tensorflow / tensorflow/probability
Copulas and discrete random variables
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Description
I've been following Copulas Primer which constructs a bivariate distribution using Kumaraswamy and Gumbel marginals, with the copula inducing correlation between the two.
This seems possible since there is tfb.KumaraswamyCDF and tfb.GumbelCDF bijectors which transform samples from [0, 1]^2 -> R^2. There aren't however any such CDF bijectors for discrete distributions, e.g. tfd.Poisson, which makes sense since the CDF is a step function.
My question is - is there any simple way to code up bivariate distributions using copulas with discrete random variables in TFP? I know there might be some issues with copulas and discrete outcomes, but it'd be great to have a play around if possible.
Thanks!
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Research direction
Start with the linked Copulas Primer and compare its KumaraswamyCDF and GumbelCDF bijectors with the absence of a CDF bijector for tfd.Poisson. Determine whether TFP can support copula-based bivariate distributions with discrete random variables, and document or prototype the resulting approach if the scope is defined.
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Assessment
- Tech stack
- tensorflow
- Domain
- machine-learning
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 25/100