Going beyond pairwise interactions by digging into Higher-Order Interactions


Going beyond pairwise interactions by digging into Higher-Order Interactions


Etienne Combrisson (@EtienneCmb), Andrea Brovelli (@brovelli) and Daniele Marinazzo (@danielemarinazzo)


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Brainhack Global 2021 Event

Brainhack Marseille

Project Description

Modern theories suggest that cognitive functions emerge from the dynamic coordination of neural activity over large-scale and hierarchical networks. Currently, the characterization of a network and therefore, the functional interactions between brain regions, is usually performed using metrics of Functional Connectivity (FC). FC analysis is mostly based on the quantification of statistical relations between pairs of brain regions. However, pairwise interactions are probably insufficient to explain the emergence of more complex brain network interactions, such as during goal-directed learning tasks. Here, we propose to move beyond pairwise interactions by studying at Higher Order Interactions (HOI) i.e. quantifying the information carried by groups of “over-two” brain regions (= multiplets). As a first step, a framework called O-information (= Information about Organizational structure) was recently proposed to characterize redundancy- and synergy-dominated systems. This framework has recently been extended with the dOinfo (= dynamic Information about Organizational structure) to quantify how multiplets of variables carry information about the future of the dynamical system they belong to. This dOinfo extension allows to separate multiplets of variables which influence synergistically the future of the system from redundant multiplets.

Since (d)OInfo frameworks are recent, the math underneath are quite new and we are not necessary familiar with it. The overall goal of this project is to understand the methods by looking at the reference papers and the Python / Matlab implementations of both (d)OInfo.


Goals for Brainhack Global

During this BainHack, we will :

  1. Go through the reference papers (i.e. Rosas et al. 2019 and Stramaglia et al. 2021) to build an intuition of the math undergoing the HOI
  2. Go through the Python toolbox HOI_toolbox to understand what are the input / output types, to identify the main accessible functions such as understanding the internals
  3. Make the package easy to install, probably clean up so files
  4. Identify whether there are coding bottlenecks that could be easily solved to speed up computations (soft Numba, multi-core, tensor-computations etc.)

If we still have time, here are some new features that could be added to the Python toolbox :

  1. Implementation of false discovery rate for the significance of the multiplets
  2. Speed up of the bootstrap
  3. Include some plotting functions

Good first issues

  1. issue one: how to move progressively away from pairwise interactions

Communication channels



Computational : 70% Information-theory : 60% Math : 50% Python : 70% Matlab : 30%

Onboarding documentation

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What will participants learn?

Data to use

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Number of collaborators


Credit to collaborators

Contributors will be added to the README





Development status

1_basic structure





Programming language




Git skills


Anything else?

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Things to do after the project is submitted.

Jan 1, 0001 12:00 AM