发表机构
CyberAgent, Inc.（CyberAgent株式会社）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对交易篮子数据中关联结构可解释性不足的问题，提出基数分层交互分解（CSID）框架，通过分层对数几率分解与信息加权岭投影估计成对及高阶组件，在模拟和真实数据中验证了其准确性和可复现性。
AI 中文摘要
交易篮子数据可以揭示商品间的关联，但观察到的共现混淆了商品特定关系与篮子规模结构以及未建模的高阶依赖性。我们引入了基数分层交互分解（CSID），这是一个可解释的框架，将按剩余商品数量分层的对数几率对比分解为商品集合特定和基数公共组件，而无需拟合全局联合分布。CSID使用信息加权、规范约束的岭投影来估计成对和三元组组件，并诊断高阶贡献对成对结构的影响。CSID主要设计用于关联结构的可解释分解，而非全分布预测。在零成对效应的模拟中，不断增强的小篮子基数势能导致普通Ising耦合虚假地变为负值，而CSID成对估计仍集中在零附近。检测能力随植入三元组效应的大小而增强，局部去投影将成对系数均方根误差从0.244降至0.073。在三个杂货数据集中，高信息三元组组件随时间可复现。在匹配的跨期部分迁移评估中，迁移的CSID三元组组件与后期分层对比的一致性优于节点对称基数感知高阶伪似然比较器，加权Lin一致性相关系数增益为0.038至0.122。这些结果支持CSID作为交易数据中成对和高阶关联结构的探索性和可解释分解框架。
英文摘要
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.
Comments29 pages
