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ODIM: Outlier Detection via Likelihood of Under-Fitted Generative Models
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Proposes ODIM, an unsupervised outlier detection method that trains an IWAE for only a few updates (stopped by a GMM-2 Wasserstein bimodality criterion) and scores samples by their loss, exploiting the observed inlier-memorization effect.
Problem
Unsupervised outlier detection on training data containing both inliers and outliers; fully trained likelihood-based deep generative models assign outliers high likelihood, making likelihood a poor outlier score.
Approach
Likelihood can be an effective outlier score if the generative model is deliberately under-fitted: early in training DGMs memorize inliers before outliers (the inlier-memorization effect), so training is stopped at the update that maximizes bimodality of the per-sample loss distribution, with min-max scaling and a 10-model ensemble.
Key results
- ODIM achieves averaged AUC 0.757 and PR 0.366 over 46 tabular datasets, the best among compared methods (next best OCSVM 0.740 AUC).
- On 6 image datasets ODIM reaches averaged AUC 0.813 and PR 0.429, versus 0.757 AUC for DTE.
- ODIM requires only a few updates (often under one epoch) and is reported at least tens of times faster than deep baselines such as DeepSVDD (e.g., 12.3 s vs 744.7 s on FMNIST).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use standardization instead of min-max scaling (ablation) | ODIM · 30 tabular datasets | AUC: 0.790 -> 0.760 | Hurt |
| Increase the IWAE sample count K (ablation) | ODIM · outlier identification benchmarks | outlier detection performance | Helped |
| Increase patience N_pat (ablation) | ODIM · outlier identification benchmarks | outlier detection performance | Helped |
| Increase ensemble size B (ablation) | ODIM · outlier identification benchmarks | outlier detection performance | Helped |
| Vary the learning rate within a reasonable range (ablation) | ODIM · outlier identification benchmarks | outlier detection performance | No clear effect |
| Use GLOW instead of IWAE (ablation) | ODIM · FMNIST | outlier detection performance | Hurt |
| Add labeled-outlier information using the CUBO-based loss modification (ablation) | ODIM · tabular datasets | AUC: 0.885 -> 0.947 -> 0.958 | Helped |
| Apply DP-SGD rather than conventional SGD-based training (ablation) | ODIM · tabular datasets, ε=10 | AUC | Mixed |
Surprising findings
- Standardization degrades ODIM relative to min-max scaling (average AUC 0.760 vs 0.790 on 30 tabular datasets), because standardization shrinks inlier norms and weakens the effect.
- Fully trained likelihood-based DGMs assign outliers higher likelihood than inliers, so likelihood must be used at an early, under-fitted stage.
Limitations
- Relies on min-max preprocessing; the optimal preprocessing choice is left open.
- Theoretical analysis covers only a linear factor VAE at initialization and gives a proposition, not a full proof for deep models.
- Stopping rule is a heuristic based on GMM-2 bimodality of losses.
Experimental setup
Datasets: ADBench tabular datasets (46) MNIST MNIST-C FMNIST CIFAR10 SVHN MVTec-AD Agnews Amazon Imdb Yelp 20news
Benchmarks: ADBench tabular (46 datasets) ADBench image (6 datasets) ADBench text (5 datasets)
Metrics: AUC PR AUC running time
Baselines: OCSVM COPOD ECOD DeepSVDD ICL DDPM DTE IForest LOF DAGMM
Builds on: IWAE VAE memorization effect in noisy-label learning ADBench
Closest papers by meaning
- ALTBI: Constructing Improved Outlier Detection Models via Optimization of Inlier-Memorization Effect (AAAI 2025 · similarity 0.93)
- Forte : Finding Outliers with Representation Typicality Estimation (ICLR 2025 · similarity 0.88)
- Out-of-Distribution Detection with Prototypical Outlier Proxy (AAAI 2025 · similarity 0.88)
- RODEO: Robust Outlier Detection via Exposing Adaptive Out-of-Distribution Samples (ICML 2024 · similarity 0.88)
- DOS: Diverse Outlier Sampling for Out-of-Distribution Detection (ICLR 2024 · similarity 0.87)
- Envisioning Outlier Exposure by Large Language Models for Out-of-Distribution Detection (ICML 2024 · similarity 0.87)
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