mean_functions.py
# Copyright 2016 James Hensman, alexggmatthews, PabloLeon, Valentine Svensson
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
r"""
Throughout GPflow, by default, latent functions being modelled with Gaussian
processes are assumed to have zero mean, f ~ GP(0, k(x,x')).

In some cases we may wish to model only the deviation from a fixed function
with a Gaussian process.  For flexibility this fixed function could be both
input dependent and parameterised function, μ(x; θ),
with some unknown parameters θ, resulting in f ~ GP(μ(x;θ), k(x,x')).

The GPflow :class:`MeanFunction <gpflow.mean_functions.MeanFunction>` class
allows this to be done whilst additionally learning parameters of the
parametric function.
"""

import tensorflow as tf
import numpy as np

from . import settings
from .params import Parameter
from .params import Parameterized
from .params import ParamList
from .decors import params_as_tensors

class MeanFunction(Parameterized):
"""
The base mean function class.
To implement a mean function, write the __call__ method. This takes a
tensor X and returns a tensor m(X). In accordance with the GPflow
standard, each row of X represents one datum, and each row of Y is computed
independently for each row of X.

MeanFunction classes can have parameters, see the Linear class for an
example.
"""
def __call__(self, X):
raise NotImplementedError("Implement the __call__ method for this mean function")

def __mul__(self, other):
return Product(self, other)

class Linear(MeanFunction):
"""
y_i = A x_i + b
"""
def __init__(self, A=None, b=None):
"""
A is a matrix which maps each element of X to Y, b is an additive
constant.

If X has N rows and D columns, and Y is intended to have Q columns,
then A must be D x Q, b must be a vector of length Q.
"""
A = np.ones((1, 1)) if A is None else A
b = np.zeros(1) if b is None else b
MeanFunction.__init__(self)
self.A = Parameter(np.atleast_2d(A), dtype=settings.float_type)
self.b = Parameter(b, dtype=settings.float_type)

@params_as_tensors
def __call__(self, X):
return tf.tensordot(X, self.A, [[-1], ]) + self.b

class Identity(Linear):
"""
y_i = x_i
"""
def __init__(self, input_dim=None):
Linear.__init__(self)
self.input_dim = input_dim

def __call__(self, X):
return X

@property
def A(self):
if self.input_dim is None:
raise ValueError("An input_dim needs to be specified when using the "
"`Identity` mean function in combination with expectations.")

return tf.eye(self.input_dim, dtype=settings.float_type)

@property
def b(self):
if self.input_dim is None:
raise ValueError("An input_dim needs to be specified when using the "
"`Identity` mean function in combination with expectations.")

return tf.zeros(self.input_dim, dtype=settings.float_type)

@A.setter
def A(self, A):
pass

@b.setter
def b(self, b):
pass

class Constant(MeanFunction):
"""
y_i = c,,
"""
def __init__(self, c=None):
MeanFunction.__init__(self)
c = np.zeros(1) if c is None else c
c = np.reshape(c, (1, -1))
self.c = Parameter(c)

@params_as_tensors
def __call__(self, X):
shape = tf.stack([tf.shape(X), 1])
return tf.tile(self.c, shape)

class Zero(Constant):
def __init__(self, output_dim=1):
Constant.__init__(self)
self.output_dim = output_dim
del self.c

def __call__(self, X):
shape = tf.concat([tf.shape(X)[:-1], [self.output_dim]], 0)
return tf.zeros(shape, dtype=settings.float_type)

class SwitchedMeanFunction(MeanFunction):
"""
This class enables to use different (independent) mean_functions respective
to the data 'label'.
We assume the 'label' is stored in the extra column of X.
"""
def __init__(self, meanfunction_list):
MeanFunction.__init__(self)
for m in meanfunction_list:
assert isinstance(m, MeanFunction)
self.meanfunction_list = ParamList(meanfunction_list)

@params_as_tensors
def __call__(self, X):
ind = tf.gather(tf.transpose(X), tf.shape(X)-1)  # ind = X[:,-1]
ind = tf.cast(ind, tf.int32)
X = tf.transpose(tf.gather(tf.transpose(X), tf.range(0, tf.shape(X)-1)))  # X = X[:,:-1]

# split up X into chunks corresponding to the relevant likelihoods
x_list = tf.dynamic_partition(X, ind, len(self.meanfunction_list))
# apply the likelihood-function to each section of the data
results = [m(x) for x, m in zip(x_list, self.meanfunction_list)]
# stitch the results back together
partitions = tf.dynamic_partition(tf.range(0, tf.size(ind)), ind, len(self.meanfunction_list))
return tf.dynamic_stitch(partitions, results)

def __init__(self, first_part, second_part):
MeanFunction.__init__(self)

def __call__(self, X):