/
random_fourier_features.py
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/
random_fourier_features.py
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# Copyright 2017 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.
# ==============================================================================
"""Approximate kernel mapper for RBF kernel based on Random Fourier Features."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import math
import numpy as np
from tensorflow.contrib.kernel_methods.python.mappers import dense_kernel_mapper as dkm
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.ops import math_ops
# TODO(sibyl-vie3Poto,felixyu): add an option to control whether the parameters in the
# kernel map are trainable.
class RandomFourierFeatureMapper(dkm.DenseKernelMapper):
r"""Class that implements Random Fourier Feature Mapping (RFFM) in TensorFlow.
The RFFM mapping is used to approximate the Gaussian (RBF) kernel:
```
exp(-||x-y||_2^2 / (2 * sigma^2))
```
The implementation of RFFM is based on the following paper:
"Random Features for Large-Scale Kernel Machines" by Ali Rahimi and Ben Recht.
(link: https://people.eecs.berkeley.edu/~brecht/papers/07.rah.rec.nips.pdf)
The mapping uses a matrix `Omega \in R^{d x D}` and a bias vector `b \in R^D`
where `d` is the input dimension (number of dense input features) and `D` is
the output dimension (i.e., dimension of the feature space the input is mapped
to). Each entry of `Omega` is sampled i.i.d. from a (scaled) Gaussian
distribution and each entry of `b` is sampled independently and uniformly from
[0, 2 * pi].
For a single input feature vector x in R^d, its RFFM is defined as:
```
sqrt(2/D) * cos(x * Omega + b)
```
where `cos` is the element-wise cosine function and `x, b` are represented as
row vectors. The aforementioned paper shows that the linear kernel of
RFFM-mapped vectors approximates the Gaussian kernel of the initial vectors.
"""
def __init__(self, input_dim, output_dim, stddev=1.0, seed=1, name=None):
"""Constructs a RandomFourierFeatureMapper instance.
Args:
input_dim: The dimension (number of features) of the tensors to be mapped.
output_dim: The output dimension of the mapping.
stddev: The standard deviation of the Gaussian kernel to be approximated.
The error of the classifier trained using this approximation is very
sensitive to this parameter.
seed: An integer used to initialize the parameters (`Omega` and `b`) of
the mapper. For repeatable sequences across different invocations of the
mapper object (for instance, to ensure consistent mapping both at
training and eval/inference if these happen in different invocations),
set this to the same integer.
name: name for the mapper object.
"""
# TODO(sibyl-vie3Poto): Maybe infer input_dim and/or output_dim (if not explicitly
# provided). input_dim can be inferred lazily, the first time map is called.
# output_dim can be inferred from input_dim using heuristics on the error of
# the approximation (and, by extension, the error of the classification
# based on the approximation).
self._input_dim = input_dim
self._output_dim = output_dim
self._stddev = stddev
self._seed = seed
self._name = name
@property
def name(self):
"""Returns a name for the `RandomFourierFeatureMapper` instance.
If the name provided in the constructor is `None`, then the object's unique
id is returned.
Returns:
A name for the `RandomFourierFeatureMapper` instance.
"""
return self._name or str(id(self))
@property
def input_dim(self):
return self._input_dim
@property
def output_dim(self):
return self._output_dim
def map(self, input_tensor):
"""Maps each row of input_tensor using random Fourier features.
Args:
input_tensor: a `Tensor` containing input features. It's shape is
[batch_size, self._input_dim].
Returns:
A `Tensor` of shape [batch_size, self._output_dim] containing RFFM-mapped
features.
Raises:
InvalidShapeError: if the shape of the `input_tensor` is inconsistent with
expected input dimension.
"""
input_tensor_shape = input_tensor.get_shape()
if len(input_tensor_shape) != 2:
raise dkm.InvalidShapeError(
'The shape of the tensor should be 2. Got %d instead.' %
len(input_tensor_shape))
features_dim = input_tensor_shape[1]
if features_dim != self._input_dim:
raise dkm.InvalidShapeError(
'Invalid dimension: expected %d input features, got %d instead.' %
(self._input_dim, features_dim))
# Add ops that compute (deterministically) omega_matrix and bias based on
# the provided seed.
# TODO(sibyl-vie3Poto): Storing the mapper's parameters (omega_matrix and bias) as
# constants incurs no RPC calls to the parameter server during distributed
# training. However, if the parameters grow too large (for instance if they
# don't fit into memory or if they blow up the size of the GraphDef proto),
# stroring them as constants is no longer an option. In this case, we should
# have a heuristic to choose out of one of the following alternatives:
# a) store them as variables (in the parameter server)
# b) store them as worker local variables
# c) generating on the fly the omega matrix at each step
np.random.seed(self._seed)
omega_matrix_shape = [self._input_dim, self._output_dim]
bias_shape = [self._output_dim]
omega_matrix = constant_op.constant(
np.random.normal(
scale=1.0 / self._stddev, size=omega_matrix_shape),
dtype=dtypes.float32)
bias = constant_op.constant(
np.random.uniform(
low=0.0, high=2 * np.pi, size=bias_shape),
dtype=dtypes.float32)
x_omega_plus_bias = math_ops.add(
math_ops.matmul(input_tensor, omega_matrix), bias)
return math.sqrt(2.0 / self._output_dim) * math_ops.cos(x_omega_plus_bias)