MCMC

[javdrher]

Adding support for performing Monte-Carlo marginalization of the hyperparameters. This integrates quite nicely into the framework. I haven't tested yet, but it seems that you would be able to construct acquisition hierarchies, mixing point estimates with MCMC.

There is one minor twist which has to addressed: the following code would currently result in errors:

....
model = GPflow.gpr.GPR(X,Y,RBF(2))
ei = ExpectedImprovement(model)
opt = BayesianOptimizer(domain, ei, hyper_draws=10)
opt.optimize(n_iter=10)
m.likelihood.variance.fixed = True
opt.optimize(n_iter=10)

The fix changes the size of the free state, but the copies still maintain the old one. Somehow, I should detect this change, and probably take new copies and replace the operands ParamList. I could verify the length of get_free_state but this is not a very robust fix: plenty of situations where no change would be detected. I could verify the position of every Param using the get_param_index, but I noticed this method does not take into account the fixed/unfixed state either (is this actually intended GPflow behaviour?)

Perhaps the easiest way out would be to detect the _needs_recompile flag in _optimize_models and maintain a flag indicating a change in the likelihood graph of the model. This would also catch changes in transforms which would also affect the semantics of the free state. Only changes of prior might introduce some overhead. Any thoughts on this?

[codecov-io]

Codecov Report

Merging #31 into master will increase coverage by 0.01%. The diff coverage is 100%.

@@            Coverage Diff             @@
##           master      #31      +/-   ##
==========================================
+ Coverage   99.69%   99.71%   +0.01%     
==========================================
  Files           8        8              
  Lines         660      690      +30     
==========================================
+ Hits          658      688      +30     
  Misses          2        2

Impacted Files	Coverage Δ
GPflowOpt/acquisition.py	100% <100%> (ø)	:arrow_up:
GPflowOpt/bo.py	98.24% <100%> (+0.09%)	:arrow_up:

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[javdrher]

I thought about this, and the rebuilding on a free state change is a broader issue, and is also tightly coupled with the callback for setting model hyperparameters (#7), so I'll build a new PR which builds on this.