Transformed Distribution
Change: 126362065
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A. Unique TensorFlower
TensorFlower Gardener
parent
aabfe1d03e
commit
e2587a0476
@ -171,6 +171,16 @@ cuda_py_tests(
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],
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)
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cuda_py_tests(
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name = "transformed_distribution_test",
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size = "small",
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srcs = ["python/kernel_tests/transformed_distribution_test.py"],
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additional_deps = [
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":distributions_py",
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"//tensorflow/python:platform_test",
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],
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)
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filegroup(
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name = "all_files",
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srcs = glob(
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@ -47,6 +47,10 @@ initialized with parameters that define the distributions.
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@@DirichletMultinomial
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### Transformed distributions
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@@ContinuousTransformedDistribution
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## Operators allowing for matrix-free methods
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### Positive definite operators
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@ -95,4 +99,5 @@ from tensorflow.contrib.distributions.python.ops.operator_pd import *
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from tensorflow.contrib.distributions.python.ops.operator_pd_cholesky import *
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from tensorflow.contrib.distributions.python.ops.operator_pd_full import *
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from tensorflow.contrib.distributions.python.ops.student_t import *
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from tensorflow.contrib.distributions.python.ops.transformed_distribution import *
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from tensorflow.contrib.distributions.python.ops.uniform import *
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@ -0,0 +1,79 @@
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# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# ==============================================================================
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"""Tests for ContinuousTransformedDistribution."""
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from __future__ import absolute_import
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from __future__ import division
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from __future__ import print_function
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import numpy as np
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from scipy import stats
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import tensorflow as tf
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class ContinuousTransformedDistributionTest(tf.test.TestCase):
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def testContinuousTransformedDistribution(self):
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with self.test_session():
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mu = 3.0
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sigma = 0.02
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log_normal = tf.contrib.distributions.ContinuousTransformedDistribution(
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base_dist_cls=tf.contrib.distributions.Normal,
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mu=mu,
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sigma=sigma,
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transform=lambda x: tf.exp(x),
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inverse=lambda y: tf.log(y),
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log_det_jacobian=(lambda x: tf.reduce_sum(x)))
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# sample
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self.assertAllClose([stats.lognorm.mean(s=sigma, scale=np.exp(mu))],
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[np.mean(log_normal.sample(100000, seed=235).eval())],
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atol=1e-2)
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# pdf, log_pdf
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test_vals = np.linspace(0.00001, 10.).astype(np.float32)
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for test_val in test_vals:
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expected = stats.lognorm.logpdf(test_val, s=sigma, scale=np.exp(mu))
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self.assertAllClose([expected], [log_normal.log_pdf(test_val).eval()])
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self.assertAllClose([np.exp(expected)],
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[log_normal.pdf(test_val).eval()])
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def testCachedSamplesWithoutInverse(self):
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with self.test_session() as sess:
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mu = 3.0
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sigma = 0.02
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log_normal = tf.contrib.distributions.ContinuousTransformedDistribution(
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base_dist_cls=tf.contrib.distributions.Normal,
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mu=mu,
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sigma=sigma,
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transform=lambda x: tf.exp(x),
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inverse=None,
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log_det_jacobian=(lambda x: tf.reduce_sum(x)))
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sample = log_normal.sample(1)
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sample_val, log_pdf_val = sess.run([sample, log_normal.log_pdf(sample)])
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self.assertAllClose(
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stats.lognorm.logpdf(sample_val, s=sigma,
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scale=np.exp(mu)),
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log_pdf_val,
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atol=1e-2)
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with self.assertRaisesRegexp(ValueError,
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"was not returned from `sample`"):
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log_normal.log_pdf(tf.constant(3.0))
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if __name__ == "__main__":
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tf.test.main()
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@ -0,0 +1,252 @@
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# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# ==============================================================================
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"""A Transformed Distribution class."""
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from __future__ import absolute_import
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from __future__ import division
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from __future__ import print_function
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from tensorflow.contrib.distributions.python.ops import distribution # pylint: disable=line-too-long
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from tensorflow.python.framework import ops
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class ContinuousTransformedDistribution(distribution.ContinuousDistribution):
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"""A Transformed Distribution.
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A Transformed Distribution models `p(y)` given a base distribution `p(x)`,
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an invertible transform, `y = f(x)`, and the determinant of the Jacobian of
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`f(x)`.
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Shapes, type, and reparameterization are taken from the base distribution.
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#### Mathematical details
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* `p(x)` - probability distribution for random variable X
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* `p(y)` - probability distribution for random variable Y
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* `f` - transform
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* `g` - inverse transform, `f(g(x)) = x`
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* `J(x)` - Jacobian of f(x)
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A Transformed Distribution exposes `sample` and `pdf`:
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* `sample`: `y = f(x)`, after drawing a sample of X.
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* `pdf`: `p(y) = p(x) / det|J(x)| = p(g(y)) / det|J(g(y))|`
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A simple example constructing a Log-Normal distribution from a Normal
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distribution:
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```
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logit_normal = ContinuousTransformedDistribution(
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base_dist=Normal(mu, sigma),
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transform=lambda x: tf.sigmoid(x),
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inverse=lambda y: tf.log(y) - tf.log(1. - y),
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log_det_jacobian=(lambda x:
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tf.reduce_sum(tf.log(tf.sigmoid(x)) + tf.log(1. - tf.sigmoid(x)),
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reduction_indices=[-1])))
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name="LogitNormalTransformedDistribution"
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)
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```
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"""
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def __init__(self,
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base_dist_cls,
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transform,
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inverse,
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log_det_jacobian,
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name="ContinuousTransformedDistribution",
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**base_dist_args):
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"""Construct a Transformed Distribution.
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Args:
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base_dist_cls: the base distribution class to transform. Must be a
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subclass of `ContinuousDistribution`.
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transform: a callable that takes a `Tensor` sample from `base_dist` and
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returns a `Tensor` of the same shape and type. `x => y`.
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inverse: a callable that computes the inverse of transform. `y => x`. If
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None, users can only call `log_pdf` on values returned by `sample`.
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log_det_jacobian: a callable that takes a `Tensor` sample from `base_dist`
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and returns the log of the determinant of the Jacobian of `transform`.
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name: The name for the distribution.
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**base_dist_args: kwargs to pass on to dist_cls on construction.
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Raises:
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TypeError: if `base_dist_cls` is not a subclass of
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`ContinuousDistribution`.
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"""
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if not issubclass(base_dist_cls, distribution.ContinuousDistribution):
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raise TypeError("base_dist_cls must be a subclass of"
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"ContinuousDistribution.")
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with ops.op_scope(base_dist_args.values(), name) as scope:
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self._name = scope
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self._base_dist = base_dist_cls(**base_dist_args)
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self._transform = transform
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self._inverse = inverse
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self._log_det_jacobian = log_det_jacobian
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self._inverse_cache = {}
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@property
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def name(self):
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return self._name
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@property
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def dtype(self):
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return self._base_dist.dtype
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def batch_shape(self, name="batch_shape"):
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"""Batch dimensions of this instance as a 1-D int32 `Tensor`.
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The product of the dimensions of the `batch_shape` is the number of
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independent distributions of this kind the instance represents.
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Args:
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name: name to give to the op.
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Returns:
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`Tensor` `batch_shape`
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"""
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with ops.name_scope(self.name):
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return self._base_dist.batch_shape(name)
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def get_batch_shape(self):
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"""`TensorShape` available at graph construction time.
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Same meaning as `batch_shape`. May be only partially defined.
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Returns:
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batch shape
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"""
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return self._base_dist.get_batch_shape()
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def event_shape(self, name="event_shape"):
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"""Shape of a sample from a single distribution as a 1-D int32 `Tensor`.
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Args:
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name: name to give to the op.
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Returns:
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`Tensor` `event_shape`
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"""
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with ops.name_scope(self.name):
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return self._base_dist.event_shape(name)
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def get_event_shape(self):
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"""`TensorShape` available at graph construction time.
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Same meaning as `event_shape`. May be only partially defined.
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Returns:
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event shape
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"""
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return self._base_dist.get_event_shape()
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@property
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def base_distribution(self):
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"""Base distribution, p(x)."""
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return self._base_dist
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@property
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def transform(self):
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"""Function transforming x => y."""
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return self._transform
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@property
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def inverse(self):
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"""Inverse function of transform, y => x."""
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return self._inverse
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@property
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def log_det_jacobian(self):
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"""Function computing the log determinant of the Jacobian of transform."""
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return self._log_det_jacobian
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def log_pdf(self, y, name="log_pdf"):
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"""Log pdf of observations in `y`.
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`log ( p(g(y)) / det|J(g(y))| )`, where `g` is the inverse of `transform`.
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Args:
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y: tensor of dtype `dtype`.
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name: The name to give this op.
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Returns:
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log_pdf: tensor of dtype `dtype`, the log-PDFs of `y`.
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Raises:
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ValueError: if `inverse` was not provided to the distribution and `y` was
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not returned from `sample`.
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"""
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with ops.name_scope(self.name):
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with ops.op_scope([y], name):
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y = ops.convert_to_tensor(y)
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if y.dtype != self.dtype:
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raise TypeError("Input x dtype does not match dtype: %s vs. %s" %
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(y.dtype, self.dtype))
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with ops.name_scope("inverse"):
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if y in self._inverse_cache:
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x = self._inverse_cache[y]
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elif self._inverse:
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x = self._inverse(y)
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else:
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raise ValueError("No inverse function exists and input `y` was not "
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"returned from `sample`.")
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with ops.name_scope("log_det_jacobian"):
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log_det_jacobian = self._log_det_jacobian(x)
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return self._base_dist.log_likelihood(x) - log_det_jacobian
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def pdf(self, y, name="pdf"):
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"""The PDF of observations in `y`.
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`p(g(y)) / det|J(g(y))|`, where `g` is the inverse of `transform`.
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Args:
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y: `Tensor` of dtype `dtype`.
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name: The name to give this op.
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Returns:
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pdf: `Tensor` of dtype `dtype`, the pdf values of `y`.
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"""
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return super(ContinuousTransformedDistribution, self).pdf(y, name=name)
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def sample(self, n, seed=None, name="sample"):
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"""Sample `n` observations.
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Samples from the base distribution and then passes through the transform.
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Args:
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n: scalar, type int32, the number of observations to sample.
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seed: Python integer, the random seed.
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name: The name to give this op.
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Returns:
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samples: `[n, ...]`, a `Tensor` of `n` samples.
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"""
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with ops.name_scope(self.name):
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with ops.name_scope(name):
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samples = self._base_dist.sample(n=n, seed=seed)
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with ops.name_scope("transform"):
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transformed = self._transform(samples)
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self._inverse_cache[transformed] = samples
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return transformed
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@property
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def is_reparameterized(self):
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return self._base_dist.is_reparameterized
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@property
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def strict_statistics(self):
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return self._base_dist.strict_statistics
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@property
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def strict(self):
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return self._base_dist.strict
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