Implement Weibull distribution

[ragulpr]

Great work everyone. I'm planning on implementing the Weibull distribution for pytorch anyways, is there any interest in merging this here?
I just wanted to give a heads up if someone else is thinking about it. I can give details about the timeline after consulting with my lab.

[fritzo]

One clean way to implement this would be via PowerBijector and a ScaleBijector. I believe that if X ~ Exponential(1) then W=X**(1/k)/lambda is Weibul(k,lambda). However I'm not sure we'll have time to implement Bijectors by the PyTorch 0.4 release.

[ragulpr]

I'll look into the Bijector, but there's other type of abstractions available. For example for the continuous weibull;
g~gumbel(u,s) -> exp(g) ~ Weibull(exp(u),1/s). But I think the discrete Weibull is the most useful in practice. To form the discrete distributions from the continuous there might be better abstractions starting with the Cumulative Hazard function, but in both continuous and discrete case there are some numerical issues to consider. I'll have to get a better understanding of Bijectors and I'll get back after that.

[fritzo]

To clarify we don't yet have Bijejctors in torch.distributions 😄 I'm just trying to gather evidence that Bijectors would simplify lots of things. I didn't realize you were implementing Discrete Weibull; Bijectors will only handle continuous distributions.

[vishwakftw]

@ragulpr Are you implementing the Weibull distribution?

[ragulpr]

Yes, I just started

[vishwakftw]

@ragulpr @fritzo I think the Weibull distribution can now be implemented based on @ragulpr 's transformations and existing transforms. Let me know what both of you think.

[ragulpr]

Is it urgent? I haven't been able to keep up with the latest API and my implementation is slightly behind, or ahead I'm not sure.
Do you propose using a power-transform? I've been experimenting with an api generating any positive distributions pdf,cdf,survivalfunction, hazard etc based on its cumulative hazard, and it seems to work well.
If there's a current demand for the weibull I could submit something similar to currently implemented distributions.

[vishwakftw]

Oh no, it wasn't urgent. Sorry if I made it sound that way. I just was looking at a possible simplistic continuous Weibull distribution using existing transforms. I also very recently realized that the discrete Weibull is a bit harder to do too.

[ragulpr]

I'm looking into it! Will ask questions on slack 👍