Tracking SVGD convergence

Questions
1

Hi,

I wanted to try replacing ADVI with SVGD in my model, but there seems to be no easy way to track its convergence. I suppose I would have to look at the gradient corresponding to each particle (?) - but how do I extract this information in a callback passed to the fit function?

2

cc @ferrine

3

Hi, thanks for mentioning me. The only way I found to track this in detail is to add a callback like in https://docs.pymc.io/notebooks/normalizing_flows_overview.html

The implementation is a bit hacky, but I can help you to implement your own

from itertools import count
from collections import defaultdict

# pm.callbacks.Tracker
# uses key->callable
# to record statistic
# the below function takes gradients for the params
# and creates the callable with `eval` method of a tensor

@theano.configparser.change_flags(compute_test_value='off')
def get_tracker(inference):
    numbers = defaultdict(count) 
    params = inference.approx.params
    grads = tt.grad(inference.objective(None), params)
    names = ['%s_%d' % (v.name, next(numbers[v.name])) for v in inference.approx.params]
    return pm.callbacks.Tracker(**OrderedDict(
      [(name, v.eval) for name, v in zip(names, params)] + [('grad_' + name, v.eval) for name, v in zip(names, grads)]
    ))

However, I have doubts that this is the best way to track convergence. I think one should use Earth Moving Distance between particles. Optimization often involves momentum term and can cause spurious oscilations. This is a hand waving argument you can ignore. But this optimization problem has an infinite amount of optimums, so optimizer has hard times telling it’s converged