https://github.com/GPflow/GPflow
Tip revision: 964cfeeb98d02f9a6356e00beb59819aa7414158 authored by Nicolas Durrande on 11 March 2020, 13:24:49 UTC
Update gpflow/kernels/stationaries.py
Update gpflow/kernels/stationaries.py
Tip revision: 964cfee
ops.py
import copy
from typing import List, Optional, Union
import tensorflow as tf
import tensorflow_probability as tfp
import numpy as np
def eye(num: int, value: tf.Tensor, dtype: Optional[tf.DType] = None) -> tf.Tensor:
if dtype is not None:
value = tf.cast(value, dtype)
return tf.linalg.diag(tf.fill([num], value))
def add_to_diagonal(to_tensor: tf.Tensor, value: tf.Tensor):
diag = tf.linalg.diag_part(to_tensor)
new_diag = diag + value
return tf.linalg.set_diag(to_tensor, new_diag)
def leading_transpose(
tensor: tf.Tensor, perm: List[Union[int, type(...)]], leading_dim: int = 0
) -> tf.Tensor:
"""
Transposes tensors with leading dimensions. Leading dimensions in
permutation list represented via ellipsis `...`.
When leading dimensions are found, `transpose` method
considers them as a single grouped element indexed by 0 in `perm` list. So, passing
`perm=[-2, ..., -1]`, you assume that your input tensor has [..., A, B] shape,
and you want to move leading dims between A and B dimensions.
Dimension indices in permutation list can be negative or positive. Valid positive
indices start from 1 up to the tensor rank, viewing leading dimensions `...` as zero
index.
Example:
a = tf.random.normal((1, 2, 3, 4, 5, 6))
# [..., A, B, C],
# where A is 1st element,
# B is 2nd element and
# C is 3rd element in
# permutation list,
# leading dimensions are [1, 2, 3]
# which are 0th element in permutation
# list
b = leading_transpose(a, [3, -3, ..., -2]) # [C, A, ..., B]
sess.run(b).shape
output> (6, 4, 1, 2, 3, 5)
:param tensor: TensorFlow tensor.
:param perm: List of permutation indices.
:returns: TensorFlow tensor.
:raises: ValueError when `...` cannot be found.
"""
perm = copy.copy(perm)
idx = perm.index(...)
perm[idx] = leading_dim
rank = tf.rank(tensor)
perm_tf = perm % rank
leading_dims = tf.range(rank - len(perm) + 1)
perm = tf.concat([perm_tf[:idx], leading_dims, perm_tf[idx + 1 :]], 0)
return tf.transpose(tensor, perm)
def broadcasting_elementwise(op, a, b):
"""
Apply binary operation `op` to every pair in tensors `a` and `b`.
:param op: binary operator on tensors, e.g. tf.add, tf.substract
:param a: tf.Tensor, shape [n_1, ..., n_a]
:param b: tf.Tensor, shape [m_1, ..., m_b]
:return: tf.Tensor, shape [n_1, ..., n_a, m_1, ..., m_b]
"""
flatres = op(tf.reshape(a, [-1, 1]), tf.reshape(b, [1, -1]))
return tf.reshape(flatres, tf.concat([tf.shape(a), tf.shape(b)], 0))
def square_distance(X, X2):
"""
Returns ||X - X2ᵀ||²
Due to the implementation and floating-point imprecision, the
result may actually be very slightly negative for entries very
close to each other.
"""
if X2 is None:
Xs = tf.reduce_sum(tf.square(X), axis=-1, keepdims=True)
dist = -2 * tf.matmul(X, X, transpose_b=True)
dist += Xs + tf.linalg.adjoint(Xs)
return dist
Xs = tf.reduce_sum(tf.square(X), axis=-1)
X2s = tf.reduce_sum(tf.square(X2), axis=-1)
dist = -2 * tf.tensordot(X, X2, [[-1], [-1]])
dist += broadcasting_elementwise(tf.add, Xs, X2s)
return dist
def pca_reduce(X: tf.Tensor, Q: tf.Tensor) -> tf.Tensor:
"""
A helpful function for linearly reducing the dimensionality of the data X
to Q.
:param X: data array of size N (number of points) x D (dimensions)
:param Q: Number of latent dimensions, Q < D
:return: PCA projection array of size N x Q.
"""
if Q > X.shape[1]: # pragma: no cover
raise ValueError("Cannot have more latent dimensions than observed")
if isinstance(X, tf.Tensor):
X = X.numpy()
# TODO why not use tf.linalg.eigh?
evals, evecs = np.linalg.eigh(np.cov(X.T))
W = evecs[:, -Q:]
return (X - X.mean(0)).dot(W)
# def pca_reduce(data: tf.Tensor, latent_dim: tf.Tensor) -> tf.Tensor:
# """
# A helpful function for linearly reducing the dimensionality of the data X
# to Q.
# :param X: data array of size N (number of points) x D (dimensions)
# :param Q: Number of latent dimensions, Q < D
# :return: PCA projection array of size [N, Q].
# """
# assert latent_dim <= data.shape[1], 'Cannot have more latent dimensions than observed'
# x_cov = tfp.stats.covariance(data)
# evals, evecs = tf.linalg.eigh(x_cov)
# W = evecs[:, -latent_dim:]
# return (data - tf.reduce_mean(data, axis=0, keepdims=True)) @ W