`SGLD`

Inherits From: `MonteCarlo`

- Class
`ed.SGLD`

- Class
`ed.inferences.SGLD`

Defined in `edward/inferences/sgld.py`

.

Stochastic gradient Langevin dynamics (Welling & Teh, 2011).

In conditional inference, we infer \(z\) in \(p(z, \beta \mid x)\) while fixing inference over \(\beta\) using another distribution \(q(\beta)\). `SGLD`

substitutes the model’s log marginal density

\(\log p(x, z) = \log \mathbb{E}_{q(\beta)} [ p(x, z, \beta) ] \approx \log p(x, z, \beta^*)\)

leveraging a single Monte Carlo sample, where \(\beta^* \sim q(\beta)\). This is unbiased (and therefore asymptotically exact as a pseudo-marginal method) if \(q(\beta) = p(\beta \mid x)\).

```
mu = Normal(loc=0.0, scale=1.0)
x = Normal(loc=mu, scale=1.0, sample_shape=10)
qmu = Empirical(tf.Variable(tf.zeros(500)))
inference = ed.SGLD({mu: qmu}, {x: np.zeros(10, dtype=np.float32)})
```

**init**

```
__init__(
*args,
**kwargs
)
```

`build_update`

`build_update()`

Simulate Langevin dynamics using a discretized integrator. Its discretization error goes to zero as the learning rate decreases.

The updates assume each Empirical random variable is directly parameterized by `tf.Variable`

s.

`finalize`

`finalize()`

Function to call after convergence.

`initialize`

```
initialize(
step_size=0.25,
*args,
**kwargs
)
```

Args: step_size: float. Constant scale factor of learning rate.

`print_progress`

`print_progress(info_dict)`

Print progress to output.

`run`

```
run(
variables=None,
use_coordinator=True,
*args,
**kwargs
)
```

A simple wrapper to run inference.

- Initialize algorithm via
`initialize`

. - (Optional) Build a TensorFlow summary writer for TensorBoard.
- (Optional) Initialize TensorFlow variables.
- (Optional) Start queue runners.
- Run
`update`

for`self.n_iter`

iterations. - While running,
`print_progress`

. - Finalize algorithm via
`finalize`

. - (Optional) Stop queue runners.

To customize the way inference is run, run these steps individually.

: list. A list of TensorFlow variables to initialize during inference. Default is to initialize all variables (this includes reinitializing variables that were already initialized). To avoid initializing any variables, pass in an empty list.`variables`

: bool. Whether to start and stop queue runners during inference using a TensorFlow coordinator. For example, queue runners are necessary for batch training with file readers. *args, **kwargs: Passed into`use_coordinator`

`initialize`

.

`update`

`update(feed_dict=None)`

Run one iteration of sampling.

: dict. Feed dictionary for a TensorFlow session run. It is used to feed placeholders that are not fed during initialization.`feed_dict`

dict. Dictionary of algorithm-specific information. In this case, the acceptance rate of samples since (and including) this iteration.

We run the increment of `t`

separately from other ops. Whether the others op run with the `t`

before incrementing or after incrementing depends on which is run faster in the TensorFlow graph. Running it separately forces a consistent behavior.

Welling, M., & Teh, Y. W. (2011). Bayesian learning via stochastic gradient Langevin dynamics. In *International conference on machine learning*.