Commit 1f598ab5 authored by Reimar Heinrich Leike's avatar Reimar Heinrich Leike Committed by Martin Reinecke

added metric operator

parent ffc6059b
Pipeline #61335 passed with stages
in 9 minutes and 21 seconds
......@@ -18,9 +18,12 @@
from .. import utilities
from ..linearization import Linearization
from ..operators.energy_operators import StandardHamiltonian
from ..operators.endomorphic_operator import EndomorphicOperator
from .energy import Energy
from mpi4py import MPI
import numpy as np
from ..probing import approximation2endo
from ..sugar import makeOp
from ..field import Field
from ..multi_field import MultiField
......@@ -56,10 +59,83 @@ def allreduce_sum_field(fld):
return MultiField(fld.domain, res)
class KLMetric(EndomorphicOperator):
def __init__(self, KL):
self._KL = KL
self._capability = self.TIMES | self.ADJOINT_TIMES
self._domain = KL.position.domain
def apply(self, x, mode):
self._check_input(x, mode)
return self._KL.apply_metric(x)
def draw_sample(self, from_inverse=False, dtype=np.float64):
self._KL.metric_sample(from_inverse, dtype)
class MetricGaussianKL_MPI(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.
The samples of this class are distributed among MPI tasks.
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.
seed_offset : int
A parameter with which one can controll from which seed the samples
are drawn. Per default, the seed is different for MPI tasks, but the
same every time this class is initialized.
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, `<https://arxiv.org/abs/1901.11033>`_
"""
def __init__(self, mean, hamiltonian, n_samples, constants=[],
point_estimates=[], mirror_samples=False,
_samples=None, seed_offset=0):
napprox=0, _samples=None, seed_offset=0):
super(MetricGaussianKL_MPI, self).__init__(mean)
if not isinstance(hamiltonian, StandardHamiltonian):
......@@ -82,6 +158,8 @@ class MetricGaussianKL_MPI(Energy):
lo, hi = _shareRange(n_samples, ntask, rank)
met = hamiltonian(Linearization.make_partial_var(
mean, point_estimates, True)).metric
if napprox > 1:
met._approximation = makeOp(approximation2endo(met, napprox))
_samples = []
for i in range(lo, hi):
if mirror_samples:
......@@ -142,8 +220,8 @@ class MetricGaussianKL_MPI(Energy):
else:
mymap = map(lambda v: self._hamiltonian(lin+v).metric,
self._samples)
self._metric = utilities.my_sum(mymap)
self._metric = self._metric.scale(1./self._n_samples)
self.unscaled_metric = utilities.my_sum(mymap)
self._metric = self.unscaled_metric.scale(1./self._n_samples)
def apply_metric(self, x):
self._get_metric()
......@@ -151,12 +229,22 @@ class MetricGaussianKL_MPI(Energy):
@property
def metric(self):
if ntask > 1:
raise ValueError("not supported when MPI is active")
return self._metric
return KLMetric(self)
@property
def samples(self):
res = _comm.allgather(self._samples)
res = [item for sublist in res for item in sublist]
return res
def unscaled_metric_sample(self, from_inverse=False, dtype=np.float64):
if from_inverse:
raise NotImplementedError()
lin = self._lin.with_want_metric()
samp = ift.full(self._hamiltonian.domain, 0.)
for s in self._samples:
samp = samp + self._hamiltonian(lin+v).metric.draw_sample(dtype)
return allreduce_sum_field(samp)
def metric_sample(self, from_inverse=False, dtype=np.float64):
return self.unscaled_metric_sample(from_inverse, dtype)/self._n_samples
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