scvi.distributions.Log1pNormal

class scvi.distributions.Log1pNormal(mu, sigma, scale=None, validate_args=False)

Bases: Distribution

Log1p-Normal distribution.

Distribution where log(X + 1) follows a Normal distribution. This allows modeling data with zeros, as the support is [0, ∞).

In the (mu, sigma) parameterization, samples from the log1p-normal are generated as follows:

1. \(z \sim \textrm{Normal}(\mu, \sigma)\)

2. \(x = \exp(z) - 1\)

The probability density function is:

\[f(x; \mu, \sigma) = \frac{1}{(x+1) \sigma \sqrt{2\pi}} \exp\left(-\frac{(\ln(x+1) - \mu)^2}{2\sigma^2}\right)\]

Parameters:

• mu (Tensor) – Mean of the normal distribution in log1p space.

• sigma (Tensor) – Standard deviation of the normal distribution in log1p space.

• scale (Tensor | None (default: None)) – Normalized mean expression of the distribution. This optional parameter is not used in any computations but allows storing normalization expression levels.

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

Attributes table

arg_constraints
mean	Mean of the distribution.
support
variance	Variance of the distribution.

Methods table

get_normalized(key)	Get normalized values.
log_prob(value)	Log probability with log1p transformation.
sample([sample_shape])	Sample from the distribution.

Attributes

Log1pNormal.arg_constraints = {'mu': Optional(Real()), 'scale': Optional(GreaterThanEq(lower_bound=0)), 'sigma': Optional(GreaterThan(lower_bound=0))}

Log1pNormal.mean

Mean of the distribution.

Log1pNormal.support = GreaterThanEq(lower_bound=0.0)

Log1pNormal.variance

Variance of the distribution.

Methods

Log1pNormal.get_normalized(key)

Get normalized values.

Return type:

Tensor

Log1pNormal.log_prob(value)

Log probability with log1p transformation.

Return type:

Tensor

Log1pNormal.sample(sample_shape=None)

Sample from the distribution.

Return type:

Tensor