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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, which addresses dually flat manifolds (and so, indirectly, information geometry).

Any other examples I have missed?

Thanks!

(Feel free to edit tags appropriately.)

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There is a very nice interpretation of entropy as a cohomology class by Baudot and Bennequin which you can read about HERE.

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.

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  • $\begingroup$ Interesting. I have the same feeling! But no real ideas so far...thanks! $\endgroup$ – geodude Feb 18 '15 at 8:15
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    $\begingroup$ Well, to plug my own work (which doesn't answer your question but which might interest you anyway), Avishy Carmi and I have a different approach to the topic of information topology, not via (co)homology, but rather via quandle-coloured tangles. Some preliminary findings are here: arxiv.org/abs/1409.5505 $\endgroup$ – Daniel Moskovich Feb 18 '15 at 8:57
  • $\begingroup$ Wow thank you. I'll take a look at it right now! $\endgroup$ – geodude Feb 18 '15 at 9:02
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Persistent homology seems to be quite fashionable right now. I've also found this blog entry by Ryan Budney quite amusing.

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  • $\begingroup$ Interesting! (Particularly since I am a musician too!) $\endgroup$ – geodude Feb 17 '15 at 12:07

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