class

Independent

extendsDistribution

Independent(base_distribution: Distribution, reinterpreted_batch_ndims: int, validate_args: bool | None = None)

source

Re-interpret rightmost batch dimensions of a base distribution as event dims.

Independent(base_distribution, reinterpreted_batch_ndims=n) takes the last $n$ dimensions of base_distribution.batch_shape and moves them into event_shape. Log-probabilities are summed over the re-interpreted axes, turning a product of independent marginals into the joint log-probability.

This is a pure structural wrapper — it does not change the sampler or the underlying computation. Its main use is to express

Diagonal multivariate Normals from batches of scalar Normals, or
Independent Bernoulli likelihoods over image pixels from a per-pixel Bernoulli batch.

Parameters

base_distributionDistribution

The underlying distribution. Its batch_shape must have at least reinterpreted_batch_ndims dimensions.

reinterpreted_batch_ndimsint

Number of rightmost batch dimensions to absorb into event_shape. Must satisfy 0 <= reinterpreted_batch_ndims <= len(batch_shape).

validate_argsbool | None= None

If True, validate parameter constraints at construction time.

Attributes

base_distDistribution

The wrapped base distribution.

reinterpreted_batch_ndimsint

Number of absorbed batch dimensions.

Notes

Given base with batch_shape = (B, D) and event_shape = (), wrapping with reinterpreted_batch_ndims=1 yields:

batch_shape = (B,)
event_shape = (D,)

The resulting log_prob(x) sums the $D$ scalar log-probabilities:

\log p(x_1, \ldots, x_D) = \sum_{i=1}^{D} \log p_i(x_i)

which is correct because the components are independent by construction.

Entropy is similarly summed:

H[X_1, \ldots, X_D] = \sum_{i=1}^{D} H[X_i]

(equality holds because independence implies $H[X_1, \ldots, X_D] = \sum_i H[X_i]$ ).

The has_rsample property mirrors base_dist.has_rsample, so gradient flow is preserved when the base distribution supports it.

Examples

>>> import lucid
>>> from lucid.distributions import Independent
>>> from lucid.distributions import Normal
>>> # Diagonal Normal: batch of D=4 scalars → single 4-d event
>>> base = Normal(lucid.zeros(4), lucid.ones(4))
>>> dist = Independent(base, reinterpreted_batch_ndims=1)
>>> dist.batch_shape, dist.event_shape
((), (4,))
>>> x = dist.rsample()
>>> x.shape  # (4,)
(4,)
>>> dist.log_prob(x)  # scalar — sum of 4 log-probs

Methods (10)

dunder

init

→None

__init__(base_distribution: Distribution, reinterpreted_batch_ndims: int, validate_args: bool | None = None)

source

Initialise an Independent distribution wrapper.

Parameters

base_distributionDistribution

The underlying distribution. Its batch_shape must have at least reinterpreted_batch_ndims dimensions.

reinterpreted_batch_ndimsint

Number of rightmost batch dimensions to move into event_shape. Must satisfy 0 <= reinterpreted_batch_ndims <= len(batch_shape).

validate_argsbool | None= None

If True, validate parameter constraints at construction time.

Raises

ValueError

If reinterpreted_batch_ndims exceeds the number of batch dimensions of base_distribution.

prop

has_rsample

→bool

has_rsample: bool

source

Whether reparameterised sampling is supported.

Mirrors base_dist.has_rsample, so gradient flow is preserved when the base distribution supports it.

Returns

bool

True if and only if the base distribution supports reparameterised sampling.

prop

support

→object

support: object

source

Support of the distribution — delegates to base_dist.support.

Returns

object

The support constraint of the underlying base distribution.

prop

mean

→Tensor

mean: Tensor

source

Mean of the distribution — delegates to base_dist.mean.

Returns

Tensor

Mean with the same shape as base_dist.mean.

prop

mode

→Tensor

mode: Tensor

source

Mode of the distribution — delegates to base_dist.mode.

Returns

Tensor

Mode with the same shape as base_dist.mode.

prop

variance

→Tensor

variance: Tensor

source

Variance of the distribution — delegates to base_dist.variance.

Returns

Tensor

Variance with the same shape as base_dist.variance.

rsample

→Tensor

rsample(sample_shape: tuple[int, ...] = ())

source

Draw reparameterised samples — delegates to base_dist.rsample.

Parameters

sample_shapetuple[int, ...]= ()

Leading shape of the output sample batch.

Returns

Tensor

Samples of shape (*sample_shape, *batch_shape, *event_shape).

sample

→Tensor

sample(sample_shape: tuple[int, ...] = ())

source

Draw samples — delegates to base_dist.sample.

Parameters

sample_shapetuple[int, ...]= ()

Leading shape of the output sample batch.

Returns

Tensor

Samples of shape (*sample_shape, *batch_shape, *event_shape).

log_prob

→Tensor

log_prob(value: Tensor)

source

Log joint probability summed over re-interpreted event dimensions.

Computes the base distribution's log-probabilities and then sums over the rightmost reinterpreted_batch_ndims axes:

\log p(x_1, \ldots, x_D) = \sum_{i=1}^{D} \log p_i(x_i)

Parameters

valueTensor

Observations of shape (*batch_shape, *event_shape).

Returns

Tensor

Log joint probability values of shape batch_shape.

entropy

→Tensor

entropy()

source

Joint entropy summed over re-interpreted event dimensions.

Because the components are independent:

H[X_1, \ldots, X_D] = \sum_{i=1}^{D} H[X_i]

Returns

Tensor

Entropy values of shape batch_shape (nats).