FOR DIFFERENTIAL TOPIC MODELING WITH TRANSFORMS 3 Algorithm 2

In this section we propose a hybrid Gibbs and variational inference for our differential topic models. The idea is to first lower bound the model likelihood with variational inference [1], so that it is conjugated to the prior, then use a Gibbs style sampler for this bound. In this method we will use the usual Chinese restaurant representation of the PYP so that the combinatorial term ( mikw tikw )−1 in Equation (4) does not exist. By applying Jensen’s inequality first in Equation (4) and then marginalising out ~ φ, we derive the following lower bound for the likelihood, p ( X,T,Z ∣∣∣~a,~b, ~ α1:I , ~γ,P)