Migrating to PyMC4 from PyMC3 Multidimensional GP

Questions v5
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Dear all,
My apologies if the question is rudimentary. I am following a notebook from @fonnesbeck presented at PyData NYC 2019, shared here on multidimensional GP, I am using the newly released PyMC4, I am not able to do any MCMC sampling or even doing any pm.find_MAP(). I keep getting an error which I think is related to the specification of sf2 variable. The error reads " **ValueError : Random variables detected in the logp graph: [l]. This can happen when DensityDist logp or Interval transform functions reference nonlocal variables.**"

nd = 15
xu1, xu2 = np.meshgrid(np.linspace(0, 300, nd), np.linspace(0, 300, nd))
Xu = np.concatenate([xu1.reshape(nd*nd, 1), xu2.reshape(nd*nd, 1)], 1)

with pm.Model() as spatial_model:
    
    l = pm.HalfCauchy("l", beta=3, shape=(2,))
    sf2 = pm.HalfCauchy("sf2", beta=3)
    sn2 = pm.HalfCauchy("sn2", beta=3)

    K = pm.gp.cov.ExpQuad(2, l) * sf2**2
    
    gp_spatial = pm.gp.MarginalSparse(cov_func=K, approx="FITC")
    obs = gp_spatial.marginal_likelihood("obs", X=X_obs, Xu=Xu, y=y_obs, noise=sn2)

    mp = pm.find_MAP()


nd = 30
z1, z2 = np.meshgrid(np.linspace(0, 300, nd), np.linspace(0, 300, nd))
Z = np.concatenate([z1.reshape(nd*nd, 1), z2.reshape(nd*nd, 1)], 1)


with spatial_model:

    f_pred = gp_spatial.conditional('f_pred', Z)
    
    samples = pm.sample_posterior_predictive([mp], vars=[f_pred], samples=100)

with sns.axes_style("white"):

    plt.figure(figsize=(10,8))
    ax = sns.heatmap(samples['f_pred'].mean(0).reshape(nd, nd), cmap='viridis')
    ax.invert_yaxis()
    ax.set_yticklabels([])
    ax.set_xticklabels([])

My questions are:

  1. Is there any thing that I could change in the model so that it could carry on with the sampling given that I am using PyMC4?

  2. Is there anything wrong with obs = gp_spatial.marginal_likelihood("obs", X=X_obs, Xu=Xu, y=y_obs, noise=sn2) that has to be updated to PyMC4 syntax?

  3. How about changes in PyMC4 calling the sample_posterior_predictive, specifically do I need to change anything in the lines

   f_pred = gp_spatial.conditional('f_pred', Z)
   
   samples = pm.sample_posterior_predictive([mp], vars=[f_pred], samples=100)

Many thanks,
Ali

2

Hey Ali,

This is a known bug that has recently been fixed, but is not yet available in the current release.

Can you try building from source and see if the problem persists? It fixes the issue for me.

Chris

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