Commit c3e36189 by Martin Reinecke

### Merge branch 'NIFTy_5' into operator_spectra

parents 548b5690 f66235b7
 ... ... @@ -190,8 +190,8 @@ class NewtonCG(DescentMinimizer): e = QuadraticEnergy(0*energy.position, energy.metric, energy.gradient) p = None if self._napprox > 1: unscmet, sc = energy.unscaled_metric() p = makeOp(approximation2endo(unscmet, self._napprox)*sc).inverse met = energy.metric p = makeOp(approximation2endo(met, self._napprox)).inverse e, conv = ConjugateGradient(ic, nreset=self._nreset)(e, p) return -e.position ... ...
 ... ... @@ -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, full 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): return 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, ``_ """ 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 = full(self._hamiltonian.domain, 0.) for v in self._samples: samp = samp + self._hamiltonian(lin+v).metric.draw_sample(from_inverse=False, dtype=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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