Hi @Ray6283,

[Ray6283]

Hi @Ray6283,

It seems you are asking about the EM/VBEM algorithm in general. I would say your description is almost right, except this part:

Then using p_ij s , we put f_j to transcripts with highest probability , say t_jm , we do this for all fragments, so for each fragment we have assigned unique transcript. So we can have new eta, call it eta_1 ( because we have abundance)

Specifically, the EM algorithm does not do "hard" assignment. That is, at no point during the algorithm, is a fragment fully assigned to a specific transcript (unless it was uniquely mapped there). Rather, the EM algorithm performs "soft" assignment. So, consider we have a fragment $f_j$ that maps to two transcripts $t_{j1}$ and $t_{j2}$. The EM algorithm will "partially" allocate this fragment to each of the transcripts. Specifically, it will allocate them proportional to $P(f_j \in t_{j1}) \propto P(t_{j1} \mid \eta) P(f_j \mid t_{j1})$ and $P(f_j \in t_{j2}) \propto P(t_{j2} \mid \eta) P(f_j \mid t_{j2})$ respectively. Then, in the "M" phase of the EM algorithm, one calculates the total mass arising from a transcript $t_i$ as $\sum_{f_j \text{ such that } f_j \text{ maps to } t_i} P(f_j \in t_i)$ (one sum). Computing these abundances for all $t_i$ gives us our next estimate of $\eta$, and then we can go back and re-compute the probabilities $P(f_j \in t_{j1})$ etc. This is done until convergence.

Originally posted by @rob-p in #889 (reply in thread)

[Ray6283]

🙏