Datasets:
license: cc-by-4.0
task_categories:
- graph-ml
tags:
- graph-anomaly-detection
- heterogeneous-graphs
- non-adversarial-anomalies
- billing-pipelines
size_categories:
- 10K<n<100K
BillSim — A Synthetic Heterogeneous Graph Benchmark for Non-Adversarial Anomaly Detection in Usage-Based Billing
Anonymous Authors Submitted to NeurIPS 2026 Evaluations & Datasets Track 2026
Overview
BillSim is a fully synthetic heterogeneous graph benchmark for non-adversarial anomaly detection in usage-based billing pipelines. Existing graph anomaly detection benchmarks (Amazon reviews, Bitcoin OTC/Alpha, Yelp, UNSW-NB15, DGraph) model adversarial behaviour: fraud, spam, attacks, intentional concealment. BillSim targets the complementary regime that dominates enterprise systems-of-record: configuration errors, integration drift, and timing mismatches that are economically consequential (revenue leakage, customer overbilling) yet not adversarial.
The headline finding the benchmark is built to expose: a 0.374 AUROC gap on peer-comparison anomalies between a hand-coded oracle (0.965) and the best GNN (0.591), localizing the limitation to message-passing aggregation rather than task ill-posedness. In abstract-level shorthand, this is the 0.37 AUROC oracle gap.
Dataset At A Glance
- 63,155 nodes across 11 entity types
- 108,930 edges across 14 relationship types
- 6 anomaly types organized by graph reasoning pattern: structural / relational / peer-comparison
- 5 baselines benchmarked: MLP, GCN, GAT, RGCN, HGT
- 10 random seeds per configuration
- 4 anomaly injection rates: 0.01, 0.03, 0.05, 0.10
- 24 simulated billing months; temporal split for dynamic entities, deterministic 75/25 random split for static entities
Schema
Node Types (11)
| Type | Count | Features |
|---|---|---|
| customer | 200 | segment, is_active, num_sub_accounts |
| contract | 389 | duration_months, payment_terms, status, total_committed_value |
| sku | 50 | category, base_price, is_active |
| pricing_rule | 1,111 | rate_type, rate_value, is_current |
| usage_record | 14,601 | volume, unit_cost |
| rated_charge | 14,601 | amount |
| invoice | 3,547 | total_amount, status |
| line_item | 14,601 | amount |
| payment | 3,547 | amount, method |
| ar_record | 3,547 | status, amount |
| gl_entry | 6,961 | abs_amount |
| Total | 63,155 |
All feature vectors are z-score normalized per node type. Categorical features are integer-encoded. The gl_entry feature deliberately omits the sign of the GL amount to prevent revenue/cash leakage into the learning task.
Edge Types (14)
| Edge | Source -> Target | Count |
|---|---|---|
| subscribes_to | customer -> contract | 389 |
| has_sku | contract -> sku | 1,111 |
| governs | pricing_rule -> sku | 1,111 |
| applies_to | pricing_rule -> contract | 1,111 |
| generates_usage | customer -> usage_record | 14,601 |
| for_sku | usage_record -> sku | 14,601 |
| rates_to | usage_record -> rated_charge | 14,601 |
| priced_by | rated_charge -> pricing_rule | 14,601 |
| billed_on | rated_charge -> line_item | 14,601 |
| part_of | line_item -> invoice | 14,601 |
| invoiced_to | invoice -> customer | 3,547 |
| settles | payment -> invoice | 3,547 |
| opens_ar | invoice -> ar_record | 3,547 |
| posts_to | invoice -> gl_entry | 6,961 |
| Total | 108,930 |
The homogeneous view doubles edge count by adding reverse edges.
Anomaly Taxonomy
Six anomaly types are organized into three graph-reasoning categories. The categorization is the analytical contribution of the benchmark: it makes the architectural success and failure modes of GNNs interpretable.
| # | Name | Target Node | Category | Mechanism |
|---|---|---|---|---|
| 1 | Missing Metering | customer | relational | Usage stops while contract remains active |
| 2 | Orphaned Lines | line_item | relational | Invoice customer differs from charge customer (cross-path violation) |
| 3 | Pricing Mismatch | rated_charge | structural | Charge amount inconsistent with volume x rate from connected pricing rule |
| 4 | Stale Discount | pricing_rule | peer-comparison | Rate diverges from peer rules governing the same SKU |
| 5 | Revenue Recognition | gl_entry | structural | Invoice missing the expected cash GL entry (sibling-count check) |
| 6 | Premature AR | ar_record | structural | AR record closed despite incomplete payment sum |
Labels are provided per node type as a binary y (0 = normal, 1 = anomalous) and as anomaly_type (0 = normal, 1-6 = the type above). Each node carries at most one anomaly label; no overlap between types.
Injection signatures have been audited for feature leakage: per-type Cohen's d remains below 0.2, ensuring detection requires graph structure rather than feature shortcuts.
Headline Result
At injection rate 0.05 across 10 seeds, the V4 result table is:
| Type | MLP | GCN | GAT | RGCN | HGT | Oracle | Best GNN | Gap |
|---|---|---|---|---|---|---|---|---|
| Missing Metering | 0.512 | 0.730 | 0.398 | 0.784 | 0.827 | 0.866 | HGT | +0.038 |
| Pricing Mismatch | 0.684 | 0.571 | 0.867 | 0.980 | 0.979 | 0.881 | RGCN | -0.099 |
| Orphaned Lines | 0.505 | 0.967 | 0.968 | 0.922 | 0.988 | 1.000 | HGT | +0.012 |
| Stale Discount | 0.560 | 0.571 | 0.476 | 0.591 | 0.540 | 0.965 | RGCN | +0.374 |
| Revenue Recognition | 0.509 | 0.965 | 0.928 | 0.497 | 0.987 | 1.000 | HGT | +0.013 |
| Premature AR | 0.509 | 0.519 | 0.533 | 0.996 | 0.991 | 1.000 | RGCN | +0.004 |
The 0.374 oracle-GNN gap on Stale Discount is an order of magnitude larger than any other gap. Because the gap is exposed by a hand-coded peer-comparison oracle that achieves 0.965 AUROC, the limitation is established as architectural — message-passing aggregation cannot represent peer-distribution comparison — rather than the task being ill-posed.
Data Generation
The dataset is fully synthetic. No real billing data was used at any stage. The generation pipeline is a configurable Python module with deterministic NumPy seeding. Default parameters:
- Revenue distribution: lognormal contract sizes producing a Pareto-like tail
- Usage volumes: log-normal (mu = 6.0, sigma = 1.2)
- Customer arrivals: front-loaded declining Poisson
- Contract durations: uniform 6-36 months
- Pricing: uniform 0.01-10.0 base rate with +/-20% per-contract variation
All parameters are documented in the configuration module of the released code.
Train / Test Split
- Dynamic entities (usage_record, rated_charge, invoice, line_item, payment, ar_record, gl_entry): temporal split. Months 1-18 -> train, months 19-24 -> test.
- Static entities (customer, contract, sku, pricing_rule): deterministic 75/25 random split keyed off
(seed + stable_offset(node_type)). The stable offset is an MD5-derived integer per node type name, ensuring split reproducibility across seeds and node types.
Preprocessing
- All features z-score normalized per column (mean 0, std 1)
- Categorical features integer-encoded
- No missing values; no NaN or Inf values (verified by automated integrity check)
- No out-of-bounds edge indices (verified)
Intended Uses
- Benchmarking GNN methods for non-adversarial anomaly detection on heterogeneous temporal graphs
- Evaluating which graph reasoning patterns (structural sibling counting, multi-hop relational path matching, relation-specific traversal, peer-distribution comparison) different architectures can or cannot represent
- Diagnostic studies of message-passing limitations, including ablations against hand-coded oracle ceilings
- Research on architectural extensions that close the peer-comparison gap
Not-Intended Uses
- Production billing system deployment. The synthetic distributions do not replicate the complexity of real billing data.
- Training fraud detection models. The anomalies in BillSim are non-adversarial system errors, not adversarial attack patterns. Fraud involves intentional concealment and shifting tactics; billing errors do not.
- Drawing conclusions about real-customer billing accuracy. The benchmark exists to evaluate model architectures, not to model any specific operator's billing platform.
Format
PyTorch Geometric HeteroData objects serialized as .pt files, accompanied by Python generation scripts that reproduce the dataset deterministically from any seed and injection rate.
Licenses
- Data: CC-BY-4.0
- Code: Apache-2.0
Citation
Anonymous Authors. BillSim: A Synthetic Heterogeneous Graph Benchmark for Non-Adversarial Anomaly Detection in Usage-Based Billing. Submitted to NeurIPS 2026 Evaluations & Datasets Track, 2026.