Base Distribution¶
Distribution¶
-
class
Distribution
(batch_shape=(), event_shape=(), validate_args=None)[source]¶ Bases:
object
Base class for probability distributions in NumPyro. The design largely follows from
torch.distributions
.Parameters: - batch_shape – The batch shape for the distribution. This designates independent (possibly non-identical) dimensions of a sample from the distribution. This is fixed for a distribution instance and is inferred from the shape of the distribution parameters.
- event_shape – The event shape for the distribution. This designates the dependent dimensions of a sample from the distribution. These are collapsed when we evaluate the log probability density of a batch of samples using .log_prob.
- validate_args – Whether to enable validation of distribution parameters and arguments to .log_prob method.
As an example:
>>> import jax.numpy as np >>> import numpyro.distributions as dist >>> d = dist.Dirichlet(np.ones((2, 3, 4))) >>> d.batch_shape (2, 3) >>> d.event_shape (4,)
-
arg_constraints
= {}¶
-
support
= None¶
-
reparametrized_params
= []¶
-
batch_shape
¶ Returns the shape over which the distribution parameters are batched.
Returns: batch shape of the distribution. Return type: tuple
-
event_shape
¶ Returns the shape of a single sample from the distribution without batching.
Returns: event shape of the distribution. Return type: tuple
-
sample
(key, sample_shape=())[source]¶ Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.
Parameters: - key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
- sample_shape (tuple) – the sample shape for the distribution.
Returns: an array of shape sample_shape + batch_shape + event_shape
Return type:
-
sample_with_intermediates
(key, sample_shape=())[source]¶ Same as
sample
except that any intermediate computations are returned (useful for TransformedDistribution).Parameters: - key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
- sample_shape (tuple) – the sample shape for the distribution.
Returns: an array of shape sample_shape + batch_shape + event_shape
Return type:
-
log_prob
(value)[source]¶ Evaluates the log probability density for a batch of samples given by value.
Parameters: value – A batch of samples from the distribution. Returns: an array with shape value.shape[:-self.event_shape] Return type: numpy.ndarray
-
mean
¶ Mean of the distribution.
-
variance
¶ Variance of the distribution.
-
to_event
(reinterpreted_batch_ndims=None)[source]¶ Interpret the rightmost reinterpreted_batch_ndims batch dimensions as dependent event dimensions.
Parameters: reinterpreted_batch_ndims – Number of rightmost batch dims to interpret as event dims. Returns: An instance of Independent distribution. Return type: Independent
Independent¶
-
class
Independent
(base_dist, reinterpreted_batch_ndims, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
Reinterprets batch dimensions of a distribution as event dims by shifting the batch-event dim boundary further to the left.
From a practical standpoint, this is useful when changing the result of
log_prob()
. For example, a univariate Normal distribution can be interpreted as a multivariate Normal with diagonal covariance:>>> import numpyro.distributions as dist >>> normal = dist.Normal(np.zeros(3), np.ones(3)) >>> [normal.batch_shape, normal.event_shape] [(3,), ()] >>> diag_normal = dist.Independent(normal, 1) >>> [diag_normal.batch_shape, diag_normal.event_shape] [(), (3,)]
Parameters: - base_distribution (numpyro.distribution.Distribution) – a distribution instance.
- reinterpreted_batch_ndims (int) – the number of batch dims to reinterpret as event dims.
-
arg_constraints
= {}¶
-
support
¶
-
reparameterized_params
¶
-
mean
¶
-
variance
¶
TransformedDistribution¶
-
class
TransformedDistribution
(base_distribution, transforms, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
Returns a distribution instance obtained as a result of applying a sequence of transforms to a base distribution. For an example, see
LogNormal
andHalfNormal
.Parameters: - base_distribution – the base distribution over which to apply transforms.
- transforms – a single transform or a list of transforms.
- validate_args – Whether to enable validation of distribution parameters and arguments to .log_prob method.
-
arg_constraints
= {}¶
-
support
¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
sample_with_intermediates
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample_with_intermediates()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
mean
¶
-
variance
¶
Unit¶
-
class
Unit
(log_factor, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
Trivial nonnormalized distribution representing the unit type.
The unit type has a single value with no data, i.e.
value.size == 0
.This is used for
numpyro.factor()
statements.-
arg_constraints
= {'log_factor': <numpyro.distributions.constraints._Real object>}¶
-
support
= <numpyro.distributions.constraints._Real object>¶
-
Continuous Distributions¶
Beta¶
-
class
Beta
(concentration1, concentration0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'concentration0': <numpyro.distributions.constraints._GreaterThan object>, 'concentration1': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._Interval object>¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
Cauchy¶
-
class
Cauchy
(loc=0.0, scale=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'loc': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._Real object>¶
-
reparametrized_params
= ['loc', 'scale']¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
Chi2¶
-
class
Chi2
(df, validate_args=None)[source]¶ Bases:
numpyro.distributions.continuous.Gamma
-
arg_constraints
= {'df': <numpyro.distributions.constraints._GreaterThan object>}¶
-
Dirichlet¶
-
class
Dirichlet
(concentration, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'concentration': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._Simplex object>¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
Exponential¶
-
class
Exponential
(rate=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
reparametrized_params
= ['rate']¶
-
arg_constraints
= {'rate': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._GreaterThan object>¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
Gamma¶
-
class
Gamma
(concentration, rate=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'concentration': <numpyro.distributions.constraints._GreaterThan object>, 'rate': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._GreaterThan object>¶
-
reparametrized_params
= ['rate']¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
GaussianRandomWalk¶
-
class
GaussianRandomWalk
(scale=1.0, num_steps=1, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'num_steps': <numpyro.distributions.constraints._IntegerGreaterThan object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._RealVector object>¶
-
reparametrized_params
= ['scale']¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
HalfCauchy¶
-
class
HalfCauchy
(scale=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
reparametrized_params
= ['scale']¶
-
support
= <numpyro.distributions.constraints._GreaterThan object>¶
-
arg_constraints
= {'scale': <numpyro.distributions.constraints._GreaterThan object>}¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
HalfNormal¶
-
class
HalfNormal
(scale=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
reparametrized_params
= ['scale']¶
-
support
= <numpyro.distributions.constraints._GreaterThan object>¶
-
arg_constraints
= {'scale': <numpyro.distributions.constraints._GreaterThan object>}¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
InverseGamma¶
-
class
InverseGamma
(concentration, rate=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.TransformedDistribution
-
arg_constraints
= {'concentration': <numpyro.distributions.constraints._GreaterThan object>, 'rate': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._GreaterThan object>¶
-
reparametrized_params
= ['rate']¶
-
LKJ¶
-
class
LKJ
(dimension, concentration=1.0, sample_method='onion', validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.TransformedDistribution
LKJ distribution for correlation matrices. The distribution is controlled by
concentration
parameter \(\eta\) to make the probability of the correlation matrix \(M\) propotional to \(\det(M)^{\eta - 1}\). Because of that, whenconcentration == 1
, we have a uniform distribution over correlation matrices.When
concentration > 1
, the distribution favors samples with large large determinent. This is useful when we know a priori that the underlying variables are not correlated.When
concentration < 1
, the distribution favors samples with small determinent. This is useful when we know a priori that some underlying variables are correlated.Parameters: - dimension (int) – dimension of the matrices
- concentration (ndarray) – concentration/shape parameter of the distribution (often referred to as eta)
- sample_method (str) – Either “cvine” or “onion”. Both methods are proposed in [1] and offer the same distribution over correlation matrices. But they are different in how to generate samples. Defaults to “onion”.
References
[1] Generating random correlation matrices based on vines and extended onion method, Daniel Lewandowski, Dorota Kurowicka, Harry Joe
-
arg_constraints
= {'concentration': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._CorrMatrix object>¶
LKJCholesky¶
-
class
LKJCholesky
(dimension, concentration=1.0, sample_method='onion', validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
LKJ distribution for lower Cholesky factors of correlation matrices. The distribution is controlled by
concentration
parameter \(\eta\) to make the probability of the correlation matrix \(M\) generated from a Cholesky factor propotional to \(\det(M)^{\eta - 1}\). Because of that, whenconcentration == 1
, we have a uniform distribution over Cholesky factors of correlation matrices.When
concentration > 1
, the distribution favors samples with large diagonal entries (hence large determinent). This is useful when we know a priori that the underlying variables are not correlated.When
concentration < 1
, the distribution favors samples with small diagonal entries (hence small determinent). This is useful when we know a priori that some underlying variables are correlated.Parameters: - dimension (int) – dimension of the matrices
- concentration (ndarray) – concentration/shape parameter of the distribution (often referred to as eta)
- sample_method (str) – Either “cvine” or “onion”. Both methods are proposed in [1] and offer the same distribution over correlation matrices. But they are different in how to generate samples. Defaults to “onion”.
References
[1] Generating random correlation matrices based on vines and extended onion method, Daniel Lewandowski, Dorota Kurowicka, Harry Joe
-
arg_constraints
= {'concentration': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._CorrCholesky object>¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
LogNormal¶
-
class
LogNormal
(loc=0.0, scale=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.TransformedDistribution
-
arg_constraints
= {'loc': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}¶
-
reparametrized_params
= ['loc', 'scale']¶
-
MultivariateNormal¶
-
class
MultivariateNormal
(loc=0.0, covariance_matrix=None, precision_matrix=None, scale_tril=None, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'covariance_matrix': <numpyro.distributions.constraints._PositiveDefinite object>, 'loc': <numpyro.distributions.constraints._RealVector object>, 'precision_matrix': <numpyro.distributions.constraints._PositiveDefinite object>, 'scale_tril': <numpyro.distributions.constraints._LowerCholesky object>}¶
-
support
= <numpyro.distributions.constraints._RealVector object>¶
-
reparametrized_params
= ['loc', 'covariance_matrix', 'precision_matrix', 'scale_tril']¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
LowRankMultivariateNormal¶
-
class
LowRankMultivariateNormal
(loc, cov_factor, cov_diag, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'cov_diag': <numpyro.distributions.constraints._GreaterThan object>, 'cov_factor': <numpyro.distributions.constraints._Real object>, 'loc': <numpyro.distributions.constraints._RealVector object>}¶
-
support
= <numpyro.distributions.constraints._RealVector object>¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
Normal¶
-
class
Normal
(loc=0.0, scale=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'loc': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._Real object>¶
-
reparametrized_params
= ['loc', 'scale']¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
Pareto¶
-
class
Pareto
(alpha, scale=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.TransformedDistribution
-
arg_constraints
= {'alpha': <numpyro.distributions.constraints._GreaterThan object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
¶
-
StudentT¶
-
class
StudentT
(df, loc=0.0, scale=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'df': <numpyro.distributions.constraints._GreaterThan object>, 'loc': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._Real object>¶
-
reparametrized_params
= ['loc', 'scale']¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
TruncatedCauchy¶
-
class
TruncatedCauchy
(low=0.0, loc=0.0, scale=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.TransformedDistribution
-
arg_constraints
= {'loc': <numpyro.distributions.constraints._Real object>, 'low': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}¶
-
reparametrized_params
= ['low', 'loc', 'scale']¶
-
TruncatedNormal¶
-
class
TruncatedNormal
(low=0.0, loc=0.0, scale=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.TransformedDistribution
-
arg_constraints
= {'loc': <numpyro.distributions.constraints._Real object>, 'low': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}¶
-
reparametrized_params
= ['low', 'loc', 'scale']¶
-
Uniform¶
-
class
Uniform
(low=0.0, high=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.TransformedDistribution
-
arg_constraints
= {'high': <numpyro.distributions.constraints._Dependent object>, 'low': <numpyro.distributions.constraints._Dependent object>}¶
-
reparametrized_params
= ['low', 'high']¶
-
Discrete Distributions¶
BernoulliLogits¶
-
class
BernoulliLogits
(logits=None, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'logits': <numpyro.distributions.constraints._Real object>}¶
-
support
= <numpyro.distributions.constraints._Boolean object>¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
BernoulliProbs¶
-
class
BernoulliProbs
(probs, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'probs': <numpyro.distributions.constraints._Interval object>}¶
-
support
= <numpyro.distributions.constraints._Boolean object>¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
BetaBinomial¶
-
class
BetaBinomial
(concentration1, concentration0, total_count=1, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
Compound distribution comprising of a beta-binomial pair. The probability of success (
probs
for theBinomial
distribution) is unknown and randomly drawn from aBeta
distribution prior to a certain number of Bernoulli trials given bytotal_count
.Parameters: - concentration1 (numpy.ndarray) – 1st concentration parameter (alpha) for the Beta distribution.
- concentration0 (numpy.ndarray) – 2nd concentration parameter (beta) for the Beta distribution.
- total_count (numpy.ndarray) – number of Bernoulli trials.
-
arg_constraints
= {'concentration0': <numpyro.distributions.constraints._GreaterThan object>, 'concentration1': <numpyro.distributions.constraints._GreaterThan object>, 'total_count': <numpyro.distributions.constraints._IntegerGreaterThan object>}¶
-
log_prob
(*args, **kwargs)¶
-
mean
¶
-
variance
¶
-
support
¶
BinomialLogits¶
-
class
BinomialLogits
(logits, total_count=1, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'logits': <numpyro.distributions.constraints._Real object>, 'total_count': <numpyro.distributions.constraints._IntegerGreaterThan object>}¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
support
¶
-
BinomialProbs¶
-
class
BinomialProbs
(probs, total_count=1, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'probs': <numpyro.distributions.constraints._Interval object>, 'total_count': <numpyro.distributions.constraints._IntegerGreaterThan object>}¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
support
¶
-
CategoricalLogits¶
-
class
CategoricalLogits
(logits, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'logits': <numpyro.distributions.constraints._Real object>}¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
support
¶
-
CategoricalProbs¶
-
class
CategoricalProbs
(probs, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'probs': <numpyro.distributions.constraints._Simplex object>}¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
support
¶
-
Delta¶
-
class
Delta
(value=0.0, log_density=0.0, event_ndim=0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'log_density': <numpyro.distributions.constraints._Real object>, 'value': <numpyro.distributions.constraints._Real object>}¶
-
support
= <numpyro.distributions.constraints._Real object>¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
GammaPoisson¶
-
class
GammaPoisson
(concentration, rate=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
Compound distribution comprising of a gamma-poisson pair, also referred to as a gamma-poisson mixture. The
rate
parameter for thePoisson
distribution is unknown and randomly drawn from aGamma
distribution.Parameters: - concentration (numpy.ndarray) – shape parameter (alpha) of the Gamma distribution.
- rate (numpy.ndarray) – rate parameter (beta) for the Gamma distribution.
-
arg_constraints
= {'concentration': <numpyro.distributions.constraints._GreaterThan object>, 'rate': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._IntegerGreaterThan object>¶
-
log_prob
(*args, **kwargs)¶
-
mean
¶
-
variance
¶
MultinomialLogits¶
-
class
MultinomialLogits
(logits, total_count=1, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'logits': <numpyro.distributions.constraints._Real object>, 'total_count': <numpyro.distributions.constraints._IntegerGreaterThan object>}¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
support
¶
-
MultinomialProbs¶
-
class
MultinomialProbs
(probs, total_count=1, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'probs': <numpyro.distributions.constraints._Simplex object>, 'total_count': <numpyro.distributions.constraints._IntegerGreaterThan object>}¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
support
¶
-
OrderedLogistic¶
-
class
OrderedLogistic
(predictor, cutpoints, validate_args=None)[source]¶ Bases:
numpyro.distributions.discrete.CategoricalProbs
A categorical distribution with ordered outcomes.
References:
- Stan Functions Reference, v2.20 section 12.6, Stan Development Team
Parameters: - predictor (numpy.ndarray) – prediction in real domain; typically this is output of a linear model.
- cutpoints (numpy.ndarray) – positions in real domain to separate categories.
-
arg_constraints
= {'cutpoints': <numpyro.distributions.constraints._OrderedVector object>, 'predictor': <numpyro.distributions.constraints._Real object>}¶
Poisson¶
-
class
Poisson
(rate, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
-
arg_constraints
= {'rate': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._IntegerGreaterThan object>¶
-
sample
(key, sample_shape=())[source]¶ See
numpyro.distributions.distribution.Distribution.sample()
-
log_prob
(*args, **kwargs)¶ See
numpyro.distributions.distribution.Distribution.log_prob()
-
PRNGIdentity¶
ZeroInflatedPoisson¶
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class
ZeroInflatedPoisson
(gate, rate=1.0, validate_args=None)[source]¶ Bases:
numpyro.distributions.distribution.Distribution
A Zero Inflated Poisson distribution.
Parameters: - gate (numpy.ndarray) – probability of extra zeros.
- rate (numpy.ndarray) – rate of Poisson distribution.
-
arg_constraints
= {'gate': <numpyro.distributions.constraints._Interval object>, 'rate': <numpyro.distributions.constraints._GreaterThan object>}¶
-
support
= <numpyro.distributions.constraints._IntegerGreaterThan object>¶
-
log_prob
(*args, **kwargs)¶
Constraints¶
nonnegative_integer¶
-
nonnegative_integer
= <numpyro.distributions.constraints._IntegerGreaterThan object>¶
positive_definite¶
-
positive_definite
= <numpyro.distributions.constraints._PositiveDefinite object>¶
Transforms¶
Transform¶
AbsTransform¶
AffineTransform¶
ComposeTransform¶
CorrCholeskyTransform¶
-
class
CorrCholeskyTransform
[source]¶ Bases:
numpyro.distributions.transforms.Transform
Transforms a uncontrained real vector \(x\) with length \(D*(D-1)/2\) into the Cholesky factor of a D-dimension correlation matrix. This Cholesky factor is a lower triangular matrix with positive diagonals and unit Euclidean norm for each row. The transform is processed as follows:
- First we convert \(x\) into a lower triangular matrix with the following order:
\[\begin{split}\begin{bmatrix} 1 & 0 & 0 & 0 \\ x_0 & 1 & 0 & 0 \\ x_1 & x_2 & 1 & 0 \\ x_3 & x_4 & x_5 & 1 \end{bmatrix}\end{split}\]2. For each row \(X_i\) of the lower triangular part, we apply a signed version of class
StickBreakingTransform
to transform \(X_i\) into a unit Euclidean length vector using the following steps:- Scales into the interval \((-1, 1)\) domain: \(r_i = \tanh(X_i)\).
- Transforms into an unsigned domain: \(z_i = r_i^2\).
- Applies \(s_i = StickBreakingTransform(z_i)\).
- Transforms back into signed domain: \(y_i = (sign(r_i), 1) * \sqrt{s_i}\).
-
domain
= <numpyro.distributions.constraints._RealVector object>¶
-
codomain
= <numpyro.distributions.constraints._CorrCholesky object>¶
-
event_dim
= 2¶
ExpTransform¶
IdentityTransform¶
InvCholeskyTransform¶
-
class
InvCholeskyTransform
(domain=<numpyro.distributions.constraints._LowerCholesky object>)[source]¶ Bases:
numpyro.distributions.transforms.Transform
Transform via the mapping \(y = x @ x.T\), where x is a lower triangular matrix with positive diagonal.
-
event_dim
= 2¶
-
codomain
¶
-
LowerCholeskyTransform¶
MultivariateAffineTransform¶
-
class
MultivariateAffineTransform
(loc, scale_tril)[source]¶ Bases:
numpyro.distributions.transforms.Transform
Transform via the mapping \(y = loc + scale\_tril\ @\ x\).
Parameters: - loc – a real vector.
- scale_tril – a lower triangular matrix with positive diagonal.
-
domain
= <numpyro.distributions.constraints._RealVector object>¶
-
codomain
= <numpyro.distributions.constraints._RealVector object>¶
-
event_dim
= 1¶
OrderedTransform¶
-
class
OrderedTransform
[source]¶ Bases:
numpyro.distributions.transforms.Transform
Transform a real vector to an ordered vector.
References:
- Stan Reference Manual v2.20, section 10.6, Stan Development Team
-
domain
= <numpyro.distributions.constraints._RealVector object>¶
-
codomain
= <numpyro.distributions.constraints._OrderedVector object>¶
-
event_dim
= 1¶
PermuteTransform¶
PowerTransform¶
SigmoidTransform¶
Flows¶
InverseAutoregressiveTransform¶
-
class
InverseAutoregressiveTransform
(autoregressive_nn, log_scale_min_clip=-5.0, log_scale_max_clip=3.0)[source]¶ Bases:
numpyro.distributions.transforms.Transform
An implementation of Inverse Autoregressive Flow, using Eq (10) from Kingma et al., 2016,
\(\mathbf{y} = \mu_t + \sigma_t\odot\mathbf{x}\)where \(\mathbf{x}\) are the inputs, \(\mathbf{y}\) are the outputs, \(\mu_t,\sigma_t\) are calculated from an autoregressive network on \(\mathbf{x}\), and \(\sigma_t>0\).
References
- Improving Variational Inference with Inverse Autoregressive Flow [arXiv:1606.04934], Diederik P. Kingma, Tim Salimans, Rafal Jozefowicz, Xi Chen, Ilya Sutskever, Max Welling
-
domain
= <numpyro.distributions.constraints._RealVector object>¶
-
codomain
= <numpyro.distributions.constraints._RealVector object>¶
-
event_dim
= 1¶
-
inv
(y)[source]¶ Parameters: y (numpy.ndarray) – the output of the transform to be inverted
-
log_abs_det_jacobian
(x, y, intermediates=None)[source]¶ Calculates the elementwise determinant of the log jacobian.
Parameters: - x (numpy.ndarray) – the input to the transform
- y (numpy.ndarray) – the output of the transform