Mixture of Poisson? about bayespy HOT 5 OPEN

In Z, the number of states is implicitly given by alpha. That is, Z doesn't have K plates axis, instead it is an integer variable in range {0, ..., K-1}, and this range is determined by the dimensionality of alpha. That is, Z doesn't have K repeated variables but each single value is in range {0, ..., K-1}. Thus, you need to remove that plate axis, because that just adds an extra plate axis which has nothing to do with the mixture clusters. The parameter cluster_plate is related to the parameters of the Poisson distribution, that is, rate_parameter has the clusters on the second last plate axis, as you have correctly done. So, I think this should fix:

Z = Categorical(alpha, plates=(NSamples, D))

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You can also simplify the following line:

rate_parameter = Gamma(alpha, beta, plates=(K,D))

You don't need to do explicit broadcasting with np.ones(D) because broadcasting of plates is done automatically.

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Also, just noting that you are using separate cluster assignments for each of the D dimensions. If you don't want to do that, this should work:

Z = Categorical(alpha, plates=(NSamples, 1))

But in case you wanted separate cluster assignments for each dimension, then never mind. Just wanted to let you know if you hadn't noticed.

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Thanks - while I understand the plates in theory, I've been having trouble getting things to align properly once I get to the mixture model (being new to python and broadcasting doesn't help). Below is my updated/working code, where the order of the plate dimensions for the rate_parameter is different than you suggest above. Any advice on symmetry breaking in this model (I get rapid, but nonsensical convergence)?

rate_parameter = Gamma(alpha, beta, plates=(D,K))
a0 = Dirichlet(1e-3*np.ones(K))
Z = Categorical(a0, plates=(NSamples, 1))
Y = Mixture(Z, Poisson, rate_parameter)
Y.observe(y)

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That looks good! I suggest you initialize randomly with:

Z.initialize_from_random()

Then, make sure rate_parameter is learned before Z. Easiest way to do this, is by listing them in that order for VB:

Q = VB(Y, rate_parameter, Z, a0)

And yep, aligning plates and other axes can sometimes be a bit of a head ache. I've been thinking about some simpler and clearer syntax which would still utilize "array properties". Haven't come up with a good solution yet. Of course, if you have an idea what kind of syntax you would find intuitive, I'd be happy to hear and take that into account. :)

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