def test_fourier_features(kernels, make_data):
"""Test random fourier kernels approximations."""
D = 100
S = 3
kern, p = kernels
k = kern(D, **p)
x, _, _ = make_data
x_, X_ = _make_placeholders(x, S)
N = x.shape[0]
Phi, KL = ab.RandomFourier(D, k)(X_)
tc = tf.test.TestCase()
with tc.test_session():
tf.global_variables_initializer().run()
P = Phi.eval(feed_dict={x_: x})
for i in range(P.shape[0]):
p = P[i]
assert p.shape == (N, 2 * D)
# Check behaving properly with k(x, x) ~ 1.0
assert np.allclose((p**2).sum(axis=1), np.ones(N))
# Make sure we get a valid KL
kl = KL.eval() if isinstance(KL, tf.Tensor) else KL
assert kl >= 0
def deep_gaussian_process(X, Y):
"""Deep Gaussian Process Regression."""
noise = ab.pos_variable(.1)
net = (
ab.InputLayer(name="X", n_samples=n_samples_) >>
ab.RandomFourier(n_features=20, kernel=ab.RBF(learn_lenscale=True)) >>
ab.DenseVariational(output_dim=5, full=False) >>
ab.RandomFourier(n_features=10, kernel=ab.RBF(1., seed=1)) >>
ab.DenseVariational(output_dim=1, full=False, learn_prior=True)
)
f, kl = net(X=X)
lkhood = tf.distributions.Normal(loc=f, scale=noise).log_prob(Y)
loss = ab.elbo(lkhood, kl, N)
return f, loss
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 my_model(features, labels, mode, params):
N = params["N"]
n_samples = NSAMPLES if mode == tf.estimator.ModeKeys.TRAIN \
else NPREDICTSAMPLES
X = tf.feature_column.input_layer(features, params['feature_columns'])
kernel = ab.RBF(LENSCALE, learn_lenscale=True)
net = (
ab.InputLayer(name="X", n_samples=n_samples) >>
ab.RandomFourier(n_features=NFEATURES, kernel=kernel) >>
ab.Dense(output_dim=64, init_fn="autonorm") >>
ab.Activation(tf.nn.selu) >>
ab.DenseVariational(output_dim=1, full=False, prior_std=1.0,
learn_prior=True)
)
phi, kl = net(X=X)
std = ab.pos_variable(NOISE, name="noise")
ll_f = tf.distributions.Normal(loc=phi, scale=std)
predict_mean = ab.sample_mean(phi)
# Compute predictions.
if mode == tf.estimator.ModeKeys.PREDICT:
predictions = {
'predictions': predict_mean,
'samples': phi
}
return tf.estimator.EstimatorSpec(mode, predictions=predictions)
ll = ll_f.log_prob(labels)
loss = ab.elbo(ll, kl, N)
tf.summary.scalar('loss', loss)
# Compute evaluation metrics.
mse = tf.metrics.mean_squared_error(labels=labels,
predictions=predict_mean,
name='mse_op')
r2 = r2_metric(labels, predict_mean)
metrics = {'mse': mse,
'r2': r2}
if mode == tf.estimator.ModeKeys.EVAL:
return tf.estimator.EstimatorSpec(
mode, loss=loss, eval_metric_ops=metrics)
# Create training op.
assert mode == tf.estimator.ModeKeys.TRAIN
optimizer = tf.train.AdamOptimizer()
train_op = optimizer.minimize(loss, global_step=tf.train.get_global_step())
return tf.estimator.EstimatorSpec(mode, loss=loss, train_op=train_op)
def gaussian_process(X, Y):
"""Gaussian Process Regression."""
noise = ab.pos_variable(.5)
kern = ab.RBF(learn_lenscale=False) # learn lengthscale
net = (
ab.InputLayer(name="X", n_samples=n_samples_) >>
ab.RandomFourier(n_features=50, kernel=kern) >>
ab.DenseVariational(output_dim=1, full=True, learn_prior=True)
)
f, kl = net(X=X)
lkhood = tf.distributions.Normal(loc=f, scale=noise).log_prob(Y)
loss = ab.elbo(lkhood, kl, N)
return f, loss
def svr(X, Y):
"""Support vector regressor."""
reg = 0.1
eps = 0.01
lenscale = 1.
kern = ab.RBF(lenscale=lenscale) # keep the length scale positive
net = (
ab.InputLayer(name="X", n_samples=1) >>
ab.RandomFourier(n_features=50, kernel=kern) >>
ab.DenseMAP(output_dim=1, l2_reg=reg, l1_reg=0.)
)
phi, reg = net(X=X)
loss = tf.reduce_mean(tf.maximum(tf.abs(Y - phi - eps), 0.)) + reg
return phi, 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 svr(X, Y):
"""Support vector regressor, kind of..."""
lambda_ = 1e-4
eps = 0.01
lenscale = 1.
# Specify which kernel to approximate with the random Fourier features
kern = ab.RBF(lenscale=lenscale)
net = (
# ab.InputLayer(name="X", n_samples=n_samples_) >>
ab.InputLayer(name="X", n_samples=1) >> ab.RandomFourier(
n_features=50, kernel=kern) >>
# ab.DropOut(keep_prob=0.9) >>
ab.DenseMAP(output_dim=1, l2_reg=lambda_, l1_reg=0.))
f, reg = net(X=X)
loss = tf.reduce_mean(tf.nn.relu(tf.abs(Y - f) - eps)) + reg
return f, loss
def main():
"""Run the demo."""
# Get Continuous and categorical data
df_train, df_test = fetch_data()
df = pd.concat((df_train, df_test))
X_con, X_cat, n_cats, Y = input_fn(df)
n_samples_ = tf.placeholder_with_default(T_SAMPLES, [])
# Define the continuous layers
con_layer = (
ab.InputLayer(name='con', n_samples=n_samples_) >>
ab.RandomFourier(100, kernel=ab.RBF(learn_lenscale=True)) >>
ab.Dense(output_dim=16, init_fn="autonorm")
)
# Now define the cateogrical layers, which we embed
# Note every Embed call can be different, this is just "lazy"
cat_layer_list = [ab.Embed(EMBED_DIMS, i, init_fn="autonorm")
for i in n_cats]
cat_layer = (
ab.InputLayer(name='cat', n_samples=n_samples_) >>
ab.PerFeature(*cat_layer_list) >> # Assign columns to embedding layers
ab.Activation(tf.nn.selu) >>
ab.Dense(16, init_fn="autonorm")
)
# Now we can feed the initial continuous and cateogrical layers to further
# "joint" layers after we concatenate them
net = (
ab.Concat(con_layer, cat_layer) >>
ab.Activation(tf.nn.selu) >>
ab.DenseVariational(output_dim=1)
)
# Split data into training and testing
Xt_con, Xs_con = np.split(X_con, [len(df_train)], axis=0)
Xt_cat, Xs_cat = np.split(X_cat, [len(df_train)], axis=0)
Yt, Ys = np.split(Y, [len(df_train)], axis=0)
# Graph place holders
X_con_ = tf.placeholder(tf.float32, [None, Xt_con.shape[1]])
X_cat_ = tf.placeholder(tf.int32, [None, Xt_cat.shape[1]])
Y_ = tf.placeholder(tf.float32, [None, 1])
# Feed dicts
train_dict = {X_con_: Xt_con, X_cat_: Xt_cat, Y_: Yt}
test_dict = {X_con_: Xs_con, X_cat_: Xs_cat, n_samples_: P_SAMPLES}
# Make model
N = len(Xt_con)
nn, kl = net(con=X_con_, cat=X_cat_)
likelihood = tf.distributions.Bernoulli(logits=nn)
prob = ab.sample_mean(likelihood.probs)
loss = ab.elbo(likelihood.log_prob(Y_), kl, N)
optimizer = tf.train.AdamOptimizer()
train = optimizer.minimize(loss)
init = tf.global_variables_initializer()
with tf.Session(config=CONFIG):
init.run()
# We're going to just use a feed_dict to feed in batches, which we
# generate here
batches = ab.batch(
train_dict,
batch_size=BSIZE,
n_iter=NITER)
for i, data in enumerate(batches):
train.run(feed_dict=data)
if i % 1000 == 0:
loss_val = loss.eval(feed_dict=data)
print("Iteration {}, loss = {}".format(i, loss_val))
# Predict
Ep = prob.eval(feed_dict=test_dict)
Ey = Ep > 0.5 # Max probability assignment
acc = accuracy_score(Ys.flatten(), Ey.flatten())
logloss = log_loss(Ys.flatten(), np.hstack((1 - Ep, Ep)))
print("Accuracy = {}, log loss = {}".format(acc, logloss))
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
NPREDICTSAMPLES = 10 # results in NSAMPLES * NPREDICTSAMPLES samples
CONFIG = tf.ConfigProto(device_count={'GPU': 1}) # Use GPU ?
def main():
"""Run the demo."""
data = fetch_gpml_sarcos_data()
Xr = data.train.data.astype(np.float32)
kern = ab.RBF(learn_lenscale=True) # keep the length scale positive
# Variational Fourier Features -- length-scale setting here is the "prior", we
# can choose to optimise this or not
# lenscale = 1.
# kern = ab.RBFVariational(lenscale=lenscale) # This is VAR-FIXED kernel from
# Cutjar et. al. 2017
# This is how we make the "latent function" of a Gaussian process, here
# n_features controls how many random basis functions we use in the
# approximation. The more of these, the more accurate, but more costly
# computationally. "full" indicates we want a full-covariance matrix Gaussian
# posterior of the model weights. This is optional, but it does greatly improve
# the model uncertainty away from the data.
n_samples_ = tf.placeholder(tf.int32)
net = (ab.InputLayer(name="X", n_samples=n_samples_) >> ab.RandomFourier(
n_features=200, kernel=kern) >> ab.DenseVariational(
output_dim=1, learn_prior=True, full=True))
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]
# Variational Fourier Features -- length-scale setting here is the "prior", we
# can choose to optimise this or not
lenscale = 1.
kern = ab.RBFVariational(lenscale=lenscale) # This is VAR-FIXED kernel from
# Cutjar et. al. 2017
# This is how we make the "latent function" of a Gaussian process, here
# n_features controls how many random basis functions we use in the
# approximation. The more of these, the more accurate, but more costly
# computationally. "full" indicates we want a full-covariance matrix Gaussian
# posterior of the model weights. This is optional, but it does greatly improve
# the model uncertainty away from the data.
n_samples_ = tf.placeholder(tf.int32)
net = (
ab.InputLayer(name="X", n_samples=n_samples_) >>
ab.RandomFourier(n_features=100, kernel=kern) >>
ab.DenseVariational(output_dim=1, std=reg, full=True)
)
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]