metric_gaussian_kl.py 5.39 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
# 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 <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2019 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.

from .. import utilities
Philipp Arras's avatar
Philipp Arras committed
19
20
21
from ..linearization import Linearization
from ..operators.energy_operators import StandardHamiltonian
from .energy import Energy
22
23
24


class MetricGaussianKL(Energy):
Martin Reinecke's avatar
Martin Reinecke committed
25
26
27
28
29
30
31
32
33
34
35
36
37
    """Provides the sampled Kullback-Leibler divergence between a distribution
    and a Metric Gaussian.

    A Metric Gaussian is used to approximate some other 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, the a stochastic estimate of the
    Kullback-Leibler divergence is minimized. This estimate is obtained by
    drawing samples from the Metric Gaussian at the current mean.
    During minimization these samples are kept constant, updating only the
    mean. Due to the typically nonlinear structure of the true distribution
    these samples have to be updated by re-initializing this class at some
    point. Here standard parametrization of the true distribution is assumed.
38
39
40
41
42

    Parameters
    ----------
    mean : Field
        The current mean of the Gaussian.
Jakob Knollmueller's avatar
Jakob Knollmueller committed
43
44
    hamiltonian : StandardHamiltonian
        The StandardHamiltonian of the approximated probability distribution.
45
46
47
48
49
50
51
52
53
54
55
56
    n_samples : integer
        The number of samples used to stochastically estimate the KL.
    constants : list
        A list of parameter keys that are kept constant during optimization.
    point_estimates : list
        A list of parameter keys for which no samples are drawn, but that are
        optimized for, corresponding to point estimates of these.
    mirror_samples : boolean
        Whether the negative of the drawn samples are also used,
        as they are equaly legitimate samples. If true, the number of used
        samples doubles. Mirroring samples stabilizes the KL estimate as
        extreme sample variation is counterbalanced. (default : False)
Philipp Arras's avatar
Philipp Arras committed
57
58
    _samples : None
        Only a parameter for internal uses. Typically not to be set by users.
59
60
61

    Notes
    -----
Martin Reinecke's avatar
Martin Reinecke committed
62
    For further details see: Metric Gaussian Variational Inference
Philipp Arras's avatar
Docs    
Philipp Arras committed
63
    (FIXME in preparation)
64
65
    """

Martin Reinecke's avatar
typo    
Martin Reinecke committed
66
    def __init__(self, mean, hamiltonian, n_samples, constants=[],
Philipp Arras's avatar
Philipp Arras committed
67
                 point_estimates=[], mirror_samples=False,
68
69
                 _samples=None):
        super(MetricGaussianKL, self).__init__(mean)
Philipp Arras's avatar
Philipp Arras committed
70
71
72

        if not isinstance(hamiltonian, StandardHamiltonian):
            raise TypeError
73
        if hamiltonian.domain is not mean.domain:
Philipp Arras's avatar
Philipp Arras committed
74
75
76
77
78
79
            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):
80
            raise TypeError
Philipp Arras's avatar
Philipp Arras committed
81

82
        self._hamiltonian = hamiltonian
Philipp Arras's avatar
Philipp Arras committed
83

84
85
86
87
        if _samples is None:
            met = hamiltonian(Linearization.make_partial_var(
                mean, point_estimates, True)).metric
            _samples = tuple(met.draw_sample(from_inverse=True)
Martin Reinecke's avatar
typo    
Martin Reinecke committed
88
                             for _ in range(n_samples))
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
            if mirror_samples:
                _samples += tuple(-s for s in _samples)
        self._samples = _samples

        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

    def at(self, position):
        return MetricGaussianKL(position, self._hamiltonian, 0,
Philipp Arras's avatar
Philipp Arras committed
109
                                self._constants, self._point_estimates,
110
111
112
113
114
115
116
117
118
119
120
121
122
                                _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()
Martin Reinecke's avatar
Martin Reinecke committed
123
124
            mymap = map(lambda v: self._hamiltonian(lin+v).metric,
                        self._samples)
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
            self._metric = utilities.my_sum(mymap)
            self._metric = self._metric.scale(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(
Philipp Arras's avatar
Philipp Arras committed
143
            self._samples)) + utilities.indent(self._hamiltonian.__repr__())