Gumbel-Softmax Trick
Thu 30 August 2018
Gumbel Distribution
cdf:
$$F(x;\mu)=e^{-e^{-(x-\mu)}}$$
pdf:
$$f(x;\mu)=e^{-(x-\mu)-e^{-(x-\mu)}}$$
mean:
$$E_{X\sim\text{Gumbel}(\mu)}[X]=\mu+\gamma$$
where \(\gamma\approx0.5772\) is the Euler-Mascheroni constant.
Sanity Check
-
Check that \(\lim_{x\to-\infty}F(x;\mu)=0 …
Category: Bayesian Machine Learning Tagged: Reparametrization Trick Gumbel
Read More