ed.SGLD

Class SGLD

Inherits From: MonteCarlo

Aliases:

• Class ed.SGLD
• Class ed.inferences.SGLD

Defined in edward/inferences/sgld.py.

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

Notes

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 $(q(\beta) = p(\beta \mid x))$.

Examples

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)})

Methods

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.

Notes

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

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.

1. Initialize algorithm via initialize.
2. (Optional) Build a TensorFlow summary writer for TensorBoard.
3. (Optional) Initialize TensorFlow variables.
4. (Optional) Start queue runners.
5. Run update for self.n_iter iterations.
6. While running, print_progress.
7. Finalize algorithm via finalize.
8. (Optional) Stop queue runners.

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

Args:

• variables: 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.
• use_coordinator: 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 initialize.

update

update(feed_dict=None)

Run one iteration of sampling.

Args:

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

Returns:

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

Notes

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.