def testValidateArgs(self):
k = psd_kernels.MaternOneHalf(
amplitude=-1., length_scale=-1., validate_args=True)
with self.assertRaises(tf.errors.InvalidArgumentError):
self.evaluate(k.amplitude)
with self.assertRaises(tf.errors.InvalidArgumentError):
self.evaluate(k.length_scale)
# But `None`'s are ok
k = psd_kernels.MaternOneHalf(
amplitude=None, length_scale=None, validate_args=True)
self.evaluate(k.apply([1.], [1.]))
def testBatchShape(self):
amplitude = np.random.uniform(2, 3., size=[3, 1, 2]).astype(np.float32)
length_scale = np.random.uniform(2, 3., size=[1, 3,
1]).astype(np.float32)
k = psd_kernels.MaternOneHalf(amplitude, length_scale)
self.assertAllEqual(tf.TensorShape([3, 3, 2]), k.batch_shape)
self.assertAllEqual([3, 3, 2], self.evaluate(k.batch_shape_tensor()))
def graph_GP(t_norm_,
w_pred_linsp_Var,
e_xyztp_s,
amplitude_init=np.array([0.1, 0.1]),
length_scale_init=np.array([.001, .001]),
obs_noise_var_init=1e-3,
LEARNING_RATE=.1,
NUM_SAMPLES=8
):
with tf.name_scope("GP"):
# ===================================================================
# AMP LENSC
# ===================================================================
with tf.name_scope("amplitude_lengthscale"):
amp, amp_assign, amp_p, \
lensc, lensc_assign, lensc_p, \
emb, emb_assign, emb_p, \
obs_noise_var \
= gpf.tf_Placeholder_assign_test(amplitude_init, length_scale_init, obs_noise_var_init)
# ===================================================================
# KERNEL
# ===================================================================
with tf.name_scope("kernel"):
kernel = tfkern.MaternOneHalf(amp, lensc) # ExponentiatedQuadratic # MaternOneHalf
# ===================================================================
# GP_FIT
# ===================================================================
with tf.name_scope("GP_fit"):
gp = tfd.GaussianProcess(
kernel=kernel, # ([2,],[2,])
index_points=e_xyztp_s,
observation_noise_variance=obs_noise_var,
validate_args=True)
log_likelihood = gp.log_prob(tf.transpose(tf.cast(t_norm_, dtype=tf.float64)))
tf.summary.scalar("log_likelihood_0", log_likelihood[0])
tf.summary.scalar("log_likelihood_1", log_likelihood[1]) # 2D GP input case
tf.summary.scalar("length_scale", lensc[0])
tf.summary.scalar("amplitude", amp[0])
train_op = gpf.tf_train_gp_adam(log_likelihood, LEARNING_RATE)
# ===================================================================
# GP REGRESSION MODEL
# ===================================================================
with tf.name_scope("GP_regression_model"):
gprm = gpf.tf_gp_regression_model(kernel,
w_pred_linsp_Var, # pred_idx_pts 1D_emb:(400,1), 2D_emb:(200,2)
e_xyztp_s, # e_xyztp_s # obs_idx_pts(15,1) (15,2)
t_norm_, # obs (15,) (15,)
obs_noise_var, 0.)
samples_1d = gprm.sample(NUM_SAMPLES)
return amp, amp_assign, amp_p, lensc, lensc_assign, lensc_p, log_likelihood, samples_1d, train_op, obs_noise_var
def testShapesAreCorrect(self):
k = psd_kernels.MaternOneHalf(amplitude=1., length_scale=1.)
x = np.ones([4, 3], np.float32)
y = np.ones([5, 3], np.float32)
self.assertAllEqual(k.matrix(x, y).shape, [4, 5])
self.assertAllEqual(
k.matrix(tf.stack([x] * 2), tf.stack([y] * 2)).shape, [2, 4, 5])
k = psd_kernels.MaternOneHalf(
amplitude=np.ones([2, 1, 1], np.float32),
length_scale=np.ones([1, 3, 1], np.float32))
self.assertAllEqual(
k.matrix(
tf.stack([x] * 2), # shape [2, 4, 3]
tf.stack([y] * 2) # shape [2, 5, 3]
).shape,
[2, 3, 2, 4, 5])
def testValuesAreCorrect(self, feature_ndims, dtype, dims):
amplitude = np.array(5., dtype=dtype)
length_scale = np.array(.2, dtype=dtype)
np.random.seed(42)
k = psd_kernels.MaternOneHalf(amplitude, length_scale, feature_ndims)
shape = [dims] * feature_ndims
for _ in range(5):
x = np.random.uniform(-1, 1, size=shape).astype(dtype)
y = np.random.uniform(-1, 1, size=shape).astype(dtype)
self.assertAllClose(
self.evaluate(k.apply(x, y)),
self._matern_one_half(amplitude, length_scale, x, y))
def testMismatchedFloatTypesAreBad(self):
with self.assertRaises(ValueError):
psd_kernels.MaternOneHalf(np.float32(1.), np.float64(1.))
def generate_noiseless_data(X, d_true, data_type,
random_seed=100):
"""A Linear Function to generates toy data for training.
Args:
X: (np.ndarray) A matrix of input features.
d_true: (int) Number of real input features.
data_type: (str) Types of data to generate.
random_seed: (int) Random seed to set for data generation.
Returns:
y: (np.ndarray of NP_DTYPE) A vector of response, shape (n, ).
variable_importance: (np.ndarray of NP_DTYPE) A vector of variable
importance for each input features, shape (d, ).
Raises:
(ValueError) If data_type does not belong to AVAIL_DATA_TYPE.
"""
if not data_type in AVAIL_DATA_TYPE:
raise ValueError("data type '{}' not available.".format(data_type))
np.random.seed(random_seed)
n, d = X.shape
x = tf.Variable(initial_value=X, dtype=dtype_util.TF_DTYPE)
if data_type == "linear":
# produce coefficient
linear_coef = np.zeros(shape=d).astype(dtype_util.NP_DTYPE)
linear_coef[:d_true] = np.random.normal(loc=1., scale=.25,
size=d_true)
# produce function
f = tf.tensordot(x, linear_coef, axes=1)
elif data_type == "barron":
if not d_true == 5:
raise ValueError("Barron class function only supports d_true=5.")
f = (5 * tf.sin(tf.reduce_max(x[:, :2], axis=1)) +
tf.atan(x[:, 1])) / (1 + (x[:, 0] + x[:, 4]) ** 2) + \
tf.sin(0.5 * x[:, 2]) * (1 + tf.exp(x[:, 3] - 0.5 * x[:, 2])) + \
x[:, 2] ** 2 + 2 * tf.sin(x[:, 3]) + 2 * x[:, 4]
# f = (10 * tf.sin(tf.reduce_max(x[:, :2], axis=1)) +
# tf.exp(x[:, 1])) / (1 + (x[:, 0] + x[:, 4]) ** 2) + \
# tf.sin(0.5 * x[:, 2]) * (1 + tf.exp(x[:, 3] - 0.5 * x[:, 2])) + \
# x[:, 2] ** 2 + 2 * tf.sin(x[:, 3]) + 2 * x[:, 4]
elif data_type == "sobolev":
sobolev_kernel = tfk.MaternOneHalf(amplitude=1.,
length_scale=.8)
x2 = tf.stop_gradient(x[:, :d_true])
sobolev_mat = sobolev_kernel.matrix(x[:, :d_true], x2)
alpha = np.random.normal(size=n).astype(dtype_util.NP_DTYPE)
f = tf.tensordot(sobolev_mat, alpha, axes=1)
# with tf.Session() as sess:
# sess.run(tf.global_variables_initializer())
# sess.run(tf.local_variables_initializer())
# f_val, x_val = sess.run([f, x[:, :d_true]])
#
# import pandas as pd
# pd_plot = pd.DataFrame({"x": x_val.flatten(), "f": f_val.flatten()})
# pd_plot = pd_plot.sort_values(by="x")
# plt.plot(pd_plot.x, pd_plot.f)
else:
raise ValueError("data type {} not available.".format(data_type))
# produce variable importance
var_imp = tf.reduce_mean(tf.gradients(f, x)[0] ** 2, axis=0)
# evaluate
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
sess.run(tf.local_variables_initializer())
f_val, var_imp_val = sess.run([f, var_imp])
return f_val, var_imp_val
def create_cov_kernel(amp, lensc):
kernel = tfkern.MaternOneHalf(amp, lensc) #ExponentiatedQuadratic # MaternOneHalf
return kernel
def graph_GP(et_Var,
t_norm_,
w_pred_linsp_Var,
e_xyztp_s,
amplitude_init=np.array([0.1, 0.1]),
length_scale_init=np.array([.001, .001]),
obs_noise_var_init=1e-3,
LEARNING_RATE=.1,
NUM_SAMPLES=8):
with tf.name_scope("GP"):
# ===================================================================
# AMP LENSC
# ===================================================================
with tf.name_scope("amplitude_lengthscale"):
amp, amp_assign, amp_p, \
lensc, lensc_assign, lensc_p, \
emb, emb_assign, emb_p, \
obs_noise_var \
= gpf.tf_Placeholder_assign_test(amplitude_init, length_scale_init, obs_noise_var_init)
# ===================================================================
# KERNEL
# ===================================================================
with tf.name_scope("kernel"):
kernel = tfkern.MaternOneHalf(
amp, lensc) # ExponentiatedQuadratic # MaternOneHalf
# ===================================================================
# GP_FIT
# ===================================================================
with tf.name_scope("GP_fit"):
# gp = gpf.fit_gp(kernel, np.array(enc_df).reshape(-1, enc_df.shape[1]).astype(np.float64), obs_noise_var) # GP fit to 3D XYZ, where Z is sinusoid of XY
gp = gpf.fit_gp(
kernel,
# np.array(enc_df).reshape(-1, enc_df.shape[1]).astype(np.float64),
e_xyztp_s, # et_Var
obs_noise_var) # GP fit to 3D XYZ, where Z is sinusoid of XY
log_likelihood = gp.log_prob(
tf.transpose(tf.cast(t_norm_, dtype=tf.float64)))
tf.summary.scalar("log_likelihood_0", log_likelihood[0])
tf.summary.scalar("log_likelihood_1",
log_likelihood[1]) # 2D GP input case
tf.summary.scalar("length_scale", lensc[0])
tf.summary.scalar("amplitude", amp[0])
train_op = gpf.tf_train_gp_adam(log_likelihood, LEARNING_RATE)
# ===================================================================
# GP REGRESSION MODEL
# ===================================================================
with tf.name_scope("GP_regression_model"):
gprm = gpf.tf_gp_regression_model(
kernel,
w_pred_linsp_Var, # pred_idx_pts 1D_emb:(400,1), 2D_emb:(200,2)
e_xyztp_s, # e_xyztp_s # obs_idx_pts(15,1) (15,2)
t_norm_, # obs (15,) (15,)
obs_noise_var,
0.)
samples_1d = gprm.sample(NUM_SAMPLES)
return amp, amp_assign, amp_p, lensc, lensc_assign, lensc_p, log_likelihood, samples_1d, train_op, obs_noise_var
