.flatten())
print("------------")
print("r-square: {:.4f}, smse: {:.4f}, msll: {:.4f}."
.format(r2_score, 1 - r2_score, snlp))
import aboleth as ab
from aboleth.datasets import fetch_gpml_sarcos_data
# Set up a python logger so we can see the output of MonitoredTrainingSession
logger = logging.getLogger()
logger.setLevel(logging.INFO)
NSAMPLES = 10 # Number of random samples to get from an Aboleth net
NFEATURES = 1500 # Number of random features/bases to use in the approximation
NOISE = 3.0 # Initial estimate of the observation noise
# Random Fourier Features, this is setting up an anisotropic length scale, or
# one length scale per dimension
LENSCALE = tf.Variable(5 * np.ones((21, 1), dtype=np.float32))
KERNEL = ab.RBF(ab.pos(LENSCALE))
# Variational Fourier Features -- length-scale setting here is the "prior"
# LENSCALE = 10.
# KERNEL = ab.RBFVariational(lenscale=LENSCALE, lenscale_posterior=LENSCALE)
# Build the approximate GP
net = ab.stack(
ab.InputLayer(name='X', n_samples=NSAMPLES),
ab.RandomFourier(n_features=NFEATURES, kernel=KERNEL),
ab.DenseVariational(output_dim=1, full=True)
)
# Learning and prediction settings
BATCH_SIZE = 50 # number of observations per mini batch
NEPOCHS = 100 # Number of times to iterate though the dataset
def main():
"""Run the demo."""
data = fetch_gpml_sarcos_data()
Xr = data.train.data.astype(np.float32)
Yr = data.train.targets.astype(np.float32)[:, np.newaxis]
Xs = data.test.data.astype(np.float32)
Ys = data.test.targets.astype(np.float32)[:, np.newaxis]
N, D = Xr.shape
print("Iterations: {}".format(int(round(N * NEPOCHS / BATCH_SIZE))))
# Scale and centre the data, as per the original experiment
ss = StandardScaler()
Xr = ss.fit_transform(Xr)
Xs = ss.transform(Xs)
ym = Yr.mean()
Yr -= ym
Ys -= ym
# Training batches
data_tr = tf.data.Dataset.from_tensor_slices({'X': Xr, 'Y': Yr}) \
.shuffle(buffer_size=1000) \
.batch(BATCH_SIZE)
# Testing iterators
data_ts = tf.data.Dataset.from_tensors({'X': Xs, 'Y': Ys}).repeat()
with tf.name_scope("DataIterators"):
iterator = tf.data.Iterator.from_structure(data_tr.output_types,
data_tr.output_shapes)
data = iterator.get_next()
training_init = iterator.make_initializer(data_tr)
testing_init = iterator.make_initializer(data_ts)
with tf.name_scope("Deepnet"):
phi, kl = net(X=data['X'])
std = tf.Variable(NOISE, name="noise")
lkhood = tf.distributions.Normal(phi, scale=ab.pos(std))
loss = ab.elbo(lkhood, data['Y'], N, kl)
tf.summary.scalar('loss', loss)
with tf.name_scope("Train"):
optimizer = tf.train.AdamOptimizer()
global_step = tf.train.create_global_step()
train = optimizer.minimize(loss, global_step=global_step)
with tf.name_scope("Test"):
Ey = ab.sample_mean(phi)
# Logging
log = tf.train.LoggingTensorHook({
'step': global_step,
'loss': loss
},
every_n_iter=1000)
with tf.train.MonitoredTrainingSession(
config=CONFIG,
scaffold=tf.train.Scaffold(local_init_op=training_init),
checkpoint_dir="./sarcos/",
save_summaries_steps=None,
save_checkpoint_secs=20,
save_summaries_secs=20,
hooks=[log]) as sess:
for i in range(NEPOCHS):
# Train for one epoch
sess.run(training_init)
try:
while not sess.should_stop():
_, g = sess.run([train, global_step])
except tf.errors.OutOfRangeError:
pass
# Init testing and assess and log R-square score on test set
sess.run(testing_init)
Eymean = sess.run(Ey, feed_dict={n_samples_: NPREDICTSAMPLES})
r2 = r2_score(Ys, Eymean)
print("Training epoch {}, r-square = {}".format(i, r2))
rsquare_summary(r2, sess, g)
print("------------")
print("r-square: {:.4f}, smse: {:.4f}".format(r2, 1 - r2))
# Optimization
NEPOCHS = 5 # Number of times to see the data in training
BSIZE = 100 # Mini batch size
CONFIG = tf.ConfigProto(device_count={'GPU': 0}) # Use GPU ?
LSAMPLES = 5 # Number of samples the mode returns
PSAMPLES = 10 # This will give LSAMPLES * PSAMPLES predictions
NCLASSES = 7 # Number of target classes
NFEATURES = 100 # Number of random features to use
# Network construction
data_input = ab.InputLayer(name='X', n_samples=LSAMPLES) # Data input
mask_input = ab.MaskInputLayer(name='M') # Missing data mask input
lenscale = ab.pos(tf.Variable(np.ones((54, 1), dtype=np.float32)))
layers = (ab.RandomArcCosine(n_features=NFEATURES, lenscale=lenscale) >>
ab.DenseVariational(output_dim=NCLASSES))
def main():
"""Run the imputation demo."""
# Fetch data, one-hot targets and standardise data
data = fetch_covtype()
X = data.data
Y = (data.target - 1)
X = StandardScaler().fit_transform(X)
# Now fake some missing data with a mask
rnd = np.random.RandomState(RSEED)
def main():
"""Run the demo."""
n_iters = int(round(n_epochs * N / batch_size))
print("Iterations = {}".format(n_iters))
# Get training and testing data
Xr, Yr, Xs, Ys = gp_draws(N, Ns, kern=kernel, noise=true_noise)
# Prediction points
Xq = np.linspace(-20, 20, Ns).astype(np.float32)[:, np.newaxis]
Yq = np.linspace(-4, 4, Ns).astype(np.float32)[:, np.newaxis]
# Set up the probability image query points
Xi, Yi = np.meshgrid(Xq, Yq)
Xi = Xi.astype(np.float32).reshape(-1, 1)
Yi = Yi.astype(np.float32).reshape(-1, 1)
_, D = Xr.shape
# Name the "data" parts of the graph
with tf.name_scope("Input"):
# This function will make a TensorFlow queue for shuffling and batching
# the data, and will run through n_epochs of the data.
Xb, Yb = batch_training(Xr,
Yr,
n_epochs=n_epochs,
batch_size=batch_size)
X_ = tf.placeholder_with_default(Xb, shape=(None, D))
Y_ = tf.placeholder_with_default(Yb, shape=(None, 1))
# This is where we build the actual GP model
with tf.name_scope("Deepnet"):
phi, kl = net(X=X_)
lkhood = tf.distributions.Normal(loc=phi, scale=ab.pos(noise))
loss = ab.elbo(lkhood, Y_, N, kl)
# Set up the trainig graph
with tf.name_scope("Train"):
optimizer = tf.train.AdamOptimizer()
global_step = tf.train.create_global_step()
train = optimizer.minimize(loss, global_step=global_step)
# This is used for building the predictive density image
with tf.name_scope("Predict"):
logprob = tf.reduce_mean(lkhood.log_prob(Y_), axis=0)
# Logging learning progress
log = tf.train.LoggingTensorHook({
'step': global_step,
'loss': loss
},
every_n_iter=1000)
# This is the main training "loop"
with tf.train.MonitoredTrainingSession(config=config,
save_summaries_steps=None,
save_checkpoint_secs=None,
hooks=[log]) as sess:
try:
while not sess.should_stop():
sess.run(
train,
feed_dict={
n_samples_: n_samples,
# tf.keras.backend.learning_phase(): 1
})
except tf.errors.OutOfRangeError:
print('Input queues have been exhausted!')
pass
# Prediction, the [[None]] is to stop the default placeholder queue
# we keep learning phase flag on even in prediction phase to draw
# samples from predictive distribution
Ey = sess.run(phi,
feed_dict={
X_: Xq,
Y_: [[None]],
n_samples_: p_samples
})
logPY = sess.run(logprob,
feed_dict={
Y_: Yi,
X_: Xi,
n_samples_: p_samples
})
Eymean = Ey.mean(axis=0) # Average samples to get mean predicted funtion
Py = np.exp(logPY.reshape(Ns, Ns)) # Turn log-prob into prob
# Plot
im_min = np.amin(Py)
im_size = np.amax(Py) - im_min
img = (Py - im_min) / im_size
f = bk.figure(tools='pan,box_zoom,reset', sizing_mode='stretch_both')
f.image(image=[img], x=-20., y=-4., dw=40., dh=8, palette=bp.Plasma256)
f.circle(Xr.flatten(), Yr.flatten(), fill_color='blue', legend='Training')
f.line(Xs.flatten(), Ys.flatten(), line_color='blue', legend='Truth')
for y in Ey:
f.line(Xq.flatten(),
y.flatten(),
line_color='red',
legend='Samples',
alpha=0.2)
f.line(Xq.flatten(), Eymean.flatten(), line_color='green', legend='Mean')
bk.show(f)
