CategoricalGibbsMetropolis vs HMC

Questions
1

Hi. Here is something that I really don’t get.

Pymc3 have a step method called CategoricalGibbsMetropolis.

I would guess that if NUTS work well for categorical distribution, there would be no need to use CategoricalGibbsMetropolis.

Does that mean NUTS and Hamiltonian Monte Carlo generally don’t work well for categorical and Bernoulli distributions? Why is this the case?

Thanks.

2

In general, Hamiltonian does not support discrete variable, as the construction of Hamiltonian Monte Carlo proposals relies on a numerical solution of a differential equation. There are some effort of embedding discrete variables into continuous space (e.g., https://arxiv.org/abs/1705.08510), but so far there is no satisfying solutions that works in practices.

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