Generalized extreme value distribution

[jedisom]

I see that the Gumbel distribution has been created based on this link: https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Gumbel
This is the xi =0 case per https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution

I would like to use a more generalized version of the extreme value distrubutions allowing xi to be non-zero; Gumbel xi =0, Frechet xi > 0, and/or Weibull xi < 0.

[brianwa84]

Does the FrechetCDF bijector help here? tfb.Invert(tfb.FrechetCDF(...))(tfd.Uniform(0,1))

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On Tue, Apr 14, 2020, 4:35 PM Jed Isom ***@***.***> wrote: I see that the Gumbel distribution has been created based on this link: https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Gumbel This is the xi =0 case per https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution I would like to use a more generalized version of the extreme value distrubutions allowing xi to be non-zero; Gumbel xi =0, Frechet xi > 0, and/or Weibull xi < 0. — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#874>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AFJFSIZY5LB4GPLQXSYIQBTRMTCITANCNFSM4MIBD4FQ> .

[jedisom]

@brianwa84, That appears to be a way to get a random variable from a Frechet distribution. The application I'm looking for is implementing these distributions within a Neural Network output layer allowing the network to learn the location, scale AND shape parameters. Something like:

tfp.layers.DistributionLambda(lambda t: tfd.GeneralizedExtremeDistribution(loc=t[..., 0], scale=tf.nn.softplus(t[..., 1]), shape=t[..., 2]))

The above obviously doesn't exist yet, but there might be a clever way to create the same effect with bijectors as you've suggested in your response above.

[srvasude]

There might be a way of chaining a PowerTransform bijector here, since essentially the difference between GEV and Gumbel is replacing the exponential in the exponent with a power transform.

Probably something like this would work (the forward of this would give you the CDF of a GEV):
Exp(Reciprocal(PowerTransform(power=xi)(Scale(1/sigma)(Shift(-mu)))))
but I'd probably recommend implementing from scratch (since I think the numerics of the above might not be so great). Contributions welcome here.

[jedisom]

I may take a stab at building the GeneralizedExtremeValue distribution class. This would be my first contribution to the repo. My initial thought was that I should be able to use the Gumbel class as a template and then just augment it with the shape/concentration parameter the generalized version needs, and then re-use the existing gumbel, frechet and weibull bijectors. Thoughts or feedback on this approach?

Also, can you point me to the documentation around how to setup my local environment (packages, directory/file locations, etc.) so that I can run, debug, and test code locally before sending a PR?

[blacksde]

Hi @srvasude @brianwa84 @jedisom I am raising a pr of Generalized extreme value distribution cdf bijector. It could be a partial solution of this issue. A future gev distribution could be added based on this. Could you help review the code?

[jedisom]

@blacksde, thanks for offering to help out. I'd love to help review your PR when it's ready. That would definitely make the class PR simpler to implement.

[blacksde]

Hi @jedisom , I am writing the gev distribution based on the gev cdf from my pr #901 . Now I have already done most of the functionalities.

Here is the code: https://github.com/blacksde/probability/blob/extreme_dist_loc/tensorflow_probability/python/distributions/gev.py

Let me know whether you have any comments or you need some more features to be added in this distribution.

[hudson-ai]

@blacksde are you planning on opening a PR to resolve this issue?

Thanks for your great work!

[blacksde]

@blacksde are you planning on opening a PR to resolve this issue?

Thanks for your great work!

Hi @hudson-ai I prepared my code but didn't have time to fix some minor issues and raise pr in the last few months. I think I can find some time this week to raise a pr.