# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0
# The implementation largely follows the design in PyTorch's `torch.distributions`
#
# Copyright (c) 2016- Facebook, Inc (Adam Paszke)
# Copyright (c) 2014- Facebook, Inc (Soumith Chintala)
# Copyright (c) 2011-2014 Idiap Research Institute (Ronan Collobert)
# Copyright (c) 2012-2014 Deepmind Technologies (Koray Kavukcuoglu)
# Copyright (c) 2011-2012 NEC Laboratories America (Koray Kavukcuoglu)
# Copyright (c) 2011-2013 NYU (Clement Farabet)
# Copyright (c) 2006-2010 NEC Laboratories America (Ronan Collobert, Leon Bottou, Iain Melvin, Jason Weston)
# Copyright (c) 2006 Idiap Research Institute (Samy Bengio)
# Copyright (c) 2001-2004 Idiap Research Institute (Ronan Collobert, Samy Bengio, Johnny Mariethoz)
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
from jax import device_put, lax
from jax.dtypes import canonicalize_dtype
from jax.nn import softmax
import jax.numpy as np
import jax.random as random
from jax.scipy.special import expit, gammaln, logsumexp, xlog1py, xlogy
from numpyro.distributions import constraints
from numpyro.distributions.distribution import Distribution
from numpyro.distributions.util import (
binary_cross_entropy_with_logits,
binomial,
categorical,
categorical_logits,
clamp_probs,
get_dtype,
lazy_property,
multinomial,
poisson,
promote_shapes,
sum_rightmost,
validate_sample,
)
from numpyro.util import copy_docs_from
def _to_probs_bernoulli(logits):
return 1 / (1 + np.exp(-logits))
def _to_logits_bernoulli(probs):
ps_clamped = clamp_probs(probs)
return np.log(ps_clamped) - np.log1p(-ps_clamped)
def _to_probs_multinom(logits):
return softmax(logits, axis=-1)
def _to_logits_multinom(probs):
minval = np.finfo(get_dtype(probs)).min
return np.clip(np.log(probs), a_min=minval)
[docs]@copy_docs_from(Distribution)
class BernoulliProbs(Distribution):
arg_constraints = {'probs': constraints.unit_interval}
support = constraints.boolean
def __init__(self, probs, validate_args=None):
self.probs = probs
super(BernoulliProbs, self).__init__(batch_shape=np.shape(self.probs), validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
return random.bernoulli(key, self.probs, shape=sample_shape + self.batch_shape)
@validate_sample
def log_prob(self, value):
return xlogy(value, self.probs) + xlog1py(1 - value, -self.probs)
@property
def mean(self):
return self.probs
@property
def variance(self):
return self.probs * (1 - self.probs)
[docs]@copy_docs_from(Distribution)
class BernoulliLogits(Distribution):
arg_constraints = {'logits': constraints.real}
support = constraints.boolean
def __init__(self, logits=None, validate_args=None):
self.logits = logits
super(BernoulliLogits, self).__init__(batch_shape=np.shape(self.logits), validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
return random.bernoulli(key, self.probs, shape=sample_shape + self.batch_shape)
@validate_sample
def log_prob(self, value):
return -binary_cross_entropy_with_logits(self.logits, value)
[docs] @lazy_property
def probs(self):
return _to_probs_bernoulli(self.logits)
@property
def mean(self):
return self.probs
@property
def variance(self):
return self.probs * (1 - self.probs)
[docs]def Bernoulli(probs=None, logits=None, validate_args=None):
if probs is not None:
return BernoulliProbs(probs, validate_args=validate_args)
elif logits is not None:
return BernoulliLogits(logits, validate_args=validate_args)
else:
raise ValueError('One of `probs` or `logits` must be specified.')
[docs]@copy_docs_from(Distribution)
class BinomialProbs(Distribution):
arg_constraints = {'total_count': constraints.nonnegative_integer,
'probs': constraints.unit_interval}
def __init__(self, probs, total_count=1, validate_args=None):
self.probs, self.total_count = promote_shapes(probs, total_count)
batch_shape = lax.broadcast_shapes(np.shape(probs), np.shape(total_count))
super(BinomialProbs, self).__init__(batch_shape=batch_shape, validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
return binomial(key, self.probs, n=self.total_count, shape=sample_shape + self.batch_shape)
@validate_sample
def log_prob(self, value):
log_factorial_n = gammaln(self.total_count + 1)
log_factorial_k = gammaln(value + 1)
log_factorial_nmk = gammaln(self.total_count - value + 1)
return (log_factorial_n - log_factorial_k - log_factorial_nmk +
xlogy(value, self.probs) + xlog1py(self.total_count - value, -self.probs))
@property
def mean(self):
return np.broadcast_to(self.total_count * self.probs, self.batch_shape)
@property
def variance(self):
return np.broadcast_to(self.total_count * self.probs * (1 - self.probs), self.batch_shape)
@property
def support(self):
return constraints.integer_interval(0, self.total_count)
[docs]@copy_docs_from(Distribution)
class BinomialLogits(Distribution):
arg_constraints = {'total_count': constraints.nonnegative_integer,
'logits': constraints.real}
def __init__(self, logits, total_count=1, validate_args=None):
self.logits, self.total_count = promote_shapes(logits, total_count)
batch_shape = lax.broadcast_shapes(np.shape(logits), np.shape(total_count))
super(BinomialLogits, self).__init__(batch_shape=batch_shape, validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
return binomial(key, self.probs, n=self.total_count, shape=sample_shape + self.batch_shape)
@validate_sample
def log_prob(self, value):
log_factorial_n = gammaln(self.total_count + 1)
log_factorial_k = gammaln(value + 1)
log_factorial_nmk = gammaln(self.total_count - value + 1)
normalize_term = (self.total_count * np.clip(self.logits, 0) +
xlog1py(self.total_count, np.exp(-np.abs(self.logits))) -
log_factorial_n)
return value * self.logits - log_factorial_k - log_factorial_nmk - normalize_term
[docs] @lazy_property
def probs(self):
return _to_probs_bernoulli(self.logits)
@property
def mean(self):
return np.broadcast_to(self.total_count * self.probs, self.batch_shape)
@property
def variance(self):
return np.broadcast_to(self.total_count * self.probs * (1 - self.probs), self.batch_shape)
@property
def support(self):
return constraints.integer_interval(0, self.total_count)
[docs]def Binomial(total_count=1, probs=None, logits=None, validate_args=None):
if probs is not None:
return BinomialProbs(probs, total_count, validate_args=validate_args)
elif logits is not None:
return BinomialLogits(logits, total_count, validate_args=validate_args)
else:
raise ValueError('One of `probs` or `logits` must be specified.')
[docs]@copy_docs_from(Distribution)
class CategoricalProbs(Distribution):
arg_constraints = {'probs': constraints.simplex}
def __init__(self, probs, validate_args=None):
if np.ndim(probs) < 1:
raise ValueError("`probs` parameter must be at least one-dimensional.")
self.probs = probs
super(CategoricalProbs, self).__init__(batch_shape=np.shape(self.probs)[:-1],
validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
return categorical(key, self.probs, shape=sample_shape + self.batch_shape)
@validate_sample
def log_prob(self, value):
batch_shape = lax.broadcast_shapes(np.shape(value), self.batch_shape)
value = np.expand_dims(value, axis=-1)
value = np.broadcast_to(value, batch_shape + (1,))
logits = _to_logits_multinom(self.probs)
log_pmf = np.broadcast_to(logits, batch_shape + np.shape(logits)[-1:])
return np.take_along_axis(log_pmf, value, axis=-1)[..., 0]
@property
def mean(self):
return np.full(self.batch_shape, np.nan, dtype=get_dtype(self.probs))
@property
def variance(self):
return np.full(self.batch_shape, np.nan, dtype=get_dtype(self.probs))
@property
def support(self):
return constraints.integer_interval(0, np.shape(self.probs)[-1])
[docs]@copy_docs_from(Distribution)
class CategoricalLogits(Distribution):
arg_constraints = {'logits': constraints.real}
def __init__(self, logits, validate_args=None):
if np.ndim(logits) < 1:
raise ValueError("`logits` parameter must be at least one-dimensional.")
self.logits = logits
super(CategoricalLogits, self).__init__(batch_shape=np.shape(logits)[:-1],
validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
return categorical_logits(key, self.logits, shape=sample_shape + self.batch_shape)
@validate_sample
def log_prob(self, value):
batch_shape = lax.broadcast_shapes(np.shape(value), self.batch_shape)
value = np.expand_dims(value, -1)
value = np.broadcast_to(value, batch_shape + (1,))
log_pmf = self.logits - logsumexp(self.logits, axis=-1, keepdims=True)
log_pmf = np.broadcast_to(log_pmf, batch_shape + np.shape(log_pmf)[-1:])
return np.take_along_axis(log_pmf, value, -1)[..., 0]
[docs] @lazy_property
def probs(self):
return _to_probs_multinom(self.logits)
@property
def mean(self):
return np.full(self.batch_shape, np.nan, dtype=get_dtype(self.logits))
@property
def variance(self):
return np.full(self.batch_shape, np.nan, dtype=get_dtype(self.logits))
@property
def support(self):
return constraints.integer_interval(0, np.shape(self.logits)[-1])
[docs]def Categorical(probs=None, logits=None, validate_args=None):
if probs is not None:
return CategoricalProbs(probs, validate_args=validate_args)
elif logits is not None:
return CategoricalLogits(logits, validate_args=validate_args)
else:
raise ValueError('One of `probs` or `logits` must be specified.')
[docs]@copy_docs_from(Distribution)
class Delta(Distribution):
arg_constraints = {'value': constraints.real, 'log_density': constraints.real}
support = constraints.real
def __init__(self, value=0., log_density=0., event_ndim=0, validate_args=None):
if event_ndim > np.ndim(value):
raise ValueError('Expected event_dim <= v.dim(), actual {} vs {}'
.format(event_ndim, np.ndim(value)))
batch_dim = np.ndim(value) - event_ndim
batch_shape = np.shape(value)[:batch_dim]
event_shape = np.shape(value)[batch_dim:]
self.value = lax.convert_element_type(value, canonicalize_dtype(np.float64))
# NB: following Pyro implementation, log_density should be broadcasted to batch_shape
self.log_density = promote_shapes(log_density, shape=batch_shape)[0]
super(Delta, self).__init__(batch_shape, event_shape, validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
shape = sample_shape + self.batch_shape + self.event_shape
return np.broadcast_to(device_put(self.value), shape)
@validate_sample
def log_prob(self, value):
log_prob = np.log(value == self.value)
log_prob = sum_rightmost(log_prob, len(self.event_shape))
return log_prob + self.log_density
@property
def mean(self):
return self.value
@property
def variance(self):
return np.zeros(self.batch_shape + self.event_shape)
[docs]class OrderedLogistic(CategoricalProbs):
"""
A categorical distribution with ordered outcomes.
**References:**
1. *Stan Functions Reference, v2.20 section 12.6*,
Stan Development Team
:param numpy.ndarray predictor: prediction in real domain; typically this is output
of a linear model.
:param numpy.ndarray cutpoints: positions in real domain to separate categories.
"""
arg_constraints = {'predictor': constraints.real,
'cutpoints': constraints.ordered_vector}
def __init__(self, predictor, cutpoints, validate_args=None):
predictor, self.cutpoints = promote_shapes(np.expand_dims(predictor, -1), cutpoints)
self.predictor = predictor[..., 0]
cumulative_probs = expit(cutpoints - predictor)
# add two boundary points 0 and 1
pad_width = [(0, 0)] * (np.ndim(cumulative_probs) - 1) + [(1, 1)]
cumulative_probs = np.pad(cumulative_probs, pad_width, constant_values=(0, 1))
probs = cumulative_probs[..., 1:] - cumulative_probs[..., :-1]
super(OrderedLogistic, self).__init__(probs, validate_args=validate_args)
[docs]class PRNGIdentity(Distribution):
"""
Distribution over :func:`~jax.random.PRNGKey`. This can be used to
draw a batch of :func:`~jax.random.PRNGKey` using the :class:`~numpyro.handlers.seed`
handler. Only `sample` method is supported.
"""
def __init__(self):
super(PRNGIdentity, self).__init__(event_shape=(2,))
[docs] def sample(self, key, sample_shape=()):
return np.reshape(random.split(key, np.product(sample_shape).astype(np.int32)),
sample_shape + self.event_shape)
[docs]@copy_docs_from(Distribution)
class MultinomialProbs(Distribution):
arg_constraints = {'total_count': constraints.nonnegative_integer,
'probs': constraints.simplex}
def __init__(self, probs, total_count=1, validate_args=None):
if np.ndim(probs) < 1:
raise ValueError("`probs` parameter must be at least one-dimensional.")
batch_shape = lax.broadcast_shapes(np.shape(probs)[:-1], np.shape(total_count))
self.probs = promote_shapes(probs, shape=batch_shape + np.shape(probs)[-1:])[0]
self.total_count = promote_shapes(total_count, shape=batch_shape)[0]
super(MultinomialProbs, self).__init__(batch_shape=batch_shape,
event_shape=np.shape(self.probs)[-1:],
validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
return multinomial(key, self.probs, self.total_count, shape=sample_shape + self.batch_shape)
@validate_sample
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
return gammaln(self.total_count + 1) \
+ np.sum(xlogy(value, self.probs) - gammaln(value + 1), axis=-1)
@property
def mean(self):
return self.probs * np.expand_dims(self.total_count, -1)
@property
def variance(self):
return np.expand_dims(self.total_count, -1) * self.probs * (1 - self.probs)
@property
def support(self):
return constraints.multinomial(self.total_count)
[docs]@copy_docs_from(Distribution)
class MultinomialLogits(Distribution):
arg_constraints = {'total_count': constraints.nonnegative_integer,
'logits': constraints.real}
def __init__(self, logits, total_count=1, validate_args=None):
if np.ndim(logits) < 1:
raise ValueError("`logits` parameter must be at least one-dimensional.")
batch_shape = lax.broadcast_shapes(np.shape(logits)[:-1], np.shape(total_count))
self.logits = promote_shapes(logits, shape=batch_shape + np.shape(logits)[-1:])[0]
self.total_count = promote_shapes(total_count, shape=batch_shape)[0]
super(MultinomialLogits, self).__init__(batch_shape=batch_shape,
event_shape=np.shape(self.logits)[-1:],
validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
return multinomial(key, self.probs, self.total_count, shape=sample_shape + self.batch_shape)
@validate_sample
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
normalize_term = self.total_count * logsumexp(self.logits, axis=-1) \
- gammaln(self.total_count + 1)
return np.sum(value * self.logits - gammaln(value + 1), axis=-1) - normalize_term
[docs] @lazy_property
def probs(self):
return _to_probs_multinom(self.logits)
@property
def mean(self):
return np.expand_dims(self.total_count, -1) * self.probs
@property
def variance(self):
return np.expand_dims(self.total_count, -1) * self.probs * (1 - self.probs)
@property
def support(self):
return constraints.multinomial(self.total_count)
[docs]def Multinomial(total_count=1, probs=None, logits=None, validate_args=None):
if probs is not None:
return MultinomialProbs(probs, total_count, validate_args=validate_args)
elif logits is not None:
return MultinomialLogits(logits, total_count, validate_args=validate_args)
else:
raise ValueError('One of `probs` or `logits` must be specified.')
[docs]@copy_docs_from(Distribution)
class Poisson(Distribution):
arg_constraints = {'rate': constraints.positive}
support = constraints.nonnegative_integer
def __init__(self, rate, validate_args=None):
self.rate = rate
super(Poisson, self).__init__(np.shape(rate), validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
return poisson(key, self.rate, shape=sample_shape + self.batch_shape)
@validate_sample
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
return (np.log(self.rate) * value) - gammaln(value + 1) - self.rate
@property
def mean(self):
return self.rate
@property
def variance(self):
return self.rate
[docs]class ZeroInflatedPoisson(Distribution):
"""
A Zero Inflated Poisson distribution.
:param numpy.ndarray gate: probability of extra zeros.
:param numpy.ndarray rate: rate of Poisson distribution.
"""
arg_constraints = {'gate': constraints.unit_interval, 'rate': constraints.positive}
support = constraints.nonnegative_integer
def __init__(self, gate, rate=1., validate_args=None):
batch_shape = lax.broadcast_shapes(np.shape(gate), np.shape(rate))
self.gate, self.rate = promote_shapes(gate, rate)
super(ZeroInflatedPoisson, self).__init__(batch_shape, validate_args=validate_args)
[docs] def sample(self, key, sample_shape=()):
key_bern, key_poisson = random.split(key)
shape = sample_shape + self.batch_shape
mask = random.bernoulli(key_bern, self.gate, shape)
samples = poisson(key_poisson, self.rate, shape)
return np.where(mask, 0, samples)
@validate_sample
def log_prob(self, value):
log_prob = np.log(self.rate) * value - gammaln(value + 1) + (np.log1p(-self.gate) - self.rate)
return np.where(value == 0, np.logaddexp(np.log(self.gate), log_prob), log_prob)
[docs] @lazy_property
def mean(self):
return (1 - self.gate) * self.rate
[docs] @lazy_property
def variance(self):
return (1 - self.gate) * self.rate * (1 + self.rate * self.gate)