empty Prob (other classes as well?) not digested cleanly

[equaeghe]

I'm not exactly sure whether this is an issue or a "we can't deal with every stupid corner case"; anyhow:

prob = Prob(PSpace('abc'), number_type='fraction')

print(prob)

Traceback (most recent call last): File "", line 1, in File "improb/lowprev/prob.py", line 49, in str [self[{omega: 1}, True][0] for omega in self.pspace])) File "improb/lowprev/lowpoly.py", line 278, in getitem return self._mapping[self._make_key(key)] KeyError: (Gamble(pspace=PSpace(['a', 'b', 'c']), mapping={'a': 1, 'b': 0, 'c': 0}), Event(pspace=PSpace(['a', 'b', 'c']), elements=set(['a', 'c', 'b'])))

prob.extend()

Traceback (most recent call last): File "", line 1, in File "improb/lowprev/lowprob.py", line 208, in extend algorithm=algorithm) File "improb/lowprev/lowpoly.py", line 736, in extend lprev, uprev = self[gamble, event] File "improb/lowprev/lowpoly.py", line 278, in getitem return self._mapping[self._make_key(key)] File "improb/lowprev/linvac.py", line 57, in _make_key raise ValueError('not a singleton') ValueError: not a singleton

[mcmtroffaes]

Currently, a Prob is taken to be a LowProb defined on singletons, and whose natural extension is calculated via expectation.

So:

• Printing an empty lowprob raises an exception because an empty Prob is not valid as some of its values are undefined - see Prob.is_valid - but we could make it do something else.
• LowProb.extend raises an exception because you cannot extend it to the set of all events (only singletons) - this seems to make sense, at least to me.

In other words, with the current design, this is expected behaviour. I've updated the documentation to make this more clear:

https://github.com/mcmtroffaes/improb/commit/0a23d7cc8df9bd85056fd09d26e5ecb39ddfb7a7

Suggestions?

[mcmtroffaes]

I've just done another commit which I think addresses the extend problems in an elegant way:

https://github.com/mcmtroffaes/improb/commit/cd7f7c4853a7f1a51bcdc802e2f2a32459c55094

You can now do prob.extend(algorithm='linprog') without having an exception raised. Of course the resulting probability will generally not be valid (unless we implement another extend method specifically for probabilities, e.g. 'uniform', which distributes the remaining mass uniformly?).

[mcmtroffaes]

Printing of incompletely specified probability measures:

https://github.com/mcmtroffaes/improb/commit/08fbdaa8e204a0e873f6d37b033b285ab291df17

[mcmtroffaes]

Linear extension for Prob:

https://github.com/mcmtroffaes/improb/commit/1bb3b872e9396fc80741c5ba4ed8a2e9218266c6

I think this now addresses everything, so closing.

[equaeghe]

Hmm, I'm afraid I wasn't clear about what I meant exactly:

• I think Probs (and other objects) with empty domain are valid and should be printable (I think you fixed this)
• I think extending partially specified Probs should return an error, just not the cryptic one I encountered (extension for LowProbs with nonempty domain was just fine; I don't know whether this was the case or not, but extension of one with empty domain to the vacuous would be a reasonable choice).

[mcmtroffaes]

Yes to all:

• Empty probs are indeed printed (undefined values show as "x : undefined").

• As a side effect of the refactoring, extending a Prob using the (now non-default) linprog algorithm does raise a clearer exception:

  from improb.lowprev.prob import Prob p = Prob(3) p.extend(algorithm='linprog') Traceback (most recent call last): ... ValueError: can only specify precise prevision

• Extending an empty LowProb obviously results in a vacuous lower probability (this has always been the case) - if you see anything different, then that's a bug, but it works for me:

  from improb.lowprev.lowprob import LowProb p = LowProb(3, number_type='fraction') p.extend() print(p) : 0 0 : 0 1 : 0 2 : 0 0 1 : 0 0 2 : 0 1 2 : 0 0 1 2 : 1