Mixture model with sample specific weights

Questions
1

In my dataset, the observations are grouped under a few categories (sample_type in the code below), and I want to find clusters within each category. I also believe that some clusters may appear in more than one category. I assumed a Dirichlet distribution for within-cluster variation. With that in mind, I started building my model:

n, k, c, t = 30, 6, 2, 5
sample_type = np.random.choice(range(t), n)
with pm.Model() as model:
  cluster_profiles = pm.Exponential("Cluster profile ratio", 1, shape=(k,c))
  cluster_weights = pm.Dirichlet("Cluster weights", np.ones((t,c))/2, shape=(t,c))
  components = pm.Dirichlet.dist(a=cluster_profiles, shape=(k, c))

Where k is the dimensionality of my observations, n is how many observations I have, c is how many clusters I am looking for and t is the number of possible categories. So far so good. Then, I added the mixture part:

with model:
  pm.MixtureSameFamily("Tumor-based prior", w=cluster_weights[ttype], comp_dists=components, shape=(n,k))

But it throws a ValueError: Input dimension mis-match. (input[0].shape[0] = 30, input[1].shape[0] = 6). I believe it is because cluster_weights is supposed to be have shape c, not (n, c). If that is the case, how can I implement a mixture with observation-specific weights? Am I using the Mixture module correctly?

I am using PyMC3 v3.11.2 on a Google Colab Linux instance. I have already tried replacing pm.MixtureSameFamily by pm.Mixture, but it did not help.

Thanks!

2

Did you ever figure this out? I’m attempting to do something similar (more mixture weights than components).