pymrmr | Python3 binding to mRMR Feature Selection algorithm | Genomics library

You'll probably need to contact either the authors of the original paper and/or the owner of the Github repo for a final answer, but most likely the differences here come from the fact that you are comparing 3 different algorithms (despite the name).

Minimum redundancy Maximum relevance algorithms are actually a family of feature selection algorithms whose common objective is to select features that are mutually far away from each other while still having "high" correlation to the classification variable.

You can measure that objective using Mutual Information measures, but the specific method to follow(i.e. what to do with the scores computed? In what order? What other post-processing methods will be used? ...) is going to be different from one author to another - even in the paper they are actually giving you two different implementations, MIQ and MID.

So my suggestion would be to just choose the implementation you are more comfortable with (or even better, the one that produces better results in your pipeline after conducting a proper validation), and just report which specific source did you choose and why.