Question regarding `gp.conditional` and `gp.prior`

1

I think I have a pretty basic question: When can I expect gp.conditional and gp.prior to agree when I run them both on the same data?

For example, the following model:

with pm.Model() as gp_model:
    # data containers
    X = pm.Data("X", item_times[:, None], shape=(None, 1))
    trials = pm.Data("trials", item_trials)
    sends = pm.Data("sends", item_sends)

    # priors
    ell1 = pm.HalfNormal("ell1", sigma=1.25)
    ell2 = pm.HalfNormal("ell2", sigma=1.25)
    eta1 = pm.HalfNormal("eta1", sigma=1.0)
    eta2 = pm.HalfNormal("eta2", sigma=1.0)

    # define the kernel
    cov = eta1 * pm.gp.cov.Matern12(1, ell1) + eta2 * pm.gp.cov.Periodic(1, 12, ls=ell2)

    gp = pm.gp.Latent(cov_func=cov)
    f = gp.prior("f", X=X)

    # logit link and Binomial likelihood
    lik = pm.Binomial("lik", n=trials, logit_p=f, observed=sends)

is sampled with nutpie:

compiled_gp_model = nutpie.compile_pymc_model(gp_model)
idata = nutpie.sample(
    compiled_gp_model, chains=2
)

and then we extend it with

with gp_model:
    f_pred = gp.conditional("f_pred", item_times[:, None])
    idata.extend(
        pm.sample_posterior_predictive(
            idata,
            var_names=["f_pred"],
        )
    )

and I would (naively) expect that the idata.posterior.f and idata.posterior_predictive.f_pred would “agree” in some sense, but they are wildly different.

For some example data this is the plot of both:

image
image1117Ă—694 51.6 KB

Am I misunderstanding what is happening?

2

I think this is because you fit the model with compiled_gp_model and then are generating conditionals with gp_model, which would explain why the conditionals look like they are coming from a prior. Try fitting the model with:

with gp_model:
    idata = pm.sample(chains=2, nuts_sampler="nutpie")

And see if things look any better.

1 Like
3

Yup! That’s it. Using gp_model in the loop gives:

image
image1104Ă—705 132 KB

Huh. I guess I cannot use a compiled model then?

and THANK YOU

4

You can use nutpie for posterior sampling, and then use the trace with the standard PyMC model for sampe_posterior_predictive, but perhaps nutpie is not returning all the info that sample_posterior_predictive needs (constant/observed data?)

Or you’re not updating the data on the regular pymc model?

5

So by “updating the data on the regular pymc model” do you mean supplying more arguments to sample_posterior_predictive?

Or by doing a pm.set_data() operation for all of the inputs?

I will try to replicate a simple example to see if I can get it to work with the compiled nutpie model.

6

I mean’t set_data but it doesn’t seem to be involved in your case.

The compiled or not nutpie model is irrelevant, it’s just used to get the posterior trace. I suspect you see the same problem if you use the sample interface with sample(nuts_sampler="nutpie")?

This can happen because nutpie is not returning the same inferencedata that pymc default sampler does, probably missing something in constant_data or observed_data?