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|---|
| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/internal/trainable_state_util.py#L327-L343) |

Constructs a distribution or bijector instance with trainable parameters.

    tfp.experimental.util.make_trainable(
        *args, seed=None, **kwargs
    )

### Used in the notebooks

| Used in the tutorials |
|---|
| - [TFP Release Notes notebook (0.13.0)](https://www.tensorflow.org/probability/examples/TFP_Release_Notebook_0_13_0) |

This is a convenience method that instantiates a class with trainable
parameters. Parameters are randomly initialized, and transformed to enforce
any domain constraints. This method assumes that the class exposes a
`parameter_properties` method annotating its trainable parameters, and that
the caller provides any additional (non-trainable) arguments required by the
class.

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| ## Args ||
|---|---|
| `cls` | Python class that implements `cls.parameter_properties()`, e.g., a TFP distribution (`tfd.Normal`) or bijector (`tfb.Scale`). |
| `initial_parameters` | a dictionary containing initial values for some or all of the parameters to `cls`, OR a Python `callable` with signature `value = parameter_init_fn(parameter_name, shape, dtype, seed, constraining_bijector)`. If a dictionary is provided, any parameters not specified will be initialized to a random value in their domain. Default value: `None` (equivalent to `{}`; all parameters are initialized randomly). |
| `batch_and_event_shape` | Optional int `Tensor` desired shape of samples (for distributions) or inputs (for bijectors), used to determine the shape of the trainable parameters. Default value: `()`. |
| `parameter_dtype` | Optional float `dtype` for trainable variables. |
| `**init_kwargs` | Additional keyword arguments passed to `cls.__init__()` to specify any non-trainable parameters. If a value is passed for an otherwise-trainable parameter---for example, `trainable(tfd.Normal, scale=1.)`---it will be taken as a fixed value and no variable will be constructed for that parameter. seed: PRNG seed; see [`tfp.random.sanitize_seed`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. |

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| ## Returns ||
|---|---|
| `instance` | instance parameterized by trainable [`tf.Variable`](https://www.tensorflow.org/api_docs/python/tf/Variable)s. |

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#### Example

Suppose we want to fit a normal distribution to observed data. We could
of course just examine the empirical mean and standard deviation of the data:

    samples = [4.57, 6.37, 5.93, 7.98, 2.03, 3.59, 8.55, 3.45, 5.06, 6.44]
    model = tfd.Normal(
      loc=tf.reduce_mean(samples),  # ==> 5.40
      scale=tf.math.reduce_std(sample))  # ==> 1.95

and this would be a very sensible approach. But that's boring, so instead,
let's do way more work to get the same result. We'll build a trainable normal
distribution, and explicitly optimize to find the maximum-likelihood estimate
for the parameters given our data:

    model = tfp.util.make_trainable(tfd.Normal)
    losses = tfp.math.minimize(
      lambda: -model.log_prob(samples),
      optimizer=tf_keras.optimizers.Adam(0.1),
      num_steps=200)
    print('Fit Normal distribution with mean {} and stddev {}'.format(
      model.mean(),
      model.stddev()))

In this trivial case, doing the explicit optimization has few advantages over
the first approach in which we simply matched the empirical moments of the
data. However, trainable distributions are useful more generally. For example,
they can enable maximum-likelihood estimation of distributions when a
moment-matching estimator is not available, and they can also serve as
surrogate posteriors in variational inference.