Inflation does not work well using CG notation if the distribution has some unspecified (np.nan) probabilities

[eliewolfe]

Suppose one is interested in the feasibility of a partially-specified distribution.
This would occur, for example, whenever two parties share the same setting: the distribution would only be known when the setting for the two parties coincides.
(This would also happen in cryptography applications, where an additional party Eve is assumed to be part of the observed distribution, but we only have observable statistics on some marginal. Though, in this example no joint probabilities are known, only marginal probabilities are known.)
In this case using set_distribution with include_all_outcomes=True will give radically different results than with include_all_outcomes=False, as marginalization will fail when some of the joint probabilities are np.nan.

We should therefore add a warning that if np.nan is detected in set_distribution that the user should go back and re-initialize InflationLP or InflationSDP with include_all_outcomes=True .

[apozas]

If you need to do this, it can be already done using set_values, as in Example 5 in the documentation. Moreover, one can use the flags use_lpi_constraints and only_specified_values for choosing whether to just fix the values that are computed or also the products.

If you want to add a warning, go for it. But I guess that we will have to be careful when handling such distributions, so parts of set_distribution and set_values may need to be rewritten.

[eliewolfe]

I agree that it can be done with set_values. That's why I am filing this an enhancement more than bug.
I just think that set_values is awkward relative to set_distribution, such that most users will want to use set_distribution whenever possible. And a distribution with some np.nans totally can be handled by set_distribution just as well as by set_values if --- and only if --- include_all_outcomes=True.
No need to rewrite any code; we just need to add a warning. OK, I'll take a crack at it.