FM / distributions

/usr/local/lib64/python3.6/site-packages/torch/distributions/

/usr/local/lib64/python3.6/site-packages/torch/distributions

Name	Size	Mode	Actions
__pycache__/	-	0755	rm
bernoulli.py	3904	0644	edit dl rm
beta.py	3406	0644	edit dl rm
binomial.py	5179	0644	edit dl rm
categorical.py	5488	0644	edit dl rm
cauchy.py	2714	0644	edit dl rm
chi2.py	909	0644	edit dl rm
constraints.py	17288	0644	edit dl rm
constraint_registry.py	10234	0644	edit dl rm
continuous_bernoulli.py	8532	0644	edit dl rm
dirichlet.py	3584	0644	edit dl rm
distribution.py	11735	0644	edit dl rm
exponential.py	2525	0644	edit dl rm
exp_family.py	2275	0644	edit dl rm
fishersnedecor.py	3152	0644	edit dl rm
gamma.py	3121	0644	edit dl rm
geometric.py	4266	0644	edit dl rm
gumbel.py	2528	0644	edit dl rm
half_cauchy.py	2257	0644	edit dl rm
half_normal.py	2058	0644	edit dl rm
independent.py	4361	0644	edit dl rm
kl.py	29998	0644	edit dl rm
kumaraswamy.py	2927	0644	edit dl rm
laplace.py	3054	0644	edit dl rm
lkj_cholesky.py	6124	0644	edit dl rm
logistic_normal.py	1983	0644	edit dl rm
log_normal.py	1772	0644	edit dl rm
lowrank_multivariate_normal.py	9930	0644	edit dl rm
mixture_same_family.py	8636	0644	edit dl rm
multinomial.py	4776	0644	edit dl rm
multivariate_normal.py	10548	0644	edit dl rm
negative_binomial.py	4091	0644	edit dl rm
normal.py	3351	0644	edit dl rm
one_hot_categorical.py	4375	0644	edit dl rm
pareto.py	2057	0644	edit dl rm
poisson.py	2066	0644	edit dl rm
relaxed_bernoulli.py	5360	0644	edit dl rm
relaxed_categorical.py	5202	0644	edit dl rm
studentT.py	3550	0644	edit dl rm
transformed_distribution.py	8270	0644	edit dl rm
transforms.py	38408	0644	edit dl rm
uniform.py	3112	0644	edit dl rm
utils.py	6196	0644	edit dl rm
von_mises.py	5091	0644	edit dl rm
weibull.py	2854	0644	edit dl rm
__init__.py	5884	0644	edit dl rm

Edit: /usr/local/lib64/python3.6/site-packages/torch/distributions/__init__.py (5884B)

r"""
The ``distributions`` package contains parameterizable probability distributions
and sampling functions. This allows the construction of stochastic computation
graphs and stochastic gradient estimators for optimization. This package
generally follows the design of the `TensorFlow Distributions`_ package.

.. _`TensorFlow Distributions`:
    https://arxiv.org/abs/1711.10604

It is not possible to directly backpropagate through random samples. However,
there are two main methods for creating surrogate functions that can be
backpropagated through. These are the score function estimator/likelihood ratio
estimator/REINFORCE and the pathwise derivative estimator. REINFORCE is commonly
seen as the basis for policy gradient methods in reinforcement learning, and the
pathwise derivative estimator is commonly seen in the reparameterization trick
in variational autoencoders. Whilst the score function only requires the value
of samples :math:`f(x)`, the pathwise derivative requires the derivative
:math:`f'(x)`. The next sections discuss these two in a reinforcement learning
example. For more details see
`Gradient Estimation Using Stochastic Computation Graphs`_ .

.. _`Gradient Estimation Using Stochastic Computation Graphs`:
     https://arxiv.org/abs/1506.05254

Score function
^^^^^^^^^^^^^^

When the probability density function is differentiable with respect to its
parameters, we only need :meth:`~torch.distributions.Distribution.sample` and
:meth:`~torch.distributions.Distribution.log_prob` to implement REINFORCE:

.. math::

\Delta\theta  = \alpha r \frac{\partial\log p(a|\pi^\theta(s))}{\partial\theta}

where :math:`\theta` are the parameters, :math:`\alpha` is the learning rate,
:math:`r` is the reward and :math:`p(a|\pi^\theta(s))` is the probability of
taking action :math:`a` in state :math:`s` given policy :math:`\pi^\theta`.

In practice we would sample an action from the output of a network, apply this
action in an environment, and then use ``log_prob`` to construct an equivalent
loss function. Note that we use a negative because optimizers use gradient
descent, whilst the rule above assumes gradient ascent. With a categorical
policy, the code for implementing REINFORCE would be as follows::

probs = policy_network(state)
    # Note that this is equivalent to what used to be called multinomial
    m = Categorical(probs)
    action = m.sample()
    next_state, reward = env.step(action)
    loss = -m.log_prob(action) * reward
    loss.backward()

Pathwise derivative
^^^^^^^^^^^^^^^^^^^

The other way to implement these stochastic/policy gradients would be to use the
reparameterization trick from the
:meth:`~torch.distributions.Distribution.rsample` method, where the
parameterized random variable can be constructed via a parameterized
deterministic function of a parameter-free random variable. The reparameterized
sample therefore becomes differentiable. The code for implementing the pathwise
derivative would be as follows::

params = policy_network(state)
    m = Normal(*params)
    # Any distribution with .has_rsample == True could work based on the application
    action = m.rsample()
    next_state, reward = env.step(action)  # Assuming that reward is differentiable
    loss = -reward
    loss.backward()
"""

from .bernoulli import Bernoulli
from .beta import Beta
from .binomial import Binomial
from .categorical import Categorical
from .cauchy import Cauchy
from .chi2 import Chi2
from .constraint_registry import biject_to, transform_to
from .continuous_bernoulli import ContinuousBernoulli
from .dirichlet import Dirichlet
from .distribution import Distribution
from .exp_family import ExponentialFamily
from .exponential import Exponential
from .fishersnedecor import FisherSnedecor
from .gamma import Gamma
from .geometric import Geometric
from .gumbel import Gumbel
from .half_cauchy import HalfCauchy
from .half_normal import HalfNormal
from .independent import Independent
from .kl import kl_divergence, register_kl
from .kumaraswamy import Kumaraswamy
from .laplace import Laplace
from .lkj_cholesky import LKJCholesky
from .log_normal import LogNormal
from .logistic_normal import LogisticNormal
from .lowrank_multivariate_normal import LowRankMultivariateNormal
from .mixture_same_family import MixtureSameFamily
from .multinomial import Multinomial
from .multivariate_normal import MultivariateNormal
from .negative_binomial import NegativeBinomial
from .normal import Normal
from .one_hot_categorical import OneHotCategorical, OneHotCategoricalStraightThrough
from .pareto import Pareto
from .poisson import Poisson
from .relaxed_bernoulli import RelaxedBernoulli
from .relaxed_categorical import RelaxedOneHotCategorical
from .studentT import StudentT
from .transformed_distribution import TransformedDistribution
from .transforms import *  # noqa: F403
from .uniform import Uniform
from .von_mises import VonMises
from .weibull import Weibull
from . import transforms

__all__ = [
    'Bernoulli',
    'Beta',
    'Binomial',
    'Categorical',
    'Cauchy',
    'Chi2',
    'ContinuousBernoulli',
    'Dirichlet',
    'Distribution',
    'Exponential',
    'ExponentialFamily',
    'FisherSnedecor',
    'Gamma',
    'Geometric',
    'Gumbel',
    'HalfCauchy',
    'HalfNormal',
    'Independent',
    'Kumaraswamy',
    'LKJCholesky',
    'Laplace',
    'LogNormal',
    'LogisticNormal',
    'LowRankMultivariateNormal',
    'MixtureSameFamily',
    'Multinomial',
    'MultivariateNormal',
    'NegativeBinomial',
    'Normal',
    'OneHotCategorical',
    'OneHotCategoricalStraightThrough',
    'Pareto',
    'RelaxedBernoulli',
    'RelaxedOneHotCategorical',
    'StudentT',
    'Poisson',
    'Uniform',
    'VonMises',
    'Weibull',
    'TransformedDistribution',
    'biject_to',
    'kl_divergence',
    'register_kl',
    'transform_to',
]
__all__.extend(transforms.__all__)

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