HOI

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Retrieving high-order information multiplets from data using the O-information

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# HOI
Retrieving high-order information multiplets from data using the O-information. The zero lag version works both for time series and for data collected across multiple subjects/trials.

Work in progress.

For the computation of entropy it uses a rank-based normalization using the inverse complementary error function (copnorm.m taken from Robin Ince's repository for gaussian copula mutual information (https://github.com/robince/gcmi)). Other estimators are possible of course (at the moment the fast bootstrap works for the covariance based ones).

The main files are

* hoi_exhaustive_loop_zerolag_all.m which validates all the multiplets until 10 in a row are nonsignificant
* hoi_exhaustive_loop_zerolag.m which validates the first n_best multiplets
* hoi_exhaustive_loop_lagged.m which validates the first n_best multiplets

which find the significant redundant and synergistic multiplets up to the desired order.

The python version https://github.com/PranavMahajan25/HOI_toolbox does not contain neither FDR correction, nor sped-up bootstrap.

Tentative todo list

* update the python repo
* plotting (already started by @renzocom)

# References
Rosas, F. E., Mediano, P. A., Gastpar, M., & Jensen, H. J. (2019). Quantifying high-order interdependencies via multivariate extensions of the mutual information. Physical Review E, 100(3), 032305. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.032305

Stramaglia, S., Scagliarini, T., Daniels, B. C., & Marinazzo, D. (2021). Quantifying dynamical high-order interdependencies from the o-information: an application to neural spiking dynamics. Frontiers in Physiology, 11, 1784. https://www.frontiersin.org/articles/10.3389/fphys.2020.595736/full

HOI

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