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We are defaulting to the numpyro implementation when that's installed, but the numpyro implementation is incredibly wasteful for large N, as it consists of doing n Categorical draws and summing up the values.
Description
We are defaulting to the numpyro implementation when that's installed, but the numpyro implementation is incredibly wasteful for large N, as it consists of doing n Categorical draws and summing up the values.
https://github.com/pyro-ppl/numpyro/blob/5af9ebda72bd7aeb08c61e4248ecd0d982473224/numpyro/distributions/util.py#L238
We should probably do sequential Binomial sampling: https://en.wikipedia.org/wiki/Multinomial_distribution#Algorithm:_Sequential_conditional_binomial_sampling
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