# Copyright 2016-2020 The GPflow Contributors. 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.
import numpy as np
import tensorflow as tf
from check_shapes import check_shapes
from .base import TensorType
from .utilities import to_default_float
[docs]
@check_shapes(
"x: [broadcast shape...]",
"mu: [broadcast shape...]",
"var: [broadcast shape...]",
"return: [shape...]",
)
def gaussian(x: TensorType, mu: TensorType, var: TensorType) -> tf.Tensor:
return -0.5 * (np.log(2 * np.pi) + tf.math.log(var) + tf.square(mu - x) / var)
[docs]
@check_shapes(
"x: [broadcast shape...]",
"mu: [broadcast shape...]",
"var: [broadcast shape...]",
"return: [shape...]",
)
def lognormal(x: TensorType, mu: TensorType, var: TensorType) -> tf.Tensor:
lnx = tf.math.log(x)
return gaussian(lnx, mu, var) - lnx
[docs]
@check_shapes(
"x: [broadcast shape...]",
"p: [broadcast shape...]",
"return: [shape...]",
)
def bernoulli(x: TensorType, p: TensorType) -> tf.Tensor:
return tf.math.log(tf.where(tf.equal(x, 1), p, 1 - p))
[docs]
@check_shapes(
"x: [broadcast shape...]",
"lam: [broadcast shape...]",
"return: [shape...]",
)
def poisson(x: TensorType, lam: TensorType) -> tf.Tensor:
return x * tf.math.log(lam) - lam - tf.math.lgamma(x + 1.0)
[docs]
@check_shapes(
"x: [broadcast shape...]",
"scale: [broadcast shape...]",
"return: [shape...]",
)
def exponential(x: TensorType, scale: TensorType) -> tf.Tensor:
return -x / scale - tf.math.log(scale)
[docs]
@check_shapes(
"x: [broadcast shape...]",
"shape: [broadcast shape...]",
"scale: [broadcast shape...]",
"return: [shape...]",
)
def gamma(x: TensorType, shape: TensorType, scale: TensorType) -> tf.Tensor:
return (
-shape * tf.math.log(scale)
- tf.math.lgamma(shape)
+ (shape - 1.0) * tf.math.log(x)
- x / scale
)
[docs]
@check_shapes(
"x: [broadcast shape...]",
"mean: [broadcast shape...]",
"scale: [broadcast shape...]",
"df: [broadcast shape...]",
"return: [shape...]",
)
def student_t(x: TensorType, mean: TensorType, scale: TensorType, df: TensorType) -> tf.Tensor:
df = to_default_float(df)
const = (
tf.math.lgamma((df + 1.0) * 0.5)
- tf.math.lgamma(df * 0.5)
- 0.5 * (tf.math.log(tf.square(scale)) + tf.math.log(df) + np.log(np.pi))
)
return const - 0.5 * (df + 1.0) * tf.math.log(
1.0 + (1.0 / df) * (tf.square((x - mean) / scale))
)
[docs]
@check_shapes(
"x: [broadcast shape...]",
"alpha: [broadcast shape...]",
"beta: [broadcast shape...]",
"return: [shape...]",
)
def beta(x: TensorType, alpha: TensorType, beta: TensorType) -> tf.Tensor:
# need to clip x, since log of 0 is nan...
x = tf.clip_by_value(x, 1e-6, 1 - 1e-6)
return (
(alpha - 1.0) * tf.math.log(x)
+ (beta - 1.0) * tf.math.log(1.0 - x)
+ tf.math.lgamma(alpha + beta)
- tf.math.lgamma(alpha)
- tf.math.lgamma(beta)
)
[docs]
@check_shapes(
"x: [broadcast shape...]",
"mu: [broadcast shape...]",
"sigma: [broadcast shape...]",
"return: [shape...]",
)
def laplace(x: TensorType, mu: TensorType, sigma: TensorType) -> tf.Tensor:
return -tf.abs(mu - x) / sigma - tf.math.log(2.0 * sigma)
[docs]
@check_shapes(
"x: [D, broadcast N]",
"mu: [D, broadcast N]",
"L: [D, D]",
"return: [N]",
)
def multivariate_normal(x: TensorType, mu: TensorType, L: TensorType) -> tf.Tensor:
"""
Computes the log-density of a multivariate normal.
:param x: sample(s) for which we want the density
:param mu: mean(s) of the normal distribution
:param L: Cholesky decomposition of the covariance matrix
:return: log densities
"""
d = x - mu
alpha = tf.linalg.triangular_solve(L, d, lower=True)
num_dims = tf.cast(tf.shape(d)[0], L.dtype)
p = -0.5 * tf.reduce_sum(tf.square(alpha), 0)
p -= 0.5 * num_dims * np.log(2 * np.pi)
p -= tf.reduce_sum(tf.math.log(tf.linalg.diag_part(L)))
return p