OOS predictions with missing input values

[junpenglao]

I am glad you find it useful so here is some more thought in reply to your questions:

@rhouck

1. In the initial model X is an observed variable. Why do you not need to define X as an observed variable in the second model used for prediction?

The way X is defined only makes sense for missing data. In fact, when X is fully observed (no missing data), it is just treated as a deterministic node. In another word, if there is no missing data in X_train, X_modeled = pm.Normal('X', mu=0, sd=1, observed=X_train) is the same as X_modeled = X_train.
But when there are missing data in X_train, the missing data is conceptually the same as replacing it with a number randomly draw from N(0, 1). That is also the reason why you should have an informative prior for X_modeled, as it fills the missing value with a much more meaningful number (e.g., draw from N(Xmu, 1) instead).

@rhouck

2. What is the purpose of tt.squeeze? Why could I not redefine X the same way it is defined in the first model: X_modeled = pm.Normal(‘X’, mu=Xmu, sd=1, observed=X_new)? Does this some how replace the original mask used in the first model during training by the new mask used for prediction?

tt.squeeze generates a matrix with right shape (shape broadcasting doesn’t work with shape=(n3, 2)). You are right; it should in principle also work by creating a new node with masked observed. It doesnt work with the current set up (at least not easily with the shape issue). Ultimately, what the sample_ppc is doing is indexing to the posterior sample (saved in the trace), and do forward pass to generate random samples.

@rhouck

3. Is there any way to see the X_missing estimates generated in the second model when running ppc? This would help me to know that the mask is working correctly.

You can sample the masked matrix:

with model:
    ppc3 = pm.sample_ppc(trace, vars=[y3, X_mask3], samples=200)

and index to the right value in ppc3[‘X_mask3’]