Convergence problems with ADVI

Questions
1

Hi,

I am using minibatch ADVI to fit models for my use case, but for some reason I often very strange convergence/hist plots like this:

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The elbo seems to stabilize at 30000, be stable for a while and then starts to get very unstable from around 60000.

I would like to know if you can point me to generic reasons that can cause such hist plots and what I could do to tackle this problem (I am new to the world of Bayesian modeling).

I would prefer not to show my model, as I got this problem with different models, so I was thinking the problem must be something more generic.
I am using hierarchical models and one thing that I saw is that when certain groups only have very small samples (1 or 2) they tend to be estimated very wrong.

2

My guess is that some RVs have gradient problem after a while.
A few generic solutions:

  1. trace the parameters at each iteration and see which one is causing the problem, see http://docs.pymc.io/notebooks/variational_api_quickstart.html#Tracking-parameters
  2. use more monte carlo sample to approximate the gradient: eg setting obj_n_mc=25 or higher (default is 1)
  3. try different optimizer with different learning rate, eg obj_optimizer=pm.adagrad(learning_rate=.01)
1 Like
3

Using a different obj_optimizer did the trick, to be specific adadelta with the defaults is providing very stable convergence results.
Thank you for pointing me there.