Sampling in ADVI

Questions v3
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1

Hello

I am fairly new to PYMC and i wanted to understand the advi sampling.
I wanted to understand what is changing from sample to sample?
Example:
If i run the following line of code

    advi_fit[channel] = pm.fit(n=200000, method='advi', callbacks=[pm.callbacks.CheckParametersConvergence(every=1000,tolerance=0.001,diff="absolute")])

As mentioned 200000 iterations are ran with average loss.

I wanted to understand what exactly is changing from iterations to iterations
I understand learnings from previous iterations are taken but i am not understanding how they are utilized for current iteration. And is there any default optimizer and learning rate used.

I would really appreciate if anybody can help me here

Thank you

2

You are fitting normal distributions, parameterized by a mean and standard deviation, to the latent variables in the model by minimizing the so-called “Evidence Lower Bound” (ELBO) loss function. Here is a nice video introducing the key ideas.

The default optimizer is pm.adagrad_window. It’s default learning rate is 1e-3. These settings are admittedly not easy to find, you have to dig in the source code somewhat.

Doc PRs very welcome :slight_smile:

3

Thank you replying. This did help us but i had few doubts.

  1. We are working with bayesian sampling and for which we are checking are there any hypermeters that we can tune if yes how can we log that and print (Except elbo).
  2. Is there a way i can log and print the effective learning rate and learning rate
    w(t) = w(t-1) - (learning_rate / (sqrt(Gt) + epsilon)) * gradient (As this is equation of adagrad so can we log and print (learning_rate / (sqrt(Gt) + epsilon))
  3. I was looking into the base code and came across line “This function maximizes the evidence lower bound (ELBO) :math:{\cal L}(\gamma, \nu, \eta)” Are these parameters tunable and can log and print them (pymc.variational.inference — PyMC dev documentation)

Thank you