Revision c6cd15415ddfe4baf80a6d0ebc3c782c00b7c388 authored by James Hensman on 13 September 2016, 14:50:43 UTC, committed by James Hensman on 13 September 2016, 14:50:43 UTC
1 parent 396eb48
transforms.py
# Copyright 2016 James Hensman, alexggmatthews
#
# 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.
from __future__ import absolute_import
import numpy as np
import tensorflow as tf
from . import tf_wraps as tfw
from ._settings import settings
float_type = settings.dtypes.float_type
np_float_type = np.float32 if float_type is tf.float32 else np.float64
class Transform(object):
def forward(self, x):
"""
Map from the free-space to the variable space, using numpy
"""
raise NotImplementedError
def backward(self, y):
"""
Map from the variable-space to the free space, using numpy
"""
raise NotImplementedError
def tf_forward(self, x):
"""
Map from the free-space to the variable space, using tensorflow
"""
raise NotImplementedError
def tf_log_jacobian(self, x):
"""
Return the log Jacobian of the tf_forward mapping.
Note that we *could* do this using a tf manipulation of
self.tf_forward, but tensorflow may have difficulty: it doesn't have a
Jacaobian at time of writing. We do this in the tests to make sure the
implementation is correct.
"""
raise NotImplementedError
def free_state_size(self, variable_shape):
return np.prod(variable_shape)
def __str__(self):
"""
A short string describing the nature of the constraint
"""
raise NotImplementedError
def __getstate__(self):
return self.__dict__.copy()
def __setstate__(self, d):
self.__dict__ = d
class Identity(Transform):
def tf_forward(self, x):
return tf.identity(x)
def forward(self, x):
return x
def backward(self, y):
return y
def tf_log_jacobian(self, x):
return tf.zeros((1,), float_type)
def __str__(self):
return '(none)'
class Exp(Transform):
def __init__(self, lower=1e-6):
self._lower = lower
def tf_forward(self, x):
return tf.exp(x) + self._lower
def forward(self, x):
return np.exp(x) + self._lower
def backward(self, y):
return np.log(y - self._lower)
def tf_log_jacobian(self, x):
return tf.reduce_sum(x)
def __str__(self):
return '+ve'
class Log1pe(Transform):
"""
A transform of the form
y = \log ( 1 + \exp(x))
x is a free variable, y is always positive.
This function is known as 'softplus' in tensorflow.
"""
def __init__(self, lower=1e-6):
"""
lower is a float that defines the minimum value that this transform can
take, default 1e-6. This helps stability during optimization, because
aggressive optimizers can take overly-long steps which lead to zero in
the transformed variable, causing an error.
"""
self._lower = lower
def forward(self, x):
return np.log(1. + np.exp(x)) + self._lower
def tf_forward(self, x):
return tf.nn.softplus(x) + self._lower
def tf_log_jacobian(self, x):
return -tf.reduce_sum(tf.log(1. + tf.exp(-x)))
def backward(self, y):
return np.log(np.exp(y - self._lower) - np.ones(1, np_float_type))
def __str__(self):
return '+ve'
class Logistic(Transform):
def __init__(self, a=0., b=1.):
Transform.__init__(self)
assert b > a
self.a, self.b = a, b
self._a = tf.constant(a, float_type)
self._b = tf.constant(b, float_type)
def tf_forward(self, x):
ex = tf.exp(-x)
return self._a + (self._b - self._a) / (1. + ex)
def forward(self, x):
ex = np.exp(-x)
return self.a + (self.b - self.a) / (1. + ex)
def backward(self, y):
return -np.log((self.b - self.a) / (y - self.a) - 1.)
def tf_log_jacobian(self, x):
return tf.reduce_sum(x - 2. * tf.log(tf.exp(x) + 1.) + tf.log(self._b - self._a))
def __str__(self):
return '[' + str(self.a) + ', ' + str(self.b) + ']'
def __getstate__(self):
d = Transform.__getstate__(self)
d.pop('_a')
d.pop('_b')
return d
def __setstate__(self, d):
Transform.__setstate__(self, d)
self._a = tf.constant(self.a, float_type)
self._b = tf.constant(self.b, float_type)
class LowerTriangular(Transform):
"""
A transform of the form
tri_mat = vec_to_tri(x)
x is a free variable, y is always a list of lower triangular matrices sized
(N x N x D).
"""
def __init__(self, num_matrices=1, squeeze=False):
"""
Create an instance of LowerTriangular transform.
Args:
num_matrices: Number of matrices to be stored.
squeeze: If num_matrices == 1, drop the redundant axis.
"""
self.num_matrices = num_matrices # We need to store this for reconstruction.
self.squeeze = squeeze
def _validate_vector_length(self, length):
"""
Check whether the vector length is consistent with being a triangular
matrix and with `self.num_matrices`.
Args:
length: Length of the free state vector.
Returns: Length of the vector with the lower triangular elements.
"""
L = length / self.num_matrices
if int(((L * 8) + 1) ** 0.5) ** 2.0 != (L * 8 + 1):
raise ValueError("The free state must be a triangle number.")
return L
def forward(self, x):
"""
Transforms from the free state to the variable.
Args:
x: Free state vector. Must have length of `self.num_matrices` *
triangular_number.
Returns:
Reconstructed variable.
"""
L = self._validate_vector_length(len(x))
matsize = int((L * 8 + 1) ** 0.5 * 0.5 - 0.5)
xr = np.reshape(x, (self.num_matrices, -1))
var = np.zeros((matsize, matsize, self.num_matrices), np_float_type)
for i in range(self.num_matrices):
indices = np.tril_indices(matsize, 0)
var[indices + (np.zeros(len(indices[0])).astype(int) + i,)] = xr[i, :]
return var.squeeze() if self.squeeze else var
def backward(self, y):
"""
Transforms from the variable to the free state.
Args:
y: Variable representation.
Returns:
Free state.
"""
N = int((y.size / self.num_matrices) ** 0.5)
y = np.reshape(y, (N, N, self.num_matrices))
return y[np.tril_indices(len(y), 0)].T.flatten()
def tf_forward(self, x):
fwd = tf.transpose(tfw.vec_to_tri(tf.reshape(x, (self.num_matrices, -1))), [1, 2, 0])
return tf.squeeze(fwd) if self.squeeze else fwd
def tf_log_jacobian(self, x):
return tf.zeros((1,), float_type) - np.inf
def free_state_size(self, variable_shape):
matrix_batch = len(variable_shape) > 2
if ((not matrix_batch and self.num_matrices != 1) or
(matrix_batch and variable_shape[2] != self.num_matrices)):
raise ValueError("Number of matrices must be consistent with what was passed to the constructor.")
if variable_shape[0] != variable_shape[1]:
raise ValueError("Matrices passed must be square.")
N = variable_shape[0]
return int(0.5 * N * (N + 1)) * (variable_shape[2] if matrix_batch else 1)
def __str__(self):
return "LoTri->vec"
positive = Log1pe()
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