The Payment Heterogeneity Index: An Integrated Unsupervised Framework for High-Volume Procurement Oversight and Decision Support
Authors: Kyriakos Christodoulides
Organizations: Philips University, Department of Computer Science, Nicosia, Cyprus · Novel Intelligence, London, UK
Abstract
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.
Fraud detection in payment networks relies on labels generated through heterogeneous and imperfect observation processes, yet existing approaches treat fraud as a homogeneous binary variable. We show that this assumption is structurally incorrect and leads to provable inefficiency. We introduce an observation-mechanism taxonomy that partitions fraud into five classes, each defined by a distinct censorship and labeling pipeline. We prove that estimating fraud rates separately by class and aggregating strictly dominates pooled estimation, with the efficiency gap characterized as a Jensen penalty arising from heterogeneous observation rates. For each class, we derive the binding theoretical constraint on detection, including endogenous label corruption, structural non-observability, and feature non-informativeness. These results establish that fraud detection is fundamentally a collection of distinct estimation problems, each governed by its own observation structure and detection limit.
Public procurement involves the allocation of substantial financial resources; therefore, continuous oversight through audits, controls, and monitoring mechanisms is essential. However, stakeholder comments and publicly available government data are often underutilized, despite their potential to reveal procedural irregularities. To address this gap, this paper analyzes metadata from Ecuador's Sistema Oficial de Contratación Pública (SOCE, Official Public Procurement System), with particular emphasis on participant comments generated during the pre-contractual phase. We propose a hybrid modeling framework that integrates unsupervised clustering and supervised classification within a natural language processing (NLP) pipeline to uncover latent patterns and detect potentially irregular procurement processes. Semantic embeddings are generated using Word2Vec, LLaMA, and RoBERTa, followed by Gaussian Mixture Models (GMMs) for unsupervised clustering. A supervised classification stage is then applied to identify accusatory or whistleblowing-style comments. Experimental results show that the combination of domain-trained Word2Vec embeddings, GMM-based clustering, and a Random Forest classifier achieves high precision and recall, even under severe class imbalance. These findings demonstrate that lightweight, domain-adapted NLP architectures can effectively support risk identification and enhance transparency in public procurement systems without requiring large-scale computational infrastructure.
Bryan Torres, Daniel Riofrío, José Vega-Sánchez +4
Payment integration is a demanding repository-level software task: agents must select a suitable product, implement coordinated client-server flows, verify payment outcomes, and preserve consistency between transaction and business states. We introduce Alipay-PIBench, a benchmark for evaluating coding agents on realistic Alipay payment integration. It contains nine product-specific projects and 18 task instances, each organized into Basic functional-completion and Advanced risk-aware hardening scenarios. Scenario-specific rubrics support deterministic static, unit, integration, and end-to-end checks, supplemented by LLM-assisted assessment for semantic requirements. We evaluate six coding-agent models and report rubric pass rate (RPR). Under the with-skill condition, mean RPR ranges from 68.58% to 91.37%. Access to the alipay-payment-integration skill improves mean RPR by 10.31 percentage points on average relative to the without-skill condition, with gains varying across models, products, and scenarios. Method-level results distinguish source-level completion, executable payment behavior, and payment-domain requirements. Alipay-PIBench provides a controlled setting for diagnosing model capability and evaluating structured guidance in payment integration.