WakeSleep
Inherits From: VariationalInference
ed.WakeSleep
ed.inferences.WakeSleep
Defined in edward/inferences/wake_sleep.py
.
Wake-Sleep algorithm (Hinton, Dayan, Frey, & Neal, 1995).
Given a probability model \(p(x, z; \theta)\) and variational distribution \(q(z\mid x; \lambda)\), wake-sleep alternates between two phases:
Hinton et al. (1995) justify wake-sleep under the variational lower bound of the description length,
\(\mathbb{E}_{q(z\mid x; \lambda)} [ \log p(x, z; \theta) - \log q(z\mid x; \lambda)].\)
Maximizing it with respect to \(\theta\) corresponds to the wake phase. Instead of maximizing it with respect to \(\lambda\) (which corresponds to minimizing \(\text{KL}(q\|p)\)), the sleep phase corresponds to minimizing the reverse KL \(\text{KL}(p\|q)\) in expectation over the data distribution.
In conditional inference, we infer \(z\) in \(p(z, \beta \mid x)\) while fixing inference over \(\beta\) using another distribution \(q(\beta)\). During gradient calculation, instead of using the model’s density
\(\log p(x, z^{(s)}), z^{(s)} \sim q(z; \lambda),\)
for each sample \(s=1,\ldots,S\), WakeSleep
uses
\(\log p(x, z^{(s)}, \beta^{(s)}),\)
where \(z^{(s)} \sim q(z; \lambda)\) and \(\beta^{(s)} \sim q(\beta)\).
The objective function also adds to itself a summation over all tensors in the REGULARIZATION_LOSSES
collection.
init
__init__(
*args,
**kwargs
)
build_loss_and_gradients
build_loss_and_gradients(var_list)
finalize
finalize()
Function to call after convergence.
initialize
initialize(
n_samples=1,
phase_q='sleep',
*args,
**kwargs
)
Initialize inference algorithm. It initializes hyperparameters and builds ops for the algorithm’s computation graph.
n_samples
: int. Number of samples for calculating stochastic gradients during wake and sleep phases.phase_q
: str. Phase for updating parameters of q. If ‘sleep’, update using a sample from p. If ‘wake’, update using a sample from q. (Unlike reparameterization gradients, the sample is held fixed.)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
.update
for self.n_iter
iterations.print_progress
.finalize
.To customize the way inference is run, run these steps individually.
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 optimization.
feed_dict
: dict. Feed dictionary for a TensorFlow session run. It is used to feed placeholders that are not fed during initialization.dict. Dictionary of algorithm-specific information. In this case, the loss function value after one iteration.
Hinton, G. E., Dayan, P., Frey, B. J., & Neal, R. M. (1995). The "wake-sleep" algorithm for unsupervised neural networks. Science.