Hard evidence in PyMC during model testing

Questions
1

Still struggling with what is possible with PyMC and what is not…
If I have a linear model with multiple likelihood-nodes, which I want to test on a new observation.
It happens so that I know the true value of one of the observed nodes, so I would like to use that value as hard evidence for other nodes calculation.

  • is it possible not to sample from the posterior for particular nodes, if their evidence is provided? Like in Bayes nets with categoricals and CPTs I can “freeze” any node by providing hard evidence and make one of the states to have P=1, and all others 0.
  • Is it possible to update the model with new knowledge? For instance, I test the model on a new observation and want the model to be updated at the same time. Or is retraining the model from scratch the only option?
2

is it possible not to sample from the posterior for particular nodes, if their evidence is provided?

Correct - if we have a random variable, then once we observe it, it is no longer a free variable and we cannot sample its distribution. Specifying observed variables is the same thing as providing an observed value to a Bayes net.

Is it possible to update the model with new knowledge?

Generally speaking, this is not one of PyMC3’s strongest points. It does not have built-in capacity for adaptively updating a Bayesian posterior with one data point at a time, in the same way that a hierarchical linear model with conjugate priors can do it.

1 Like
3

That is what happens during training the model:

pred1,..., data_resp1, data_resp2 = pm.Data(...), ..., pm.Data(...)
...
mu_resp1 ~ linear(pred1,...)
resp1 = pm.Normal('resp1', mu=mu_resp1, sd=error_std_resp1, observed=data_resp1)
...
mu_resp2 ~ linear(resp1,...)
resp2 = pm.Normal('resp2', mu=mu_resp2, sd=error_std_resp2, observed=data_resp2)

Then during testing I have an observation= {'pred1':p1,...'resp1':R1} which means I know true value for resp1 and want to use that to model resp2. It may sound strange to treat it now as Deterministic, but the rationale is that I want to create a model with many likelihoods (similar to Bayes net in my understanding of it), covering several use-cases at once (different test cases may contain different known variables).

I substitute all pm.Data() in the model and run post_pred = pm.sample_posterior_predictive().
post_pred['resp1'] still gives me a distributions, which, I think, is used internally by the model, not my value R1.

Thanks, now I know that for sure. I am confused by functionality behind different tools. What are the main differences of PyMC3 and alike (Stan?) from what is implemented by Netica Software (pomegranate?)?
The latter, I guess, is called Bayes Net and it supports only categorical values, requires CPTs, but there are ways to deduct network structure and CPTs from a large enough dataset.
PyMC operates continuous distributions, model structure needs to be defined manually through many iterations, doesn’t learn on the fly…