Step Function for model with Categorical RV

Questions
1

I have the following model, based on Latent Dirichlet Allocation (Blei, D.M., Ng, A.Y., Jordan, M.I., 2003. Latent Dirichlet allocation. J. Mach. Learn. Res. 3, 993–1022.) that has a pm.Categorical in it:

alpha = np.ones((1, K))
beta_prior = np.ones((1, V))
num_words = df.shape[0]

with pm.Model() as model:
    doc_num = pm.Data('i', df['Document'])
    theta = pm.Dirichlet("θ", a=alpha, shape=(D, K)) # topic probabilities
    beta = pm.Dirichlet("beta", a=beta_prior, shape=(K, V)) # word probabilities
    w = pm.Categorical("w", 
                       p=t.dot(theta[doc_num], beta),
                       shape=6583,
                       observed=df['Word']
                      )

I was a little surprised to see that NUTS was automatically assigned as a sampler (and that it is expected to take approximately 24h on my MacBook Pro!). Should I be using a different sampling method for this? In the past I had seen a hybrid NUTS, M-H sampler. Is this because it has only the observed RV as categorical (I marginalized away an internal variable)?

Also, should I be replacing my use of Categorical with a Mixture?

2

NUTS is used alone because you don’t have any latent discrete variables as you were reasoning. As to why it is so painfully slow I don’t know. What’s the size of your dataset?

Edit: I see you specified shape. It doesn’t look like anything absurd.