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Quantile-Based Maximum Likelihood Training for Outlier Detection
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Proposes QuantOD, which fits a Glow normalizing flow to frozen pre-trained WideResNet40 features using a q-quantile negative log-likelihood loss (q=0.05) for unsupervised outlier detection in image classification.
Problem
Discriminative image classifiers produce false positives on outliers; unsupervised density modeling in pixel space has performed poorly for outlier detection, and self-supervised methods rely on synthetic or real outlier data.
Approach
Train a normalizing flow on pre-trained discriminative features with a loss equal to the negated q-quantile (low q) of per-batch log-likelihoods, so boundary inliers are pushed to high likelihood, and threshold the log-likelihood at 95% TPR on validation inliers.
Key results
- On CIFAR-10 inliers, QuantOD averages 17.17% FPR95 and 96.19% AUROC across six outlier datasets, versus 33.01% FPR95 for Energy and 37.08% for Mahalanobis.
- QuantOD reaches 99.15% average AUPR on CIFAR-10, the best among compared unsupervised methods.
- On CIFAR-100 inliers, QuantOD averages 67.90% FPR95 and 82.32% AUROC, improving on Energy by about 5.7 and 2.76 points.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use quantile-based negative log-likelihood with q = 0.05 instead of mean-based negative log-likelihood (ablation) | QuantOD flow · CIFAR-10 inlier, six outlier datasets | FPR95 and AUROC | Helped |
| replace WideResNet40 with ResNet18 and use 512-dimensional features (ablation) | QuantOD · CIFAR-10 inlier, SVHN outlier | FPR95: 9.39 -> 31.01 | Hurt |
| replace WideResNet40 with ResNet18 and use 512-dimensional features (ablation) | QuantOD · CIFAR-10 inlier, SVHN outlier | AUROC: 97.94 -> 94.85 | Hurt |
| replace Glow with NICE (ablation) | QuantOD flow · CIFAR-10 inlier, six outlier datasets average | FPR95: 17.17 -> 27.68 | Hurt |
| replace Glow with GIN (ablation) | QuantOD flow · CIFAR-10 inlier, six outlier datasets average | FPR95: 17.17 -> 18.45 | Hurt |
| replace Glow with RealNVP (ablation) | QuantOD flow · CIFAR-10 inlier, six outlier datasets average | FPR95: 17.17 -> 20.18 | Hurt |
| reduce Glow coupling blocks from 8 to 2 (ablation) | QuantOD flow · CIFAR-10 inlier, six outlier datasets average | FPR95: 17.17 -> 19.26 | Hurt |
| reduce Glow coupling blocks from 8 to 4 (ablation) | QuantOD flow · CIFAR-10 inlier, six outlier datasets average | FPR95: 17.17 -> 17.67 | Hurt |
| increase Glow coupling blocks from 8 to 16 (ablation) | QuantOD flow · CIFAR-10 inlier, six outlier datasets average | FPR95: 17.17 -> 17.28 | No clear effect |
| reduce FC layers per coupling block from 2 to 1 (ablation) | QuantOD flow · CIFAR-10 inlier, six outlier datasets average | FPR95: 17.17 -> 19.80 | Hurt |
| increase FC layers per coupling block from 2 to 3 (ablation) | QuantOD flow · CIFAR-10 inlier, six outlier datasets average | FPR95: 17.17 -> 16.98 | Helped |
| increase FC layers per coupling block from 2 to 4 (ablation) | QuantOD flow · CIFAR-10 inlier, six outlier datasets average | FPR95: 17.17 -> 17.03 | Helped |
Surprising findings
- Mean-based NLL loss peaks after a few epochs and then degrades outlier detection, while the 0.05-quantile loss keeps improving.
- Higher-dimensional ResNet18 features (512-d) give much worse OOD performance (31.01% FPR95 on SVHN) than 128-d WideResNet40 features.
Limitations
- Evaluated only on CIFAR-10/100 with a single small backbone (WideResNet40) and no ImageNet-scale experiments.
- Flow is not class-conditional, and the authors note it underperforms class-conditional Mahalanobis on CIFAR-100.
Experimental setup
Datasets: CIFAR-10 CIFAR-100
Benchmarks: Textures SVHN Places365 LSUN-C LSUN-R iSUN
Metrics: FPR95 AUROC AUPR inference time classification accuracy
Baselines: MSP Mahalanobis ODIN Energy GEM VOS
Builds on: Glow Energy-based OOD detection Mahalanobis OOD detection RealNVP
Closest papers by meaning
- ALTBI: Constructing Improved Outlier Detection Models via Optimization of Inlier-Memorization Effect (AAAI 2025 · similarity 0.87)
- DOS: Diverse Outlier Sampling for Out-of-Distribution Detection (ICLR 2024 · similarity 0.87)
- Outlier Synthesis via Hamiltonian Monte Carlo for Out-of-Distribution Detection (ICLR 2025 · similarity 0.87)
- RODEO: Robust Outlier Detection via Exposing Adaptive Out-of-Distribution Samples (ICML 2024 · similarity 0.87)
- ODIM: Outlier Detection via Likelihood of Under-Fitted Generative Models (ICML 2024 · similarity 0.86)
- Tight Rates in Supervised Outlier Transfer Learning (ICLR 2024 · similarity 0.85)
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