ADERH — Anomaly Detection by an Ensemble of Random Pairs of Hyperspheres

Official implementation of the NeurIPS 2025 paper "Anomaly Detection by an Ensemble of Random Pairs of Hyperspheres" (Walid Durani, Collin Leiber, Khalid Durani, Claudia Plant, Christian Böhm).

ADERH is a fast, hyperparameter-robust, isolation-based unsupervised anomaly detector for tabular data. Guided by a δ-separation argument, it covers normal regions with an ensemble of small hyperspheres built from randomly paired points; each sphere's isolation signal is refined by Pitch (a boundary-proximity ratio) and NDensity (a sparsity-aware density weight), and signals are averaged over the ensemble.

Install

pip install aderh

or from source:

git clone https://github.com/Walid10010/ADERH.git && cd ADERH
pip install -e .

Runtime dependencies: numpy, scikit-learn only.

Quickstart

from aderh import ADERH

det = ADERH(random_state=0).fit(X_train)      # unsupervised
scores = det.decision_function(X_test)        # higher = more anomalous
labels = det.predict(X_test)                  # 1 = anomaly, 0 = normal

Key parameters: n_estimators=256 (ensemble size), n=18 (hyperspheres per member), contamination=0.1 (sets the label threshold). Defaults reproduce the paper.

Reproducing the paper

Experiments are based on the ADBench benchmark:

pip install -r requirements-experiments.txt
git clone https://github.com/Minqi824/ADBench.git && mv ADBench data
python experiments/run_experiment.py

Protocol: MinMax scaling to [0, 1], 3 stratified 70/30 splits (StratifiedShuffleSplit, random_state=0), seeds 0, 1, 2, 1000, 10000 for stochastic methods, AUC-ROC and AUC-PR averaged over splits × seeds, results appended to results.csv.

Implementation notes

The packaged detector is verified score-identical to the original reference script (tests/test_equivalence.py). Scoring convention follows PyOD: higher decision_function values indicate anomalies (score_samples provides the scikit-learn sign convention). Hypersphere radii are defined in squared-distance space; see IMPLEMENTATION_NOTES.md for the precise reference semantics.

Citation

@inproceedings{durani2025aderh,
  title     = {Anomaly Detection by an Ensemble of Random Pairs of Hyperspheres},
  author    = {Durani, Walid and Leiber, Collin and Durani, Khalid and
               Plant, Claudia and B{\"o}hm, Christian},
  booktitle = {Advances in Neural Information Processing Systems 38 (NeurIPS)},
  year      = {2025}
}

License

Released under the MIT License.