# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see .
#
# Copyright(C) 2013-2019 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
from .. import utilities
from ..linearization import Linearization
from ..operators.energy_operators import StandardHamiltonian
from ..probing import approximation2endo
from ..sugar import makeOp
from .energy import Energy
class MetricGaussianKL(Energy):
"""Provides the sampled Kullback-Leibler divergence between a distribution
and a Metric Gaussian.
A Metric Gaussian is used to approximate another probability distribution.
It is a Gaussian distribution that uses the Fisher information metric of
the other distribution at the location of its mean to approximate the
variance. In order to infer the mean, a stochastic estimate of the
Kullback-Leibler divergence is minimized. This estimate is obtained by
sampling the Metric Gaussian at the current mean. During minimization
these samples are kept constant; only the mean is updated. Due to the
typically nonlinear structure of the true distribution these samples have
to be updated eventually by intantiating `MetricGaussianKL` again. For the
true probability distribution the standard parametrization is assumed.
Parameters
----------
mean : Field
Mean of the Gaussian probability distribution.
hamiltonian : StandardHamiltonian
Hamiltonian of the approximated probability distribution.
n_samples : integer
Number of samples used to stochastically estimate the KL.
constants : list
List of parameter keys that are kept constant during optimization.
Default is no constants.
point_estimates : list
List of parameter keys for which no samples are drawn, but that are
(possibly) optimized for, corresponding to point estimates of these.
Default is to draw samples for the complete domain.
mirror_samples : boolean
Whether the negative of the drawn samples are also used,
as they are equally legitimate samples. If true, the number of used
samples doubles. Mirroring samples stabilizes the KL estimate as
extreme sample variation is counterbalanced. Default is False.
napprox : int
Number of samples for computing preconditioner for sampling. No
preconditioning is done by default.
_samples : None
Only a parameter for internal uses. Typically not to be set by users.
Note
----
The two lists `constants` and `point_estimates` are independent from each
other. It is possible to sample along domains which are kept constant
during minimization and vice versa.
See also
--------
`Metric Gaussian Variational Inference`, Jakob Knollmüller,
Torsten A. Enßlin, ``_
"""
def __init__(self, mean, hamiltonian, n_samples, constants=[],
point_estimates=[], mirror_samples=False,
napprox=0, _samples=None):
super(MetricGaussianKL, self).__init__(mean)
if not isinstance(hamiltonian, StandardHamiltonian):
raise TypeError
if hamiltonian.domain is not mean.domain:
raise ValueError
if not isinstance(n_samples, int):
raise TypeError
self._constants = list(constants)
self._point_estimates = list(point_estimates)
if not isinstance(mirror_samples, bool):
raise TypeError
self._hamiltonian = hamiltonian
if _samples is None:
met = hamiltonian(Linearization.make_partial_var(
mean, point_estimates, True)).metric
if napprox > 1:
met._approximation = makeOp(approximation2endo(met, napprox))
_samples = tuple(met.draw_sample(from_inverse=True)
for _ in range(n_samples))
if mirror_samples:
_samples += tuple(-s for s in _samples)
self._samples = _samples
# FIXME Use simplify for constant input instead
self._lin = Linearization.make_partial_var(mean, constants)
v, g = None, None
for s in self._samples:
tmp = self._hamiltonian(self._lin+s)
if v is None:
v = tmp.val.local_data[()]
g = tmp.gradient
else:
v += tmp.val.local_data[()]
g = g + tmp.gradient
self._val = v / len(self._samples)
self._grad = g * (1./len(self._samples))
self._metric = None
self._napprox = napprox
def at(self, position):
return MetricGaussianKL(position, self._hamiltonian, 0,
self._constants, self._point_estimates,
napprox=self._napprox, _samples=self._samples)
@property
def value(self):
return self._val
@property
def gradient(self):
return self._grad
def _get_metric(self):
if self._metric is None:
lin = self._lin.with_want_metric()
mymap = map(lambda v: self._hamiltonian(lin+v).metric,
self._samples)
self._unscaled_metric = utilities.my_sum(mymap)
self._metric = self._unscaled_metric.scale(1./len(self._samples))
def unscaled_metric(self):
self._get_metric()
return self._unscaled_metric, 1/len(self._samples)
def apply_metric(self, x):
self._get_metric()
return self._metric(x)
@property
def metric(self):
self._get_metric()
return self._metric
@property
def samples(self):
return self._samples
def __repr__(self):
return 'KL ({} samples):\n'.format(len(
self._samples)) + utilities.indent(self._hamiltonian.__repr__())