I think this question related to membership assignment and have little thing to do with topic modeling.
Assign a membership based on probability is a question frequently asked. See here as an example.
To maximize the chance of correctly guessing the result of a coin flip, should I always choose the most probable outcome?
We can assign the membership based on Maximum a posteriori estimation or others.
Think about two examples:
- Suppose there are only $2$ topics, we can easily set the threshold to be $0.5$.
- Suppose there are $100$ topics, and the probability distribution for a given document is $[0.1, 0.9/99, \cdots, 0.9/99]$. How do we assign the membership? If we assign it to be topic 1 (which is the MAP estimation) but we will get 90% wrong !
So, the answer is just use the probability (Bayesian way), and do not use a threshold to assign membership.