Real-world systems are often characterized by higher-order interactions (HOIs) within multiplets i.e. groups of three or more units (Battiston et al., 2021). In neuroscience, most pieces of evidence we have about brain networks come from the interactions between pairs of brain regions but little is known about what type of information remains hidden in the non-pairwise interactions (Luppi et al. 2023, Luppi et al. 2024). Interestingly, recent findings suggest that HOIs might be a better neural marker of neurodegeneration than standard pairwise approaches (Herzog et al., 2022).
Several methods have been proposed to estimate HOIs, from popular fields like graph- and information-theory. The O-information (short name for “information about Organisational structure”) is an information-theoretical quantity to characterize statistical interdependencies within multiplets of three and more variables (Rosas et al., 2019). It allows us to not only quantify how much information multiplets of brain regions are carrying but also informs us on the nature of the information i.e. whether multiplets are carrying mainly redundant or synergistic information.
Estimating HOIs is computationally intensive. As an example, a cortical parcellation dividing the brain into 80 distinct regions involves estimating HOIs in 80.000 triplets, in 1.5 million quadruplets, in 24 million quintuplets, etc. The computational burden of the O-information only relies on simple quantities like entropies, which makes the O-information an ideal candidate to estimate HOIs in a reasonable time. Still, there is yet no neuroinformatic gold standard to estimate HOIs, in a decent amount of time and accessible to network enthusiasts encompassing experts and non-experts.
Currently an R implementation is missing, limiting the adoption to a relevant part of the community, in particular colleagues working with behavioral data and psychometrics.
Project aims and tasks
This project aims at building a R package, missing at the moment, for the computation of this quantity.
We divided this project into five main tasks:
- Test current implementation in Matlab and Python
- Build R functions to compute the Total Correlation and the Dual Total correlation
- Implement and test statistical validation for the multiplets
- Data simulation: add a function to simulate HOIs
- Explore plotting solutions, in R or preparing the output for plotting with existing packages such as XGI
- Explore interfaces with other R packages used in psychometrics (https://lavaan.ugent.be/ http://psychonetrics.org/ CRAN - Package psychotools)
- Prepare a package to be submitted to CRAN
Ultimately, this project could lead to the establishment of a gold standard to go beyond pairwise interactions by measuring HOIs, accessible to R experts such as to users with little programming knowledge.
Skill level: Intermediate/advanced
Required skills: R, some Python
Time commitment: Full-time (350 h)
Lead mentor: Daniele Marinazzo (daniele.marinazzo@gmail.com)
Project website:
Backup mentors: Fernando E. Rosas (f.rosas@imperial.ac.uk), Pedro Martinez Mediano (p.mediano@imperial.ac.uk)
Tech keywords: R, Python