Is sklearn_fork handling tweedie correctly?

[ElizabethSantorellaQC]

if isinstance(self._family_instance, TweedieDistribution):
    if self._family_instance.power <= 0:
        self._link_instance = IdentityLink()
    if self._family_instance.power >= 1:
        self._link_instance = LogLink()

This looks wrong to me, based on this: https://stats.stackexchange.com/questions/137227/what-is-the-canonical-link-function-for-a-tweedie-glm
power == 1 should be the special case of the log link, and otherwise there should be something like a TweedieLink equal to mu ** (1 - p) / (1 - p), which doesn't currently exist.

@MarcAntoineSchmidtQC : Could you add a test for whether we're getting the right answer in the tweedie-1.5 benchmark? (Regarding Issue #43 )

[lbittarello]

The fork follows actuarial practice:

• Identity for the normal.
• Logit for the binomial.
• Log for everything else.

The documentation mentions the use of the log for the Gamma and the Inverse Gaussian, but it left the Tweedie out, which we should presumably fix. Actuaries never use the canonical link function for the Tweedie or the Gamma, since they aren't terribly interpretable. I am fine with keeping current behavior.

[ElizabethSantorellaQC]

@lbittarello Thanks for clarifying. The sklearn-fork logic still doesn't seem to follow the actuarial convention. Is this correct?

if power == 0:
    link = IdentityLink()
elif 0 < power < 1:
    error, no distribution exists (this currently happens downstream)
else:
    link = LogLink()

[lbittarello]

Are you referring to the error if power is between zero and one? That is correct: the Tweedie family is not defined in that interval (i.e. no distribution exists).

[lbittarello]

And power == 0 is just the Normal, as you probably know.

[ElizabethSantorellaQC]

What I find odd about the sklearn-fork code is that the link is identity if power < 0; based on your comment it sounds like it should be log

[lbittarello]

To be honest, there is no actuarial practice for power < 0 because actuaries never use it. 😂 Sorry, I may have been misleading there.

[ElizabethSantorellaQC]

Conclusion: It's fine. This will be further clarified in the code by #68