What is the Continuous Bernoulli distribution good for?
Edit: I see it’s equivalent to a Beta distribution.
Edit: I see it’s equivalent to a Beta distribution.
It's not.
The beta distribution is p(x) ∝ x^(α-1) (1-x)^(β-1). x is in the bases.
The continuous Bernoulli distribution is p(x) ∝ λ^x (1-λ)^x. x is in the exponents.
As https://arxiv.org/abs/1907.06845 says:
> the continuous Bernoulli is not a beta distribution (the main difference between these two distributions is how they concentrate mass around the extrema, see appendix 1 for details)
The appendix is available here (under "Supplemental"): https://papers.nips.cc/paper/2019/hash/f82798ec8909d23e55679...