Allow inclusive bounds in Adapter.constrain()

[LarsKue]

Simply adds a small value to bounds that are specified as inclusive.

[paul-buerkner]

thank you! looks good. Question: Why would you make the lower bound inclusive but the upper exclusive by default?

[LarsKue]

@paul-buerkner In my opinion, the most common case for double-bounded variables is uniform distribution. This is typically in the half-open interval [lower, upper).

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[paul-buerkner]

In statistics, we do not treat upper and lower bounds differently, specifically if variables are continuous (which they need to be for now if we use them as parameters in generative neural networks). I would treat upper and lower boundaries the same. So probably inclusive = "both" as default straight. This would of course internally translate to "lower" or "upper" for single bounded variables.

[paul-buerkner]

Looks good except for my suggestion for symmetric default values that I added as direct comment to the issue.

[paul-buerkner]

@LarsKue do i have permission to edit this PR in the direction I mentioned aboved?

[LarsKue]

@paul-buerkner yes. I do feel like it could be a bit opaque to new users though, since most randomly generated numbers are in open or half-open intervals, regardless of the statistical interpretation of the bounds.

[paul-buerkner]

Is there even a difference for continuous distributions? I mean, the probability of sampling exactly from the boundary is zero. So I am confused by your statement that intervals would ever be half open in software. For discrete variables perhaps but those are not our main concern in the adapter transformations.

[paul-buerkner]

Just to add one thought. Our point here is not to determine whether a null-set is included in an interval or not, but to ensure numerical stability. And for the latter, we need the epsilon, i.e., both inclusive bounds.

[paul-buerkner]

From my side, the PR is ready now. I change the default inclusive to "both" and added some tests. During testing, I also noticed that epsilon 1e-16 is too small to ensure finite outputs if the input is exactly at the upper boundary. So I changed it to 1e-15 which seems to work well.

[paul-buerkner]

I further extended the tests to now hopefully cover all relevant cases. Will merge now.