# 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.val[()] g = tmp.gradient else: v += tmp.val.val[()] 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__())