# 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) 2013-2021 Max-Planck-Society
# Authors: Philipp Frank, Philipp Arras
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
from functools import reduce
import numpy as np
from .. import random, utilities
from ..domain_tuple import DomainTuple
from ..linearization import Linearization
from ..multi_field import MultiField
from ..operators.adder import Adder
from ..operators.endomorphic_operator import EndomorphicOperator
from ..operators.energy_operators import GaussianEnergy, StandardHamiltonian
from ..operators.inversion_enabler import InversionEnabler
from ..operators.sampling_enabler import SamplingDtypeSetter
from ..operators.sandwich_operator import SandwichOperator
from ..operators.scaling_operator import ScalingOperator
from ..probing import approximation2endo
from ..sugar import makeOp
from ..utilities import myassert
from .descent_minimizers import ConjugateGradient, DescentMinimizer
from .energy import Energy
from .energy_adapter import EnergyAdapter
from .quadratic_energy import QuadraticEnergy
def _get_lo_hi(comm, n_samples):
ntask, rank, _ = utilities.get_MPI_params_from_comm(comm)
return utilities.shareRange(n_samples, ntask, rank)
def _modify_sample_domain(sample, domain):
"""Takes only keys from sample which are also in domain and inserts zeros
for keys which are not in sample.domain."""
from ..domain_tuple import DomainTuple
from ..field import Field
from ..multi_domain import MultiDomain
from ..sugar import makeDomain
domain = makeDomain(domain)
if isinstance(domain, DomainTuple) and isinstance(sample, Field):
if sample.domain is not domain:
raise TypeError
return sample
elif isinstance(domain, MultiDomain) and isinstance(sample, MultiField):
if sample.domain is domain:
return sample
out = {kk: vv for kk, vv in sample.items() if kk in domain.keys()}
out = MultiField.from_dict(out, domain)
return out
raise TypeError
def _reduce_by_keys(field, operator, keys):
"""Partially insert a field into an operator
If the domain of the operator is an instance of `DomainTuple`
Parameters
----------
field : Field or MultiField
Potentially partially constant input field.
operator : Operator
Operator into which `field` is partially inserted.
keys : list
List of constant `MultiDomain` entries.
Returns
-------
list
The variable part of the field and the contracted operator.
"""
from ..sugar import is_fieldlike, is_operator
myassert(is_fieldlike(field))
myassert(is_operator(operator))
if isinstance(field, MultiField):
cst_field = field.extract_by_keys(keys)
var_field = field.extract_by_keys(set(field.keys()) - set(keys))
_, new_ham = operator.simplify_for_constant_input(cst_field)
return var_field, new_ham
myassert(len(keys) == 0)
return field, operator
class _SelfAdjointOperatorWrapper(EndomorphicOperator):
def __init__(self, domain, func):
from ..sugar import makeDomain
self._func = func
self._capability = self.TIMES | self.ADJOINT_TIMES
self._domain = makeDomain(domain)
def apply(self, x, mode):
self._check_input(x, mode)
return self._func(x)
class _SampledKLEnergy(Energy):
"""Base class for Energies representing a sampled Kullback-Leibler
divergence for the variational approximation of a distribution with another
distribution.
Supports the samples to be distributed across MPI tasks."""
def __init__(self, mean, hamiltonian, n_samples, mirror_samples, comm,
local_samples, nanisinf):
super(_SampledKLEnergy, self).__init__(mean)
myassert(mean.domain is hamiltonian.domain)
self._hamiltonian = hamiltonian
self._n_samples = int(n_samples)
self._mirror_samples = bool(mirror_samples)
self._comm = comm
self._local_samples = local_samples
self._nanisinf = bool(nanisinf)
lin = Linearization.make_var(mean)
v, g = [], []
for s in self._local_samples:
s = _modify_sample_domain(s, mean.domain)
tmp = hamiltonian(lin+s)
tv = tmp.val.val
tg = tmp.gradient
if mirror_samples:
tmp = hamiltonian(lin-s)
tv = tv + tmp.val.val
tg = tg + tmp.gradient
v.append(tv)
g.append(tg)
self._val = utilities.allreduce_sum(v, self._comm)[()]/self.n_eff_samples
if np.isnan(self._val) and self._nanisinf:
self._val = np.inf
self._grad = utilities.allreduce_sum(g, self._comm)/self.n_eff_samples
@property
def value(self):
return self._val
@property
def gradient(self):
return self._grad
def at(self, position):
return _SampledKLEnergy(
position, self._hamiltonian, self._n_samples, self._mirror_samples,
self._comm, self._local_samples, self._nanisinf)
def apply_metric(self, x):
lin = Linearization.make_var(self.position, want_metric=True)
res = []
for s in self._local_samples:
s = _modify_sample_domain(s, self._hamiltonian.domain)
tmp = self._hamiltonian(lin+s).metric(x)
if self._mirror_samples:
tmp = tmp + self._hamiltonian(lin-s).metric(x)
res.append(tmp)
return utilities.allreduce_sum(res, self._comm)/self.n_eff_samples
@property
def n_eff_samples(self):
if self._mirror_samples:
return 2*self._n_samples
return self._n_samples
@property
def metric(self):
return _SelfAdjointOperatorWrapper(self.position.domain,
self.apply_metric)
@property
def samples(self):
ntask, rank, _ = utilities.get_MPI_params_from_comm(self._comm)
if ntask == 1:
for s in self._local_samples:
yield s
if self._mirror_samples:
yield -s
else:
rank_lo_hi = [utilities.shareRange(self._n_samples, ntask, i) for i in range(ntask)]
lo, _ = _get_lo_hi(self._comm, self._n_samples)
for itask, (l, h) in enumerate(rank_lo_hi):
for i in range(l, h):
data = self._local_samples[i-lo] if rank == itask else None
s = self._comm.bcast(data, root=itask)
yield s
if self._mirror_samples:
yield -s
class _MetricGaussianSampler:
def __init__(self, position, H, n_samples, mirror_samples, napprox=0):
if not isinstance(H, StandardHamiltonian):
raise NotImplementedError
lin = Linearization.make_var(position.extract(H.domain), True)
self._met = H(lin).metric
if napprox >= 1:
self._met._approximation = makeOp(approximation2endo(self._met, napprox))
self._n = int(n_samples)
def draw_samples(self, comm):
local_samples = []
sseq = random.spawn_sseq(self._n)
for i in range(*_get_lo_hi(comm, self._n)):
with random.Context(sseq[i]):
local_samples.append(self._met.draw_sample(from_inverse=True))
return tuple(local_samples)
class _GeoMetricSampler:
def __init__(self, position, H, minimizer, start_from_lin,
n_samples, mirror_samples, napprox=0, want_error=False):
if not isinstance(H, StandardHamiltonian):
raise NotImplementedError
# Check domain dtype
dts = H._prior._met._dtype
if isinstance(H.domain, DomainTuple):
real = np.issubdtype(dts, np.floating)
else:
real = all([np.issubdtype(dts[kk], np.floating) for kk in dts.keys()])
if not real:
raise ValueError("_GeoMetricSampler only supports real valued latent DOFs.")
# /Check domain dtype
if isinstance(position, MultiField):
self._position = position.extract(H.domain)
else:
self._position = position
tr = H._lh.get_transformation()
if tr is None:
raise ValueError("_GeoMetricSampler only works for likelihoods")
dtype, f_lh = tr
scale = ScalingOperator(f_lh.target, 1.)
if isinstance(dtype, dict):
sampling = reduce((lambda a,b: a*b),
[dtype[k] is not None for k in dtype.keys()])
else:
sampling = dtype is not None
scale = SamplingDtypeSetter(scale, dtype) if sampling else scale
fl = f_lh(Linearization.make_var(self._position))
self._g = (Adder(-self._position) + fl.jac.adjoint@Adder(-fl.val)@f_lh)
self._likelihood = SandwichOperator.make(fl.jac, scale)
self._prior = SamplingDtypeSetter(ScalingOperator(fl.domain,1.), np.float64)
self._met = self._likelihood + self._prior
if napprox >= 1:
self._approximation = makeOp(approximation2endo(self._met, napprox)).inverse
else:
self._approximation = None
self._ic = H._ic_samp
self._minimizer = minimizer
self._start_from_lin = start_from_lin
self._want_error = want_error
sseq = random.spawn_sseq(n_samples)
if mirror_samples:
mysseq = []
for seq in sseq:
mysseq += [seq, seq]
else:
mysseq = sseq
self._sseq = mysseq
self._neg = (False, True)*n_samples if mirror_samples else (False, )*n_samples
self._n_samples = n_samples
self._mirror_samples = mirror_samples
@property
def n_eff_samples(self):
return 2*self._n_samples if self._mirror_samples else self._n_samples
@property
def position(self):
return self._position
def _draw_lin(self, neg):
s = self._prior.draw_sample(from_inverse=True)
s = -s if neg else s
nj = self._likelihood.draw_sample()
nj = -nj if neg else nj
y = self._prior(s) + nj
if self._start_from_lin:
energy = QuadraticEnergy(s, self._met, y,
_grad=self._likelihood(s) - nj)
inverter = ConjugateGradient(self._ic)
energy, convergence = inverter(energy,
preconditioner=self._approximation)
yi = energy.position
else:
yi = s
return y, yi
def _draw_nonlin(self, y, yi):
en = EnergyAdapter(self._position+yi, GaussianEnergy(mean=y)@self._g,
nanisinf=True, want_metric=True)
en, _ = self._minimizer(en)
sam = en.position - self._position
if self._want_error:
er = y - self._g(sam)
er = er.s_vdot(InversionEnabler(self._met, self._ic).inverse(er))
return sam, er
return sam
def draw_samples(self, comm):
local_samples = []
prev = None
for i in range(*_get_lo_hi(comm, self.n_eff_samples)):
with random.Context(self._sseq[i]):
neg = self._neg[i]
if (prev is None) or not self._mirror_samples:
y, yi = self._draw_lin(neg)
if not neg:
prev = (-y, -yi)
else:
(y, yi) = prev
prev = None
local_samples.append(self._draw_nonlin(y, yi))
return tuple(local_samples)
def MetricGaussianKL(mean, hamiltonian, n_samples, mirror_samples, constants=[],
point_estimates=[], napprox=0, comm=None, nanisinf=False):
"""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 can be 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.
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. Since it improves stability in
many cases, it is recommended to set `mirror_samples` to `True`.
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.
napprox : int
Number of samples for computing preconditioner for sampling. No
preconditioning is done by default.
comm : MPI communicator or None
If not None, samples will be distributed as evenly as possible
across this communicator. If `mirror_samples` is set, then a sample and
its mirror image will always reside on the same task.
nanisinf : bool
If true, nan energies which can happen due to overflows in the forward
model are interpreted as inf. Thereby, the code does not crash on
these occasions but rather the minimizer is told that the position it
has tried is not sensible.
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, ``_
"""
if not isinstance(hamiltonian, StandardHamiltonian):
raise TypeError
if hamiltonian.domain is not mean.domain:
raise ValueError
if not isinstance(n_samples, int):
raise TypeError
if not isinstance(mirror_samples, bool):
raise TypeError
if isinstance(mean, MultiField) and set(point_estimates) == set(mean.keys()):
raise RuntimeError(
'Point estimates for whole domain. Use EnergyAdapter instead.')
n_samples = int(n_samples)
mirror_samples = bool(mirror_samples)
_, ham_sampling = _reduce_by_keys(mean, hamiltonian, point_estimates)
sampler = _MetricGaussianSampler(mean, ham_sampling, n_samples,
mirror_samples, napprox)
local_samples = sampler.draw_samples(comm)
mean, hamiltonian = _reduce_by_keys(mean, hamiltonian, constants)
return _SampledKLEnergy(mean, hamiltonian, n_samples, mirror_samples, comm,
local_samples, nanisinf)
def GeoMetricKL(mean, hamiltonian, n_samples, minimizer_samp, mirror_samples,
start_from_lin=True, constants=[], point_estimates=[],
napprox=0, comm=None, nanisinf=True):
"""Provides the sampled Kullback-Leibler used in geometric Variational
Inference (geoVI).
In geoVI a probability distribution is approximated with a standard normal
distribution in the canonical coordinate system of the Riemannian manifold
associated with the metric of the other distribution. The coordinate
transformation is approximated by expanding around a point. In order to
infer the expansion point, a stochastic estimate of the Kullback-Leibler
divergence is minimized. This estimate is obtained by sampling from the
approximation using the current expansion point. During minimization these
samples are kept constant; only the expansion point is updated. Due to the
typically nonlinear structure of the true distribution these samples have
to be updated eventually by instantiating `GeoMetricKL` again. For the true
probability distribution the standard parametrization is assumed.
The samples of this class can be distributed among MPI tasks.
Parameters
----------
mean : Field
Expansion point of the coordinate transformation.
hamiltonian : StandardHamiltonian
Hamiltonian of the approximated probability distribution.
n_samples : integer
Number of samples used to stochastically estimate the KL.
minimizer_samp : DescentMinimizer
Minimizer used to draw samples.
mirror_samples : boolean
Whether the mirrored version of the drawn samples are also used.
If true, the number of used samples doubles.
Mirroring samples stabilizes the KL estimate as extreme
sample variation is counterbalanced.
start_from_lin : boolean
Whether the non-linear sampling should start using the inverse
linearized transformation (i.e. the corresponding MGVI sample).
If False, the minimization starts from the prior sample.
Default is True.
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.
napprox : int
Number of samples for computing preconditioner for linear sampling.
No preconditioning is done by default.
comm : MPI communicator or None
If not None, samples will be distributed as evenly as possible
across this communicator. If `mirror_samples` is set, then a sample and
its mirror image will preferably reside on the same task if necessary.
nanisinf : bool
If true, nan energies which can happen due to overflows in the forward
model are interpreted as inf. Thereby, the code does not crash on
these occasions but rather the minimizer is told that the position it
has tried is not sensible.
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.
DomainTuples should never be created using the constructor, but rather
via the factory function :attr:`make`!
Note
----
As in MGVI, mirroring samples can help to stabilize the latent mean as it
reduces sampling noise. But unlike MGVI a mirrored sample involves an
additional solve of the non-linear transformation. Therefore, when using
MPI, the mirrored samples also get distributed if enough tasks are
available. If there are more total samples than tasks, the mirrored
counterparts try to reside on the same task as their non mirrored partners.
This ensures that at least the starting position can be re-used.
See also
--------
`Geometric Variational Inference`, Philipp Frank, Reimar Leike,
Torsten A. Enßlin, ``_
``_
"""
if not isinstance(hamiltonian, StandardHamiltonian):
raise TypeError
if hamiltonian.domain is not mean.domain:
raise ValueError
if not isinstance(n_samples, int):
raise TypeError
if not isinstance(mirror_samples, bool):
raise TypeError
if not isinstance(minimizer_samp, DescentMinimizer):
raise TypeError
if isinstance(mean, MultiField) and set(point_estimates) == set(mean.keys()):
s = 'Point estimates for whole domain. Use EnergyAdapter instead.'
raise RuntimeError(s)
n_samples = int(n_samples)
mirror_samples = bool(mirror_samples)
_, ham_sampling = _reduce_by_keys(mean, hamiltonian, point_estimates)
sampler = _GeoMetricSampler(mean, ham_sampling, minimizer_samp,
start_from_lin, n_samples, mirror_samples,
napprox)
local_samples = sampler.draw_samples(comm)
mean, hamiltonian = _reduce_by_keys(mean, hamiltonian, constants)
return _SampledKLEnergy(mean, hamiltonian, sampler.n_eff_samples, False,
comm, local_samples, nanisinf)