What would the right way to model a Multivariate Normal distribution be when on every observation some values are missing, ie., I have a very sparse input. Note that we For example, my observations may look something like [[1.11, --, 0.9, --, 1.23, --], [--, 1.2, 0.81, --, --, --], [--, --, --…

Oh it’s much simpler than that. In PyMC3, potential are things you want to add to the model logp. For example, if you write with pm.Model() as m1: ... obs = pm.MvNormal('obs', mu, cov, observed=Xdata) What pymc3 does within the model m1 is that the logp of obs will be summed along with oth…

Thanks for your reply! Indeed your response on the post was super helpful, it really helped me think in the right direction. I did get how your notebook worked around the problem I just mentioned and I should be able to write it with pm.Potential. If you could perhaps point me to some literature on…

Ah alright, that makes sense. The name was a little misleading, so I dug into some old PyMC2 documentation to find that it was indeed named after factor potentials (though not quite the same one).

@junpenglao , a related question about the following line from your notebook: for i, im in enumerate(uni_case): pm.MvNormal('obs%i'%(i), mu[im == False], cov[im == False, :][:, im == False], observed=X_slice[np.sum(maskall == im, axis=1) > 0, :][:…

The free parameter mu and cov is indexed as well (eg mu[im == False]), so the MvNormal is now a 3*3 instead of 5*5

@junpenglao , it seems that with the current model (using unique masks for the data) it is impossible to generalize the distribution to conditionals that do not occur in the dataset. Intuitively, this isn’t accurate because the right way of looking at this is as a generative process and a truly Bayes…

Not sure I got what you mean - once you sample from your model, you have the full posterior of mu and cov of the MvNormal, which is your target generative process - you can then compute the conditional MvNormal on each slice of the MCMC samples and generate for unseen data.

You’re right, I was thinking of something else (which was, in fact, incorrect).

Multivariate Normal with missing inputs

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junpenglao November 27, 2018, 4:37pm 2

See: How to marginalize on a Multivariate Normal distribution

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Multivariate Normal with missing inputs

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