MetaEns: Automatic Unsupervised Ensemble Outlier Model Selection

Official implementation of "Automatic Unsupervised Ensemble Outlier Model Selection", accepted at ICML 2026.

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Table of Contents

• Overview
• How It Works
• Installation
• Quick Start
• Reproduce Paper Results
• Benchmark Datasets
• Citation

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Overview

MetaEns is a meta-learning framework that automatically constructs small, high-quality outlier detection ensembles without any labels on the target dataset. Given a pool of pre-trained detectors and their raw anomaly scores on a new dataset, MetaEns selects a compact, diverse subset that tends to outperform individual detectors and naive ensemble averaging.

Key capabilities:

• Unsupervised — no ground-truth labels required at test time
• Score-only — operates on detector output scores, independent of the input modality (tabular, image, text)
• Plug-and-play — scikit-learn-style fit / select / predict API
• Extensible — works with any detector that outputs a scalar anomaly score per sample

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How It Works

MetaEns operates in two phases:

Offline (meta-training)

Given a collection of historical datasets with ground-truth labels, MetaEns learns a two-part meta-model (ExtraTrees classifier + regressor) that predicts the marginal AP gain of adding a candidate detector to a growing ensemble. Meta-features are computed from raw score statistics.

Online (test time)

For a new, unlabeled dataset:

1. Primary selection — A kNN search over historical datasets (optionally guided by ELECT) identifies a strong single detector as a starting point.
2. Partner selection — The meta-model iteratively proposes candidates and predicts their marginal gain. Two regularisers discourage degenerate ensembles:
   • Submodular diversity discount — penalises candidates whose top-ranked samples heavily overlap with already-selected detectors (Jaccard similarity).
   • Family-risk prior — penalises selecting multiple detectors from the same algorithmic family (e.g. multiple IForest variants), using an Empirical-Bayes prior calibrated from historical data.
3. Adaptive stopping — Partners are added only when the predicted (discounted) gain exceeds a threshold.

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Installation

Requirements

• Python 3.9 or later (3.10 recommended)
• Dependencies listed in requirements.txt

Setup

git clone https://github.com/ph-phuc/MetaEns.git
cd MetaEns
python3 -m venv venv
source venv/bin/activate # Windows: venv\Scripts\activate
pip install -r requirements.txt

Core dependencies:

Package	Purpose
numpy, scipy, pandas	Numerical computing and data handling
scikit-learn	ExtraTrees meta-model
polars, pyarrow	Fast score-matrix I/O
lightgbm	ELECT primary selector (optional)
networkx, tqdm	ELECT graph features (optional)

Note:lightgbm, networkx, and tqdm are only required if you use ELECT as the primary selector (full paper configuration). The default kNN-based primary selector has no additional dependencies.

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Quick Start

The following snippet demonstrates the full MetaEns workflow on your own detector pool.

importnumpyasnpfrommetaensimportMetaEns# ------------------------------------------------------------------# 1. Collect score matrices from your detector pool# historical_scores : dict[dataset_name -> np.ndarray (n_samples, n_models)]# historical_labels : dict[dataset_name -> np.ndarray (n_samples,)] 0/1# ------------------------------------------------------------------historical_scores= {
"cardio": scores_cardio, # shape (n_samples, n_models) — one column per detector"shuttle": scores_shuttle,
# ...
}
historical_labels= {
"cardio": y_cardio,
"shuttle": y_shuttle,
# ...
}
model_names= ["IForest_1", "LOF_1", "HBOS_1", ...] # must align with columns# ------------------------------------------------------------------# 2. Fit the meta-model (offline phase)# ------------------------------------------------------------------selector=MetaEns(model_names=model_names, seed=42)
selector.fit(historical_scores, historical_labels)
# ------------------------------------------------------------------# 3. Apply to a new, unlabelled dataset (online phase)# X_test : np.ndarray (n_samples, n_models) — same column order as model_names# ------------------------------------------------------------------selected_detectors=selector.select(X_test) # e.g. ["IForest_1", "LOF_1"]anomaly_scores=selector.predict(X_test) # np.ndarray shape (n_samples,)

Run the included demo (requires benchmark data — see Benchmark Datasets):

# Hold out 'annthyroid' as test, kNN primary selector; cache meta-features for fast reruns
python3 example_usage.py --cache cache/cache_train_meta_ens.npz
# Specify a different test dataset
python3 example_usage.py --cache cache/cache_train_meta_ens.npz --test-dataset mnist
# Full paper configuration: use ELECT as the primary selector
python3 example_usage.py --cache cache/cache_train_meta_ens.npz --elect

On the first run the meta-feature cache is built automatically; subsequent runs reuse it.

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Reproduce Paper Results

run_metaens.py reproduces the LODO evaluation reported in Table 1 of the paper.

Leave-One-Dataset-Out (LODO) benchmark — 39 datasets, pool of 297 detectors:

Method	AP	Avg. Rank
MetaEns (ours)	0.4308	59.3
ELECT Top-1	0.413	87.0
ELECT Top-10	0.414	86.0
Mega Ensemble (all 297)	0.397	100.0
IForest (best single)	0.398	102.0

Numbers above are from the paper (mean over seeds [0, 1, 2, 3, 4, 5, 6, 42, 100, 1000]). To closely match the paper's reported numbers, set SEEDS in run_metaens.py to that list. (Minor numerical differences may still arise due to library versions and hardware.)

The default SEEDS = [100] runs a single seed for a quick check.

python3 run_metaens.py

This runs Leave-One-Dataset-Out cross-validation across all 39 benchmark datasets with ELECT as the primary selector (full paper configuration).

The meta-feature cache in cache/ is built automatically on the first run; subsequent runs reuse it.

Output files:

File	Contents
results/baseline_results.csv	Summary: AP, ROC-AUC, Median AP Rank per method
results/metaens_elect_detailed.csv	Per-dataset breakdown

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Benchmark Datasets

The benchmark uses 39 real-world tabular datasets drawn from the ELECT benchmark (ICDM 2022), originally sourced from the ODDS and UCI Machine Learning Repository repositories. Datasets cover a range of domains and sizes, with contamination rates from 0.03% to 35%.

The detector pool comprises 297 detectors from 8 algorithm families with diverse hyperparameter configurations:

Family	Algorithm
ABOD	Angle-Based Outlier Detection
COF	Connectivity-Based Outlier Factor
HBOS	Histogram-Based Outlier Score
IForest	Isolation Forest
kNN	k-Nearest Neighbour distance
LODA	Lightweight Online Detector of Anomalies
LOF	Local Outlier Factor
OCSVM	One-Class Support Vector Machine

Download

The precomputed score matrices and ground-truth labels are hosted on Google Drive:

Download benchmark data (Google Drive)

After downloading, extract the archive so the directory layout matches:

MetaEns/
└── datasets/
└── benchmark/
├── data/ # ground-truth label CSVs
└── intermediate_files/ # score matrices, datasets.txt, models.txt, ...

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Citation

If you use MetaEns in your research, please cite:

@inproceedings{metaens2026,
title = {Automatic Unsupervised Ensemble Outlier Model Selection},
author = {Hong-Phuc Phan and Tuan-Anh Vu and Tung Kieu and Son Ha Xuan and Bin Yang and Christian S. Jensen},
booktitle = {Proceedings of the 43rd International Conference on Machine Learning (ICML)},
year = {2026},
}