def cauchy_alternative_to_gaussian(current_times, current_values, outputs):
"""A Cauchy anomaly distribution, centered at a Gaussian prediction.
Performs an entropy-matching approximation of the scale parameters of
independent Cauchy distributions given the covariance matrix of a multivariate
Gaussian in outputs["covariance"], and centers the Cauchy distributions at
outputs["mean"]. This requires that the model that we are creating an
alternative/anomaly distribution for produces a mean and covariance.
Args:
current_times: A [batch size] Tensor of times, unused.
current_values: A [batch size x num features] Tensor of values to evaluate
the anomaly distribution at.
outputs: A dictionary of Tensors with keys "mean" and "covariance"
describing the Gaussian to construct an anomaly distribution from. The
value corresponding to "mean" has shape [batch size x num features], and
the value corresponding to "covariance" has shape [batch size x num
features x num features].
Returns:
A [batch size] Tensor of log likelihoods; the anomaly log PDF evaluated at
`current_values`.
"""
del current_times # unused
cauchy_scale = math_utils.entropy_matched_cauchy_scale(outputs["covariance"])
individual_log_pdfs = distributions.StudentT(
df=array_ops.ones([], dtype=current_values.dtype),
loc=outputs["mean"],
scale=cauchy_scale).log_prob(current_values)
return math_ops.reduce_sum(individual_log_pdfs, axis=1)
def __init__(self, tf, valid_data_len, train_and_valid_data,
hyper_param_dim):
self._valid_data = train_and_valid_data[:, :valid_data_len]
self._train_data = train_and_valid_data[:, valid_data_len:]
self._l2_reg_strength = tf.placeholder(tf.float32,
shape=[hyper_param_dim])
self._model_lr = tf.placeholder(tf.float32)
self._cross_entropy = None
self._params = StudentTParams(tf)
self._model_distribution = dist.StudentT(df=self._params.shape,
loc=self._params.y,
scale=self._params.scale)
def _anomaly_log_prob(self, targets, prediction_ops):
prediction = prediction_ops["mean"]
if self._anomaly_distribution == AnomalyMixtureARModel.GAUSSIAN_ANOMALY:
anomaly_variance = prediction_ops["anomaly_params"]
anomaly_sigma = math_ops.sqrt(
gen_math_ops.maximum(anomaly_variance, 1e-5))
normal = distributions.Normal(loc=targets, scale=anomaly_sigma)
log_prob = normal.log_prob(prediction)
else:
assert self._anomaly_distribution == AnomalyMixtureARModel.CAUCHY_ANOMALY
anomaly_scale = prediction_ops["anomaly_params"]
cauchy = distributions.StudentT(df=array_ops.ones(
[], dtype=anomaly_scale.dtype),
loc=targets,
scale=anomaly_scale)
log_prob = cauchy.log_prob(prediction)
return log_prob
from tensorflow.contrib import distributions as tfcd
g = tf.Graph()
"""
The idea comes from Lemma 1 from the paper "Some Characterizations of the Multivariate t Distribution":
https://ac.els-cdn.com/0047259X72900218/1-s2.0-0047259X72900218-main.pdf?_tid=9035319c-e165-4b9a-8851-ec6837fcfe0e&acdnat=1527542834_a6193c0ddc8296cfcf2bc38c73536890
"""
with g.as_default():
# Create a vectorized t-distribution.
studentT = tfcd.StudentT(
df=2.1,
loc=[[0.0,0.0]],
scale=[[1.0,1.0]]
)
# Scale matrix for the multivariate t-distribution.
scale_matrix = [[2.0, 0.5], [0.5, 2.0]]
# Compute the Cholesky decomposition of the scale matrix.
tril = tf.cholesky([scale_matrix])[0]
# In this name scope we create affine transform of the vectorized t-distribution
# which will result in a 2-D t-distribution with a prescribed scale matrix.
with tf.name_scope("multi_studentT"):
# Create the multivariate t-distribution via an affine transform with
# a lower-trianguler matrix.
def __init__(self):
self.studentT_dist = tfcd.StudentT(df=4, loc=0., scale=1.)
super(StudentTCDF, self).__init__(forward_min_event_ndims=0,
validate_args=False,
name="StudentTCDF")
