Reparameterization trick for exponential distribution

Question

Is there way to generate Exponential(lambda) distributed samples via a reparameterization trick?

As in: Reparameterization trick for gamma distribution

And also: How does the reparameterization trick for VAEs work and why is it important?

My motivation is to compare Exponential priors with Normal priors, in a neural network, having the latter solved as per the second link.

Though I have no experience in this field (and a general understanding), I am coding a project in MXNet where I compare different architectures in terms of predictive accuracy on IHDP data.

Answer 1

If you can generate an exponential rv. with rate 1 (call this X), then you can generate an exponential random variable with rate lambda by multiplying X with 1/lambda.

So, if you want to use an exponential function as a posterior, you can use the re-parametrization trick in variational autoencoders by only generating exponential rv. with rate 1.