zhusuan.distributions.base

class Distribution(dtype, param_dtype, is_continuous, is_reparameterized, use_path_derivative=False, group_ndims=0, **kwargs)

Bases: object

The Distribution class is the base class for various probabilistic distributions which support batch inputs, generating batches of samples and evaluate probabilities at batches of given values.

The typical input shape for a Distribution is like batch_shape + input_shape. where input_shape represents the shape of non-batch input parameter, batch_shape represents how many independent inputs are fed into the distribution.

Samples generated are of shape ([n_samples]+ )batch_shape + value_shape. The first additional axis is omitted only when passed n_samples is None (by default), in which case one sample is generated. value_shape is the non-batch value shape of the distribution. For a univariate distribution, its value_shape is [].

There are cases where a batch of random variables are grouped into a single event so that their probabilities should be computed together. This is achieved by setting group_ndims argument, which defaults to 0. The last group_ndims number of axes in batch_shape are grouped into a single event. For example, Normal(..., group_ndims=1) will set the last axis of its batch_shape to a single event, i.e., a multivariate Normal with identity covariance matrix.

When evaluating probabilities at given values, the given Var should be broadcastable to shape (... + )batch_shape + value_shape. The returned Var has shape (... + )batch_shape[:-group_ndims].

See also

For more details and examples, please refer to Basic Concepts in ZhuSuan.

For both, the parameter dtype represents type of samples. For discrete, can be set by user. For continuous, automatically determined from parameter types.

The value type of log_prob will be param_dtype which is deduced from the parameter(s) when initializating. And dtype must be among int16, int32, int64, float16, float32 and float64.

When two or more parameters are vars and they have different type, TypeError will be raised.

Parameters

• dtype – The value type of samples from the distribution.

• param_dtype – The parameter(s) type of the distribution.

• is_continuous – Whether the distribution is continuous.

• is_reparameterized – A bool. Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).

• use_path_derivative – A bool. Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”

• group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See above for more detailed explanation.

property batch_shape

The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.

property is_reparameterized

Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).

log_prob(given)

Compute log probability density (mass) function at given value.

Parameters

given – A Var. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape.

Returns

A Var of shape (... + )batch_shape[:-group_ndims].

sample(n_samples=None)

Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Var has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.

Parameters

n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution.

Returns

A Var of samples.