Clarification on the random variable W in the decoder

[ori-kron-wis]

See if this helps:

The mean of the the scVI ZINB model distribution (related to supplementary note 3)

To bring more explanation in the supplement the definition is the logits total_counts convention for a negative binomial (r, p and lambda instead of rho, theta and l_n). See our code on how this changes computation: scvi-tools/src/scvi/distributions/_negative_binomial.py at main · scverse/scvi-tools · GitHub. To make it very short, theta is the mean variance relationship and the mean is independent of theta.

In short, there is some confusion of the notations of the supplemental section