Implementation of replica exchange MCMC

[YoshikawaMasashi]

Hi all,

I am implementing replica exchange MCMC(Parallel tempering)(https://en.wikipedia.org/wiki/Parallel_tempering).

Replica exchange MCMC is known as a sampling method that is not much affected by local minimums. In this method, multiple sampling is performed with different temperatures in parallel, and frequently exchanged. In high temperature, Markov Chain jump from a local minimum to another local minimum. And, by exchanging, sampling that does not stay in one local minimum is possible.

For example, I sample from mixture gaussian distribution.

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])))

In MetropolisHastings, sampling is looks like this.

inference = ed.MetropolisHastings(latent_vars={x: qx},
                                 proposal_vars={x: proposal_x})

In HMC, sampling is looks like this.

inference = ed.HMC(latent_vars={x: qx})

In SGHMC, sampling is looks like this.

inference = ed.SGHMC(latent_vars={x: qx})

And, in replica exchange MCMC, sampling is looks like this.

inference = ed.ReplicaExchangeMC(latent_vars={x: qx},
                                 proposal_vars={x: proposal_x})

Thanks.

[dustinvtran]

Cool! Is the implementation available somewhere? We would love a contribution to merge it in.

[YoshikawaMasashi]

Thanks!

The implementation is this.
6f3175a

And forked repository is this.
https://github.com/YoshikawaMasashi/edward

I would appreciate it if you would give me some advice.

[dustinvtran]

Cool! Maybe send a PR (https://help.github.com/articles/about-pull-requests/)? Happy to review it and provide in-line comments.

[YoshikawaMasashi]

Thank you for your kindness. I close.