# scvi.distributions.NegativeBinomial#

class scvi.distributions.NegativeBinomial(total_count=None, probs=None, logits=None, mu=None, theta=None, scale=None, validate_args=False)[source]#

Negative binomial distribution.

One of the following parameterizations must be provided:

(1), (total_count, probs) where total_count is the number of failures until the experiment is stopped and probs the success probability. (2), (mu, theta) parameterization, which is the one used by scvi-tools. These parameters respectively control the mean and inverse dispersion of the distribution.

In the (mu, theta) parameterization, samples from the negative binomial are generated as follows:

1. $$w \sim \textrm{Gamma}(\underbrace{\theta}_{\text{shape}}, \underbrace{\theta/\mu}_{\text{rate}})$$

2. $$x \sim \textrm{Poisson}(w)$$

Parameters:
• total_count ( (default: None)) – Number of failures until the experiment is stopped.

• probs ( (default: None)) – The success probability.

• mu ( (default: None)) – Mean of the distribution.

• theta ( (default: None)) – Inverse dispersion.

• scale ( (default: None)) – Normalized mean expression of the distribution.

• validate_args (bool (default: False)) – Raise ValueError if arguments do not match constraints

## Attributes table#

 arg_constraints batch_shape Returns the shape over which parameters are batched. event_shape Returns the shape of a single sample (without batching). has_enumerate_support has_rsample mean Returns the mean of the distribution. mode Returns the mode of the distribution. stddev Returns the standard deviation of the distribution. support variance Returns the variance of the distribution.

## Methods table#

 cdf(value) Returns the cumulative density/mass function evaluated at value. Returns entropy of distribution, batched over batch_shape. enumerate_support([expand]) Returns tensor containing all values supported by a discrete distribution. expand(batch_shape[, _instance]) Returns a new distribution instance (or populates an existing instance provided by a derived class) with batch dimensions expanded to batch_shape. icdf(value) Returns the inverse cumulative density/mass function evaluated at value. log_prob(value) Returns the log of the probability density/mass function evaluated at value. Returns perplexity of distribution, batched over batch_shape. rsample([sample_shape]) Generates a sample_shape shaped reparameterized sample or sample_shape shaped batch of reparameterized samples if the distribution parameters are batched. sample([sample_shape]) Sample from the distribution. Generates n samples or n batches of samples if the distribution parameters are batched. Sets whether validation is enabled or disabled.

## Attributes#

NegativeBinomial.arg_constraints = {'mu': Optional(GreaterThanEq(lower_bound=0)), 'scale': Optional(GreaterThanEq(lower_bound=0)), 'theta': Optional(GreaterThanEq(lower_bound=0))}#
NegativeBinomial.batch_shape[source]#

Returns the shape over which parameters are batched.

NegativeBinomial.event_shape[source]#

Returns the shape of a single sample (without batching).

NegativeBinomial.has_enumerate_support = False#
NegativeBinomial.has_rsample = False#
NegativeBinomial.mean[source]#
NegativeBinomial.mode[source]#

Returns the mode of the distribution.

NegativeBinomial.stddev[source]#

Returns the standard deviation of the distribution.

NegativeBinomial.support = IntegerGreaterThan(lower_bound=0)#
NegativeBinomial.variance[source]#

## Methods#

NegativeBinomial.cdf(value)[source]#

Returns the cumulative density/mass function evaluated at value.

Parameters:

value (Tensor) –

Return type:

Tensor

NegativeBinomial.entropy()[source]#

Returns entropy of distribution, batched over batch_shape.

Return type:

Tensor

Returns:

Tensor of shape batch_shape.

NegativeBinomial.enumerate_support(expand=True)[source]#

Returns tensor containing all values supported by a discrete distribution. The result will enumerate over dimension 0, so the shape of the result will be (cardinality,) + batch_shape + event_shape (where event_shape = () for univariate distributions).

Note that this enumerates over all batched tensors in lock-step [[0, 0], [1, 1], …]. With expand=False, enumeration happens along dim 0, but with the remaining batch dimensions being singleton dimensions, [[0], [1], ...

To iterate over the full Cartesian product use itertools.product(m.enumerate_support()).

Parameters:

expand (bool) – whether to expand the support over the batch dims to match the distribution’s batch_shape.

Return type:

Tensor

Returns:

Tensor iterating over dimension 0.

NegativeBinomial.expand(batch_shape, _instance=None)[source]#

Returns a new distribution instance (or populates an existing instance provided by a derived class) with batch dimensions expanded to batch_shape. This method calls expand on the distribution’s parameters. As such, this does not allocate new memory for the expanded distribution instance. Additionally, this does not repeat any args checking or parameter broadcasting in __init__.py, when an instance is first created.

Parameters:
• batch_shape (torch.Size) – the desired expanded size.

• _instance (default: None) – new instance provided by subclasses that need to override .expand.

Returns:

New distribution instance with batch dimensions expanded to batch_size.

NegativeBinomial.icdf(value)[source]#

Returns the inverse cumulative density/mass function evaluated at value.

Parameters:

value (Tensor) –

Return type:

Tensor

NegativeBinomial.log_prob(value)[source]#

Returns the log of the probability density/mass function evaluated at value.

Parameters:

value (Tensor) –

Return type:

Tensor

NegativeBinomial.perplexity()[source]#

Returns perplexity of distribution, batched over batch_shape.

Return type:

Tensor

Returns:

Tensor of shape batch_shape.

NegativeBinomial.rsample(sample_shape=())[source]#

Generates a sample_shape shaped reparameterized sample or sample_shape shaped batch of reparameterized samples if the distribution parameters are batched.

Return type:

Tensor

NegativeBinomial.sample(sample_shape=None)[source]#

Sample from the distribution.

Return type:

Tensor

NegativeBinomial.sample_n(n)[source]#

Generates n samples or n batches of samples if the distribution parameters are batched.

Return type:

Tensor

static NegativeBinomial.set_default_validate_args(value)[source]#

Sets whether validation is enabled or disabled.

The default behavior mimics Python’s assert statement: validation is on by default, but is disabled if Python is run in optimized mode (via python -O). Validation may be expensive, so you may want to disable it once a model is working.

Parameters:

value (bool) – Whether to enable validation.

Return type:

None