Generate Candidate Hyperedges Using the Possenti et al. (2026) Pipeline
Source:R/multiplets_generation.R
generate_candidate_multiplets_possenti.RdImplements the candidate-selection strategy proposed by Possenti et al. (2026) for identifying promising higher-order interactions prior to O-information estimation.
Usage
generate_candidate_multiplets_possenti(
data,
k_range = 3:5,
ebic.gamma = 0.5,
top_seed_prop = 0.2,
expansion_gain = 0.05,
cor_matrix = NULL,
n_obs = nrow(data)
)Arguments
- data
Numeric data matrix or data frame.
- k_range
Vector of hyperedge orders to generate. Typical values are
3:5.- ebic.gamma
EBIC tuning parameter for
EBICglasso.- top_seed_prop
Proportion of top-scoring maximal cliques retained as expansion seeds.
- expansion_gain
Minimum score improvement required for adding a node during greedy expansion.
- cor_matrix
Optional correlation matrix used for EBICglasso. If NULL, Pearson correlations are computed from
data.- n_obs
Effective sample size supplied to EBICglasso. Defaults to the number of rows in
data.
Value
A list containing:
- candidates
Generated candidate hyperedges.
- adjacency_matrix
EBICglasso adjacency matrix.
- graph
Estimated igraph network.
- communities
Community assignment vector.
- affinity_matrix
Community affinity matrix.
- n_candidates
Number of generated candidates.
Details
The method combines sparse pairwise network estimation, community detection, clique scoring, and greedy expansion to reduce the combinatorial burden associated with exhaustive hyperedge search.
The procedure consists of:
Estimating an EBICglasso network;
Detecting communities using the spin-glass algorithm;
Constructing a community affinity matrix;
Extracting maximal cliques;
Ranking cliques according to community affinity;
Selecting top-scoring seed cliques;
Greedily expanding seeds;
Generating all candidate subsets within the requested order range.
Candidate selection is motivated by the assumption that meaningful higher-order dependencies are more likely to occur among variables located in densely connected and topologically coherent regions of the psychometric network.
This candidate-generation procedure follows the conceptual framework introduced by Possenti et al. (2026) to address the exponential growth of candidate hyperedges in psychometric hypergraph analysis.
Rather than evaluating all \(\binom{p}{k}\) possible variable subsets, the method restricts the search to topologically plausible regions of an EBICglasso network, substantially reducing computational complexity while preserving interpretable higher-order structures.