# TransformedDistribution

Source: https://www.tensorplay.cn/docs/generated/tensorplay.distributions.TransformedDistribution.html

```python
class tensorplay.distributions.TransformedDistribution(base_distribution: Distribution, transforms: Transform | list[Transform], validate_args: bool | None = None)
```

Extension of the Distribution class, which applies a sequence of Transforms
to a base distribution.  Let f be the composition of transforms applied:

```
X ~ BaseDistribution
Y = f(X) ~ TransformedDistribution(BaseDistribution, f)
log p(Y) = log p(X) + log |det (dX/dY)|
```

Note that the .event_shape of a [TransformedDistribution](#tensorplay.distributions.TransformedDistribution) is the
maximum shape of its base distribution and its transforms, since transforms
can introduce correlations among events.

An example for the usage of [TransformedDistribution](#tensorplay.distributions.TransformedDistribution) would be:

```
# Building a Logistic Distribution
# X ~ Uniform(0, 1)
# f = a + b * logit(X)
# Y ~ f(X) ~ Logistic(a, b)
base_distribution = Uniform(0, 1)
transforms = [SigmoidTransform().inv, AffineTransform(loc=a, scale=b)]
logistic = TransformedDistribution(base_distribution, transforms)
```

For more examples, please look at the implementations of
[Gumbel](/docs/generated/tensorplay.distributions.Gumbel.html#tensorplay.distributions.Gumbel),
[HalfCauchy](/docs/generated/tensorplay.distributions.HalfCauchy.html#tensorplay.distributions.HalfCauchy),
[HalfNormal](/docs/generated/tensorplay.distributions.HalfNormal.html#tensorplay.distributions.HalfNormal),
[LogNormal](/docs/generated/tensorplay.distributions.LogNormal.html#tensorplay.distributions.LogNormal),
[Pareto](/docs/generated/tensorplay.distributions.Pareto.html#tensorplay.distributions.Pareto),
[Weibull](/docs/generated/tensorplay.distributions.Weibull.html#tensorplay.distributions.Weibull),
[RelaxedBernoulli](/docs/generated/tensorplay.distributions.RelaxedBernoulli.html#tensorplay.distributions.RelaxedBernoulli) and
[RelaxedOneHotCategorical](/docs/generated/tensorplay.distributions.RelaxedOneHotCategorical.html#tensorplay.distributions.RelaxedOneHotCategorical)

```python
property batch_shape: Size
```

Returns the shape over which parameters are batched.

```python
cdf(value)
```

Computes the cumulative distribution function by inverting the
transform(s) and computing the score of the base distribution.

```python
entropy() → Tensor
```

Returns entropy of distribution, batched over batch_shape.

Returns:

Tensor of shape batch_shape.

```python
enumerate_support(expand: bool = True) → Tensor
```

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](https://docs.python.org/3/builtins/functions.html#bool)) – whether to expand the support over the
batch dims to match the distribution’s batch_shape.

Returns:

Tensor iterating over dimension 0.

```python
property event_shape: Size
```

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

```python
icdf(value)
```

Computes the inverse cumulative distribution function using
transform(s) and computing the score of the base distribution.

```python
log_prob(value)
```

Scores the sample by inverting the transform(s) and computing the score
using the score of the base distribution and the log abs det jacobian.

```python
property mean: Tensor
```

Returns the mean of the distribution.

```python
property mode: Tensor
```

Returns the mode of the distribution.

```python
perplexity() → Tensor
```

Returns perplexity of distribution, batched over batch_shape.

Returns:

Tensor of shape batch_shape.

```python
rsample(sample_shape: Size | Sequence[int] = ()) → Tensor
```

Generates a sample_shape shaped reparameterized sample or sample_shape
shaped batch of reparameterized samples if the distribution parameters
are batched. Samples first from base distribution and applies
transform() for every transform in the list.

```python
sample(sample_shape=())
```

Generates a sample_shape shaped sample or sample_shape shaped batch of
samples if the distribution parameters are batched. Samples first from
base distribution and applies transform() for every transform in the
list.

```python
sample_n(n: int) → Tensor
```

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

```python
static set_default_validate_args(value: bool) → None
```

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](https://docs.python.org/3/builtins/functions.html#bool)) – Whether to enable validation.

```python
property stddev: Tensor
```

Returns the standard deviation of the distribution.

```python
property variance: Tensor
```

Returns the variance of the distribution.