Feature Request: Alternative Horseshoe Parameterization as tfp distribution

[bryorsnef]

The currently implemented version of the horseshoe distribution is not the parameterization that most ML papers use. This limits the ease of use of this as, for example, a prior in a tfp.layers.KLDivergenceAddLoss or in tfp.layers.DenseReparameterization. The regularized horseshoe would also be useful as an implemented distribution.

The alternative parameterization is shown here: https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SparseLinearRegression And here: http://proceedings.mlr.press/v80/ghosh18a/ghosh18a.pdf

[srvasude]

PRs welcome here. Feel free to send a PR that does something similar to this (alternative parameterization of a NegativeBinomial): https://cs.opensource.google/tensorflow/probability/+/main:tensorflow_probability/python/distributions/negative_binomial.py;drc=bcdf53024ef9f35d81be063093ccfb3a762dab3f;l=115

[aryangupta01]

Hello I am interested in this issue can someone guide how to approach this issue. Thank You