README.md

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Conformal Anomaly Detection

Thresholds for anomaly detection are often arbitrary and lack theoretical guarantees. nonconform wraps anomaly detectors (from PyOD, scikit-learn, or custom implementations) and transforms their raw anomaly scores into conformal p-values. Under the assumptions of the selected method, these p-values support controlled false discovery rate (FDR) workflows with explicit, assumption-dependent guarantees.

Note: The methods in nonconform assume that training and test data are exchangeable. The package is therefore not suited for spatial or temporal autocorrelation unless such dependencies are explicitly handled in preprocessing or model design.

Guarantee scope: nonconform calibrates detector scores; it does not make an unsuitable detector or mismatched calibration set valid. Standard conformal claims require exchangeability. Weighted workflows require plausible covariate shift, support overlap, and reliable weights. FDR claims require valid p-values and the relevant multiple-testing assumptions.

Feature Overview

Need	nonconform Functionality	Start Here
Principled anomaly decisions	ConformalDetector.select(...) combines conformal p-values with FDR-controlled selection	FDR Control
Post-hoc threshold certificates	conformal_fdp_upper_bound_from_result(...) attaches FDP and precision bounds to raw conformal p-value thresholds	FDR Control
Flexible calibration strategies	Split, CrossValidation, and JackknifeBootstrap for different data/compute tradeoffs	Conformalization Strategies
Covariate-shift aware workflows	Weighted conformal prediction with density-ratio estimators and weighted FDR control (requires sufficient calibration/test support overlap)	Weighted Conformal
Rich p-value estimation	Empirical, probabilistic KDE, and conditional calibration estimators	Common Workflows
Sequential monitoring	Exchangeability martingales (PowerMartingale, SimpleMixtureMartingale, SimpleJumperMartingale)	Exchangeability Martingales
Custom detector integration	Support for any detector implementing the AnomalyDetector protocol	Detector Compatibility

Citation

If you use nonconform in academic work, reports, or other published material, please cite the accompanying paper:

@misc{hennhoefer2026,
      title={Conformal Anomaly Detection in Python: Moving Beyond Heuristic Thresholds with 'nonconform'},
      author={Oliver Hennhöfer and Maximilian Kirsch and Christine Preisach},
      year={2026},
      eprint={2605.13642},
      archivePrefix={arXiv},
      primaryClass={stat.ML},
      url={https://arxiv.org/abs/2605.13642},
}

Getting Started

Installation via PyPI:

pip install nonconform

Note: The example below uses an external dataset API. Install with pip install oddball or pip install "nonconform[data]".

Classical Conformal Workflow

Example: Isolation Forest on the Shuttle benchmark. This trains a base detector, calibrates conformal scores, then applies FDR-controlled selection through select(...). Raw p-values remain available via detector.last_result.p_values.

from pyod.models.iforest import IForest

from nonconform import ConformalDetector, Split
from nonconform.metrics import false_discovery_rate, statistical_power
from oddball import Dataset, load

x_train, x_test, y_test = load(Dataset.SHUTTLE, setup=True, seed=42)

detector = ConformalDetector(
    detector=IForest(),
    strategy=Split(n_calib=1_000),
    seed=42,
)
detector.fit(x_train)

decisions = detector.select(x_test, alpha=0.2)

print(f"Empirical FDR: {false_discovery_rate(y_test, decisions)}")
print(f"Statistical Power: {statistical_power(y_test, decisions)}")

Output:

Empirical FDR: 0.18
Statistical Power: 0.99

Advanced Methods

nonconform includes advanced workflows for practitioners:

• Weighted Conformal Prediction (weight_estimator=...): reweights calibration evidence for covariate shift settings where test and calibration distributions differ, assuming enough support overlap between calibration and test features.
• Exchangeability Martingales (nonconform.martingales): sequential evidence monitoring over conformal p-value streams.

Weighted Conformal Setup:

from pyod.models.iforest import IForest

from nonconform import ConformalDetector, Split, logistic_weight_estimator

detector = ConformalDetector(
    detector=IForest(),
    strategy=Split(n_calib=1_000),
    weight_estimator=logistic_weight_estimator(),
    seed=42,
)

Note: In weighted mode, ConformalDetector.select(...) dispatches weighted FDR control automatically.

Martingale Setup for Sequential Monitoring:

from nonconform.martingales import AlarmConfig, PowerMartingale

alpha = 0.01
martingale = PowerMartingale(
    epsilon=0.5,
    alarm_config=AlarmConfig(
        ville_threshold=1 / alpha,
        restarted_ville_threshold=1 / alpha,
    ),
)

state = martingale.update(p_t)
states = martingale.update_many(p_values_chunk)

Note: update(...) already validates and normalizes numeric scalar p-values, so an explicit float(...) cast is optional. Use ville_threshold or restarted_ville_threshold when you need an anytime false-alarm bound for a monitored stream. CUSUM and Shiryaev-Roberts thresholds are change-evidence triggers for diagnosing possible stream changes; they need separate calibration and do not replace cross-hypothesis FDR control. See Exchangeability Martingales for threshold interpretation details.

Beyond Static Data

While primarily designed for static (single-batch) workflows, optional onlinefdr integration supports streaming FDR procedures.

Custom Detectors

Any detector implementing the AnomalyDetector protocol works with nonconform:

from typing import Self

import numpy as np

class MyDetector:
    def fit(self, X, y=None) -> Self: ...
    def decision_function(self, X) -> np.ndarray: ...  # higher = more anomalous
    def get_params(self, deep=True) -> dict: ...
    def set_params(self, **params) -> Self: ...

For custom detectors, either set score_polarity explicitly ("higher_is_anomalous" in most cases), or omit it to use the default score-polarity policy. Use score_polarity="auto" only when you want strict detector-family validation.

See Detector Compatibility for details and examples.

Optional Dependencies

For additional features, you might need optional dependencies:

• pip install nonconform[pyod] - Includes PyOD anomaly detection library
• pip install nonconform[data] - Includes oddball for loading benchmark datasets
• pip install nonconform[fdr] - Includes advanced FDR control methods (online-fdr)
• pip install nonconform[probabilistic] - Includes KDEpy and Optuna for probabilistic approximation
• pip install nonconform[all] - Includes all optional dependencies

Please refer to the pyproject.toml for details.

Contact

Bug reporting: https://github.com/OliverHennhoefer/nonconform/issues

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