Are there interesting/useful applications of cohomology (and homological algebra in general) to probability and statistics, or information theory?


By "interesting/useful", I mean "not merely descriptive", that is, they can actually say something new and not just formalize well known concepts. 


For example, I have recently found [this paper](http://link.springer.com/chapter/10.1007%2F978-3-642-30232-9_4), which addresses dually flat manifolds (and so, indirectly, information geometry). 


Any other examples I have missed?


Thanks!


(Feel free to edit tags appropriately.)



Applications of cohomology to probability and statistics
There is a very nice interpretation of entropy as a cohomology class by Baudot and Bennequin which you can read about [HERE](http://djafari.free.fr/MaxEnt2014/papers/97_paper.pdf).


In general, I strongly believe that there is an underlying topological content to parts of information theory- as there is information geometry, there will be information topology.


