`ReplicaExchangeMC`

Inherits From: `MonteCarlo`

- Class
`ed.ReplicaExchangeMC`

- Class
`ed.inferences.ReplicaExchangeMC`

Defined in `edward/inferences/replica_exchange_mc.py`

.

Replica Exchange MCMC (Hukushima & Nemoto, 1996; Swendsen & Wang, 1986).

```
cat = Categorical(probs=[0.5,0.5])
x = Mixture(cat=cat, components=[
MultivariateNormalDiag([0.0,0.0], [1.0,1.0]),
MultivariateNormalDiag([10.0,10.0], [1.0,1.0])])
proposal_x = MultivariateNormalDiag(x, [1.0,1.0])
qx = Empirical(tf.Variable(tf.zeros([10000, 2])))
inference = ed.ReplicaExchangeMC(latent_vars={x: qx},
proposal_vars={x: proposal_x})
```

**init**

```
__init__(
latent_vars,
proposal_vars,
data=None,
inverse_temperatures=np.logspace(0, -2, 5),
exchange_freq=0.1
)
```

Create an inference algorithm.

: dict of RandomVariable to RandomVariable. Collection of random variables to perform inference on; each is binded to a proposal distribution \(g(z' \mid z)\).`proposal_vars`

: list of inverse temperature.`inverse_temperatures`

: frequency of exchanging replica.`exchange_freq`

`build_update`

`build_update()`

Perform sampling and exchange.

`finalize`

`finalize()`

Function to call after convergence.

`initialize`

```
initialize(
*args,
**kwargs
)
```

`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.

Hukushima, K., & Nemoto, K. (1996). Exchange monte carlo method and application to spin glass simulations. *Journal of the Physical Society of Japan*, *65*(6), 1604–1608.

Swendsen, R. H., & Wang, J.-S. (1986). Replica monte carlo simulation of spin-glasses. *Physical Review Letters*, *57*(21), 2607.