We have been reading a paper -
It proposes an alternative to expectation maximization methods for computing RNAseq expression levels. (RSEM, sailfish).
In this paper we propose a novel radically different method based on minimum-cost network flows. This has a two-fold advantage: on the one hand, it translates the problem as an established one in the field of network flows, which can be solved in polynomial time, with different existing solvers; on the other hand, it is general enough to encompass many of the previous proposals under the least sum of squares model. Our method works as follows: in order to find the transcripts which best explain, under a given fitness model, a splicing graph resulting from an RNA-Seq experiment, we find a min- cost flow in an offset flow network, under an equivalent cost model. Under very weak assumptions on the fitness model, the optimal flow can be computed in polynomial time. Parsimoniously splitting the flow back into few path transcripts can be done with any of the heuristics and approximations available from the theory of network flows. In the present implementation, we choose the simple strategy of repeatedly removing the heaviest path.
The elegant part of the paper is in how it converted the RNA-seq expression estimation problem to min cost flow. After the conversion is done, a number of standard algorithms can be used to determine expression levels and there will not be any need for time-consuming expectation maximization loops. The following tutorials are useful for you to catch up with those standard procedures.