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# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""The Chi2 distribution class."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops.distributions import gamma
__all__ = [
"Chi2",
"Chi2WithAbsDf",
]
class Chi2(gamma.Gamma):
"""Chi2 distribution.
The Chi2 distribution is defined over positive real numbers using a degrees of
freedom ("df") parameter.
#### Mathematical Details
The probability density function (pdf) is,
```none
pdf(x; df, x > 0) = x**(0.5 df - 1) exp(-0.5 x) / Z
Z = 2**(0.5 df) Gamma(0.5 df)
```
where:
* `df` denotes the degrees of freedom,
* `Z` is the normalization constant, and,
* `Gamma` is the [gamma function](
https://en.wikipedia.org/wiki/Gamma_function).
The Chi2 distribution is a special case of the Gamma distribution, i.e.,
```python
Chi2(df) = Gamma(concentration=0.5 * df, rate=0.5)
```
"""
def __init__(self,
df,
validate_args=False,
allow_nan_stats=True,
name="Chi2"):
"""Construct Chi2 distributions with parameter `df`.
Args:
df: Floating point tensor, the degrees of freedom of the
distribution(s). `df` must contain only positive values.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
(e.g., mean, mode, variance) use the value "`NaN`" to indicate the
result is undefined. When `False`, an exception is raised if one or
more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
"""
parameters = locals()
# Even though all stats of chi2 are defined for valid parameters, this is
# not true in the parent class "gamma." therefore, passing
# allow_nan_stats=True
# through to the parent class results in unnecessary asserts.
with ops.name_scope(name, values=[df]):
self._df = ops.convert_to_tensor(df, name="df")
super(Chi2, self).__init__(
concentration=0.5 * self._df,
rate=constant_op.constant(0.5, dtype=self._df.dtype),
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
@staticmethod
def _param_shapes(sample_shape):
return {"df": ops.convert_to_tensor(sample_shape, dtype=dtypes.int32)}
@property
def df(self):
return self._df
class Chi2WithAbsDf(Chi2):
"""Chi2 with parameter transform `df = floor(abs(df))`."""
def __init__(self,
df,
validate_args=False,
allow_nan_stats=True,
name="Chi2WithAbsDf"):
parameters = locals()
with ops.name_scope(name, values=[df]):
super(Chi2WithAbsDf, self).__init__(
df=math_ops.floor(
math_ops.abs(df, name="abs_df"),
name="floor_abs_df"),
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
|
