Cardinality-Stratified Interaction Decomposition for Interpretable Pairwise and Higher-Order Structure in Transactional Basket Data

2026-09-28

AI Summary

This study addresses the confounding effects of shopping basket size and the poor interpretability of higher-order dependencies in transactional data by proposing the CSID framework. Through hierarchical log-odds decomposition contrasts, this framework decouples item-specific effects from cardinality-dependent common components. Furthermore, it introduces information-weighted constrained ridge projections to effectively disentangle the interference of higher-order contributions on pairwise structures without fitting a global joint distribution. Experimental results demonstrate that the proposed method significantly reduces estimation errors in pairwise coefficients while enhancing detection power. Evaluations on real-world datasets further validate the temporal reproducibility and cross-period consistency of the extracted higher-order components.

Abstract

Transactional basket data can reveal associations among items, but observed co-occurrence conflates item-specific relations with basket-size structure and unmodeled higher-order dependence. We introduce Cardinality-Stratified Interaction Decomposition (CSID), an interpretable framework that decomposes log-odds contrasts stratified by the number of remaining items into item-set-specific and cardinality-common components, without fitting a global joint distribution. CSID uses an information-weighted, gauge-constrained ridge projection to estimate pair and triple components and to diagnose higher-order contributions to pairwise structure. CSID is designed primarily for interpretable decomposition of association structure rather than for full-distribution prediction. In a simulation with zero pair effects, increasingly strong small-basket cardinality potentials drive ordinary Ising couplings spuriously negative, whereas CSID pair estimates remain centered near zero. Detection power rises with the magnitude of planted triple effects, and local deprojection reduces pair-coefficient RMSE from 0.244 to 0.073. Across three grocery datasets, high-information triple components are reproducible over time. In the matched cross-period partial-transfer evaluation, transferred CSID triple components show closer agreement with later-period stratified contrasts than the nodewise-symmetrized cardinality-aware higher-order pseudolikelihood comparator, with gains in weighted Lin's concordance correlation of 0.038--0.122. These results support CSID as an exploratory and interpretable decomposition framework for pairwise and higher-order association structure in transactional data.

Problem

• transactional basket data
• higher-order dependence
• association structure
• co-occurrence confounding
• interpretable decomposition

Innovation

• Cardinality-Stratified Interaction Decomposition
• Interpretable framework
• Higher-order dependence
• Ridge projection
• Transactional basket data