I am trying to fit a hidden Markov model with hierarchical emission to 4 million data points. The emission consists of categorical and Bernoulli distributions. Sub-sampling seems a bad idea because mini-batch and stochastic gradient seem to not work with NUTS (Minibatch and NUTS).
Is it a good idea to run the NUTS implementation in pymc4 on a GPU? The HMC of pymc4 doesn’t have mass matrix adaptation. I worry that if I use HMC, the emissions would all get stuck near 0 and 1.