Permutation Test for O-information

Performs a permutation-based significance test for the O-information of a candidate variable subset.

Usage

permutation_Oinfo(data, vars, n_perm = 1000, cor_method = "pearson")

Arguments

data

Preprocessed numeric data frame.

vars

Integer vector indicating variables belonging to the candidate multiplet.

n_perm

Number of random permutations. Must be a positive integer.

cor_method

Correlation method passed to compute_correlation().

Value

A list containing:

obs_O

Observed O-information.

pval

Permutation p-value.

Details

This procedure corresponds to the first stage of the hypergraph construction framework proposed by Possenti et al. (2026).

The null hypothesis assumes mutual independence of the variables. A null distribution is generated by independently permuting each variable, thereby preserving univariate distributions while destroying multivariate dependence structure.

The Monte Carlo p-value is computed as:

$$ p = \frac{ \#(|\Omega_{perm}| \ge |\Omega_{obs}|) + 1 }{ N_{perm} + 1 } $$

where \(\Omega_{obs}\) is the observed O-information and \(\Omega_{perm}\) are values obtained from permuted datasets. The smallest possible p-value is \(1/(N_{perm}+1)\).

References

Possenti, F., Girelli, L., Tieri, P., & Petti, M. (2026). Multiplex Hypergraph Modeling of Higher Order Structures in Psychometric Networks (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2604.22744