arXiv:2605.12547econ.EMcs.LG2026-05

提出支付异质性指数,自动识别采购中异常付款模式。

The Payment Heterogeneity Index: An Integrated Unsupervised Framework for High-Volume Procurement Oversight and Decision Support

论文配图:The Payment Heterogeneity Index: An Integrated Unsupervised Framework for High-Volume Procurement Oversight and Decision Support
图 1 · 摘自论文原文
  • 构建融合高斯混合模型与非参数统计的支付异质性指数
  • 发现0.6%供应商占10.1%高额采购量且付款结构异常
  • 可解释性强,适合审计人员快速定位高风险供应商

公共采购易受错误、欺诈和腐败影响,尤其在交易量巨大时监管难以覆盖。现有研究多关注招标阶段异常,而对中标后的支付监控仍缺乏有效手段。由于标注数据稀少,传统方法如本福德定律依赖严格假设,因此亟需可解释、无监督的高容量采购监管框架。本文提出结构异质性指数(SHI)及其支付专用版本——支付异质性指数(PHI),用于刻画支付结构与潜在分组特征。PHI整合了高斯混合模型参数与非参数统计,包含四个可解释成分:模态性、偏度、尾部行为与结构离散度。其中尾部行为同时捕捉分布厚重性与极端值集中性,结构离散度则综合变异程度、分组出现频率与分离程度。应用于英国市政采购数据,PHI识别出0.6%的供应商(占高量级供应商的10.1%)具有显著不同的付款模式。统计检验验证差异显著,人工核查也确认优先案例合理。对比分析显示,PHI揭示了协方差系数(ρ=0.310)未能捕捉的分组边界。该框架具备透明、可分解、计算轻量等优势,适用于采购诚信监督与精准审计排序。

原文摘要 · Abstract (English)

Public procurement is vulnerable to error, fraud, and corruption, particularly as high transaction volumes overwhelm oversight. While research often focuses on tender-stage anomalies, post-award payment monitoring remains underexplored. Since labelled datasets are rare and methods like Benford's Law face restrictive assumptions, there is a need for interpretable, unsupervised frameworks for high-volume procurement oversight and decision support. This paper introduces the Structural Heterogeneity Index (SHI), a composite statistic for one-dimensional samples, and its payment-specific instantiation, the Payment Heterogeneity Index (PHI), characterising payment structure and latent regimes. It incorporates Gaussian Mixture Model (GMM) parameters alongside non-parametric statistics, integrating four interpretable components: modality, asymmetry, tail behaviour, and structural dispersion. Uniquely, the tail-behaviour component captures both distributional heaviness and extreme-value concentration, while structural-dispersion combines the variability, prevalence, and separation of latent payment regimes. Applied to UK municipal procurement data, PHI identifies a financially significant cohort (0.6\% of suppliers; 10.1\% of high-volume vendors) with structurally distinct payment patterns. Statistical testing further supports these differences, and targeted human verification confirms the plausibility of prioritised cases. Comparative analysis shows PHI reveals regime separation obscured by the Coefficient of Variation ($ρ= 0.310$). PHI provides a transparent, decomposable, and computationally lightweight framework for procurement integrity oversight and targeted audit prioritisation.

采购监管无监督学习异常检测可解释性

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